Gaussian widths:
[ 0.2         0.25        0.33333333  0.5         1.          1.        ]
Computing dimensionless free energies analytically...
This script will perform 200 replicates of an experiment where samples are drawn from 6 harmonic oscillators.
The harmonic oscillators have equilibrium positions
[0 1 2 3 4 5]
and spring constants
[25 16  9  4  1  1]
and the following number of samples will be drawn from each (can be zero if no samples drawn):
[2000 2000 2000 2000 2000    0]

Performing replicate 1 / 200
[  0.03872209   1.04685416   4.12103712   9.20415087  16.68377262
  25.06687405]
[ 0.00119439  0.01076232  0.02579093  0.04837197  0.17128761  0.41789113]
Performing replicate 2 / 200
[  0.03879351   1.06011432   4.13567374   9.29859965  16.7879643
  25.25336846]
[ 0.00118318  0.01057124  0.02609688  0.04868193  0.17017228  0.55549544]
Performing replicate 3 / 200
[  0.04061115   1.06267931   4.09118803   9.31631727  17.11739421
  26.34770003]
[ 0.00121496  0.01094449  0.02609262  0.049216    0.1778032   0.52499722]
Performing replicate 4 / 200
[  0.04023556   1.06041097   4.10851042   9.25855859  17.05498693
  25.94615061]
[ 0.00122054  0.0107666   0.02572417  0.04917176  0.17527207  0.50158067]
Performing replicate 5 / 200
[  0.03647946   1.05641694   4.10395192   9.26248942  16.92409026
  26.70029366]
[ 0.0011224   0.01062546  0.02651769  0.04913448  0.17630464  0.72125854]
Performing replicate 6 / 200
[  0.04071179   1.0741896    4.10644023   9.25740792  17.26691921
  26.38829607]
[ 0.00122768  0.0109696   0.02558388  0.05002294  0.17694455  0.54839682]
Performing replicate 7 / 200
[  0.03852271   1.07731379   4.05550188   9.14657717  16.98357886
  25.68571325]
[ 0.00118577  0.0107274   0.02537818  0.04896032  0.17669887  0.45346642]
Performing replicate 8 / 200
[  0.04189319   1.0422559    4.14801407   9.32298719  16.95873926
  25.52876044]
[ 0.00125463  0.01064661  0.02606403  0.04913193  0.17378307  0.45504856]
Performing replicate 9 / 200
[  0.03949911   1.05865144   4.10665833   9.26083539  16.77483914
  25.4414167 ]
[ 0.0012102   0.01094915  0.02516846  0.05049548  0.16926067  0.66967896]
Performing replicate 10 / 200
[  0.04096164   1.06280468   4.05615563   9.25905453  16.81709043
  25.69905597]
[ 0.00121286  0.01066403  0.02541121  0.04878758  0.17561748  0.44487128]
Performing replicate 11 / 200
[  0.0395926    1.05378135   4.12253523   9.30643066  16.86864261
  25.84667359]
[ 0.0012157   0.01054471  0.02617439  0.04923988  0.17454875  0.52326162]
Performing replicate 12 / 200
[  0.04116302   1.05230261   4.11942716   9.2614536   17.20360418
  27.36197648]
[ 0.00123948  0.01088472  0.0259626   0.04819764  0.18388569  0.74267001]
Performing replicate 13 / 200
[  0.03959043   1.07498064   4.12712509   9.25017716  17.03684815
  25.44762484]
[ 0.00122506  0.01053447  0.02585077  0.04890638  0.17236186  0.4605473 ]
Performing replicate 14 / 200
[  0.03925093   1.07331923   4.08678058   9.23983598  16.87978644
  25.41324602]
[ 0.00116227  0.01097319  0.02577474  0.04923042  0.17285919  0.45938337]
Performing replicate 15 / 200
[  0.03762626   1.04784302   4.03419136   9.33848968  17.40656179
  26.36889993]
[ 0.00111624  0.01067943  0.02593927  0.05008926  0.17922841  0.44141555]
Performing replicate 16 / 200
[  0.03876492   1.06515491   4.09690167   9.27350331  16.77611792
  25.01321228]
[ 0.00117713  0.01075901  0.02563043  0.0495557   0.16873891  0.47542929]
Performing replicate 17 / 200
[  0.04117979   1.03454658   4.08782507   9.33505631  16.80413583
  25.06372215]
[ 0.00128456  0.01105017  0.02581496  0.0496832   0.16863834  0.46387006]
Performing replicate 18 / 200
[  0.04062881   1.07206111   4.0969758    9.24632326  17.31070092
  26.92703323]
[ 0.00119615  0.01108858  0.02562033  0.04919329  0.18085265  0.62970446]
Performing replicate 19 / 200
[  0.04098208   1.05961615   4.12128125   9.30962447  16.94397297
  26.10232369]
[ 0.00130547  0.01062386  0.02598146  0.04859003  0.1754179   0.60580545]
Performing replicate 20 / 200
[  0.04032528   1.0879548    4.10343721   9.27519979  17.10785345
  24.92711846]
[ 0.00118806  0.01079223  0.02565946  0.05027662  0.16847159  0.40262822]
Performing replicate 21 / 200
[  0.04192865   1.08243361   4.10875391   9.13949752  16.73047727
  25.25316306]
[ 0.00125237  0.01112332  0.02530055  0.04940065  0.17186284  0.47276263]
Performing replicate 22 / 200
[  0.04118777   1.06384005   4.06494675   9.23753441  16.91621066
  25.3139594 ]
[ 0.00119204  0.01106297  0.02513047  0.04994734  0.17268006  0.41454497]
Performing replicate 23 / 200
[  0.0390993    1.05894713   4.14002099   9.36712507  17.47224873
  26.89336801]
[ 0.00122367  0.01087071  0.0266841   0.05049485  0.17834154  0.59493525]
Performing replicate 24 / 200
[  0.03864583   1.05714593   4.06372096   9.25449474  17.15422843
  25.97207072]
[ 0.00118399  0.01058439  0.02637373  0.04956499  0.177942    0.43099336]
Performing replicate 25 / 200
[  0.03948336   1.07547801   4.13191518   9.26925592  16.93290468
  26.06858333]
[ 0.001216    0.01101932  0.02574317  0.04979459  0.17438801  0.5499484 ]
Performing replicate 26 / 200
[  0.03809543   1.05961283   4.1290362    9.34039516  17.10617443
  25.64693642]
[ 0.00117995  0.01100063  0.02622283  0.04886901  0.17419206  0.45025915]
Performing replicate 27 / 200
[  0.03837429   1.06098132   4.13139397   9.23627861  16.98050859
  25.9840404 ]
[ 0.00116184  0.01099719  0.02600496  0.04870765  0.17490437  0.56004253]
Performing replicate 28 / 200
[  0.04089901   1.06094596   4.1084931    9.18954094  17.03366022
  27.19739676]
[  1.22335536e-03   1.09111714e-02   2.55241975e-02   4.91532731e-02
   1.79780353e-01   1.29700947e+00]
Performing replicate 29 / 200
[  0.03932373   1.06061798   4.14257651   9.25772679  17.1040141
  26.89166801]
[ 0.0012619   0.01106427  0.02624291  0.04818845  0.18052819  0.58651533]
Performing replicate 30 / 200
[  0.03830555   1.07675025   4.10593691   9.22379068  17.25475091
  27.46908558]
[ 0.00119107  0.01069722  0.02492837  0.04989302  0.18135647  1.18037019]
Performing replicate 31 / 200
[  0.04098643   1.07165904   4.13401233   9.23907172  16.76914282
  25.29474999]
[ 0.00123635  0.01066206  0.02597318  0.04915641  0.16994564  0.51959529]
Performing replicate 32 / 200
[  0.04214462   1.07084635   4.09901783   9.23740736  16.87358986
  25.83382194]
[ 0.00129874  0.01103236  0.02595043  0.04924991  0.17238572  0.65428254]
Performing replicate 33 / 200
[  0.04094335   1.07237575   4.10376286   9.19839308  16.89793352
  25.47194317]
[ 0.00128309  0.01119435  0.0261842   0.04887926  0.17367087  0.44363813]
Performing replicate 34 / 200
[  0.03943088   1.06345318   4.0892416    9.21663741  16.7218649
  25.38903272]
[ 0.00122541  0.01092207  0.02559204  0.0492007   0.17321738  0.45618271]
Performing replicate 35 / 200
[  0.04149619   1.08217791   4.08063046   9.20549221  16.74606988
  26.0494642 ]
[ 0.00125865  0.01093689  0.02551306  0.0487514   0.17804127  0.55025066]
Performing replicate 36 / 200
[  0.04155688   1.08030244   4.09280753   9.27662628  16.70768417
  26.03504328]
[ 0.00134798  0.01093258  0.02565731  0.04920167  0.17433314  0.62904366]
Performing replicate 37 / 200
[  0.03974489   1.07335977   4.08413552   9.25952372  17.29665173
  28.28563725]
[ 0.0011814   0.01110251  0.02563585  0.04962323  0.18547217  0.9038873 ]
Performing replicate 38 / 200
[  0.039329     1.08464059   4.10384123   9.24106683  16.80232203
  25.42109822]
[ 0.00119081  0.0110945   0.02596492  0.04873169  0.17260663  0.46046607]
Performing replicate 39 / 200
[  0.03920473   1.05686959   4.11568943   9.3071148   17.04466949
  25.61952895]
[ 0.00125859  0.01073203  0.02602774  0.04948098  0.1721275   0.55936092]
Performing replicate 40 / 200
[  0.04056849   1.04744608   4.10377396   9.31741397  16.84758713
  26.29780248]
[ 0.00123547  0.01095544  0.02572242  0.04949721  0.17546794  0.59808464]
Performing replicate 41 / 200
[  0.03906703   1.05905044   4.12239641   9.18702067  16.82501777
  27.10982459]
[ 0.00124812  0.01104048  0.0257842   0.04933316  0.17916364  0.73373553]
Performing replicate 42 / 200
[  0.0398643    1.0860701    4.10147125   9.24407548  16.61495954
  25.66198849]
[ 0.00121349  0.01086776  0.02609446  0.04894354  0.1697657   0.87173028]
Performing replicate 43 / 200
[  0.04357665   1.05215961   4.10655597   9.17246431  17.33293253
  26.43350197]
[ 0.00132046  0.01078445  0.02569501  0.04937881  0.18181417  0.47190957]
Performing replicate 44 / 200
[  0.04005254   1.06836077   4.09590863   9.24323524  17.10990874
  26.00920421]
[ 0.00121285  0.0109505   0.02576628  0.04892032  0.17786524  0.43780567]
Performing replicate 45 / 200
[  0.04218812   1.05051556   4.08913382   9.29222086  16.94372273
  25.70293783]
[ 0.00134885  0.01094122  0.02527946  0.05010525  0.17262884  0.55128067]
Performing replicate 46 / 200
[  0.03929456   1.06406797   4.10668074   9.28700209  16.95653585
  25.52549522]
[ 0.0011973   0.01118786  0.02571773  0.05017221  0.17154892  0.49591939]
Performing replicate 47 / 200
[  0.03858335   1.03859111   4.12398683   9.30506514  17.10646775
  26.93208427]
[ 0.00114838  0.01080016  0.02575895  0.04931567  0.17915994  0.67339173]
Performing replicate 48 / 200
[  0.04033213   1.07390753   4.11973596   9.23159698  16.91778576
  25.36657204]
[ 0.00119412  0.01101255  0.02606908  0.0485239   0.17345891  0.44675537]
Performing replicate 49 / 200
[  0.03871061   1.05666491   4.12859303   9.20442253  16.96974794
  25.48725212]
[ 0.00114953  0.01109879  0.02532095  0.04958064  0.17279435  0.48974638]
Performing replicate 50 / 200
[  0.03817402   1.06825838   4.12405373   9.2687802   16.93024192
  25.60551154]
[ 0.00114902  0.011056    0.0253581   0.04956405  0.17307368  0.53240711]
Performing replicate 51 / 200
[  0.03962726   1.06215511   4.09561533   9.23442119  16.86799682
  26.40502022]
[ 0.0012121   0.01098618  0.0256175   0.04944702  0.17583399  0.77539775]
Performing replicate 52 / 200
[  0.03775153   1.08306049   4.08540509   9.22652442  16.96619078
  25.61464196]
[ 0.00113408  0.01121581  0.02503859  0.04921422  0.17451926  0.45703963]
Performing replicate 53 / 200
[  0.03809178   1.063273     4.1281617    9.27912326  17.07750772
  25.78878478]
[ 0.00112335  0.01085543  0.02552272  0.05002676  0.17362101  0.47762955]
Performing replicate 54 / 200
[  0.03988228   1.07086552   4.11554818   9.31917477  16.76564162
  25.47704926]
[ 0.00124647  0.01092716  0.02542296  0.0488907   0.17320091  0.44892903]
Performing replicate 55 / 200
[  0.03886668   1.04589804   4.15400504   9.18556453  16.92029095
  26.07227412]
[ 0.00118187  0.01084346  0.02535141  0.04877413  0.17799295  0.55600099]
Performing replicate 56 / 200
[  0.03940752   1.08780748   4.07378082   9.36011112  16.71736056
  26.09256179]
[ 0.00119906  0.01085569  0.02559264  0.04941776  0.17490801  0.55308288]
Performing replicate 57 / 200
[  0.03976834   1.05531585   4.12090988   9.25871227  17.05469332
  25.47384457]
[ 0.00116692  0.01091533  0.02545316  0.04961602  0.17314039  0.45619244]
Performing replicate 58 / 200
[  0.04022509   1.05304624   4.14279309   9.20411507  16.9114254
  25.23909446]
[ 0.00123073  0.01062749  0.02592157  0.04935883  0.17137561  0.4372685 ]
Performing replicate 59 / 200
[  0.04198442   1.09190931   4.1003484    9.24980997  17.09171136
  25.71404008]
[ 0.00126643  0.01104939  0.0254546   0.0495251   0.1747193   0.44425839]
Performing replicate 60 / 200
[  0.03836887   1.06013407   4.12801476   9.29639658  17.0862348
  25.97428981]
[ 0.00115669  0.01106848  0.02634074  0.04874742  0.17621757  0.47391828]
Performing replicate 61 / 200
[  0.04150982   1.04670208   4.07322963   9.25497209  17.02406772
  26.44909264]
[ 0.0012138   0.01079625  0.02563196  0.04881978  0.17865798  0.57299729]
Performing replicate 62 / 200
[  0.03934155   1.05389633   4.05520843   9.25180382  16.82299188
  25.96934134]
[ 0.00122482  0.01077927  0.02552698  0.04931858  0.17203859  0.72561108]
Performing replicate 63 / 200
[  0.0394505    1.06810984   4.14807615   9.26106136  17.14652708
  26.54316709]
[ 0.00119534  0.0110708   0.0262439   0.04923901  0.17967353  0.48537348]
Performing replicate 64 / 200
[  0.0386403    1.06666599   4.12295467   9.22205775  16.81061593
  25.49891838]
[ 0.00116541  0.01088585  0.02538442  0.04898985  0.17387773  0.4558854 ]
Performing replicate 65 / 200
[  0.03716103   1.06737994   4.10813167   9.2499215   17.1217963
  26.62964854]
[ 0.00118407  0.01068737  0.02567345  0.04938239  0.17844138  0.6512197 ]
Performing replicate 66 / 200
[  0.04031913   1.05198072   4.1507701    9.17412615  16.84593107
  26.14885276]
[ 0.0013035   0.01093227  0.02562355  0.04907074  0.17765979  0.5370083 ]
Performing replicate 67 / 200
[  0.03923131   1.06769487   4.10739247   9.27047662  16.59407627
  25.41735903]
[ 0.00118793  0.01106223  0.02600184  0.0487558   0.17095783  0.55762204]
Performing replicate 68 / 200
[  0.03867774   1.05728148   4.13095151   9.31766963  17.1178145
  25.38953995]
[ 0.00116589  0.01076585  0.02561717  0.04914847  0.17286508  0.39079478]
Performing replicate 69 / 200
[  0.03988349   1.05983514   4.13566499   9.22941366  16.73269908
  25.64926831]
[ 0.00120628  0.01064541  0.02615612  0.04820797  0.17394324  0.5293269 ]
Performing replicate 70 / 200
[  0.03933935   1.05549177   4.11624344   9.2629141   16.86525097
  25.08007774]
[ 0.00118636  0.01115085  0.0259921   0.04963559  0.16991464  0.45969049]
Performing replicate 71 / 200
[  0.03882391   1.06580309   4.11033449   9.27573771  16.97549046
  24.96251834]
[ 0.00121027  0.01088758  0.02607206  0.04916825  0.17026025  0.40913918]
Performing replicate 72 / 200
[  0.0409446    1.05733141   4.07181996   9.37976135  17.03248256
  26.91117293]
[ 0.00125731  0.01059108  0.02552714  0.05026152  0.17300802  1.19786023]
Performing replicate 73 / 200
[  0.03811781   1.06789553   4.11516307   9.32446679  17.43640884
  26.61405269]
[ 0.00116659  0.01094016  0.02570927  0.05062876  0.17742682  0.65746405]
Performing replicate 74 / 200
[  0.0381458    1.05887914   4.09796857   9.30892834  16.88784495
  25.71487556]
[ 0.00112839  0.01085114  0.02572465  0.05028719  0.17065214  0.82761706]
Performing replicate 75 / 200
[  0.0401521    1.06236363   4.11017279   9.35329751  17.26570635
  25.60108332]
[ 0.00120785  0.01071492  0.02592803  0.05015632  0.17163907  0.46673607]
Performing replicate 76 / 200
[  0.04208477   1.07481956   4.08766469   9.21995234  17.04520851
  26.23069767]
[ 0.00128655  0.01111018  0.02506267  0.0485317   0.17912092  0.46343036]
Performing replicate 77 / 200
[  0.04039995   1.06145861   4.13692693   9.25592441  16.80346774
  25.68093991]
[ 0.0012299   0.01062708  0.02570854  0.04899283  0.17400377  0.47454473]
Performing replicate 78 / 200
[  0.03910017   1.0564547    4.13071047   9.29914633  16.81259322
  24.58244981]
[ 0.00116647  0.01073716  0.02630342  0.04940024  0.16571311  0.44709115]
Performing replicate 79 / 200
[  0.04034019   1.06444659   4.09987915   9.25370012  16.89709345
  25.84146065]
[ 0.00120831  0.0109684   0.02552749  0.04958401  0.17512119  0.47899182]
Performing replicate 80 / 200
[  0.03983444   1.07391485   4.11666155   9.22797895  16.90323485
  26.33098555]
[ 0.00122238  0.01078531  0.02588733  0.049162    0.17522583  0.65654687]
Performing replicate 81 / 200
[  0.03970533   1.06197558   4.11074636   9.19174751  17.07448554
  26.01918528]
[ 0.00121541  0.01084445  0.02529696  0.04798404  0.17642051  0.58650156]
Performing replicate 82 / 200
[  0.03677122   1.06105984   4.11488616   9.23809298  16.73061564
  25.71098515]
[ 0.00112503  0.01078944  0.02585207  0.04903198  0.17322011  0.5000389 ]
Performing replicate 83 / 200
[  0.04107467   1.0653355    4.13172002   9.25239326  17.01280283
  26.27385885]
[ 0.00121333  0.01112249  0.02577792  0.04912166  0.17699378  0.54697921]
Performing replicate 84 / 200
[  0.03845724   1.05619663   4.10560125   9.25294263  17.11784669
  26.88939422]
[ 0.00112274  0.01061671  0.02623139  0.04863759  0.17992137  0.74058104]
Performing replicate 85 / 200
[  0.03986881   1.05518542   4.12486834   9.25122772  16.89936544
  25.57645412]
[ 0.00130498  0.01089083  0.02541555  0.04986187  0.17140671  0.57647852]
Performing replicate 86 / 200
[  0.04232009   1.0540681    4.08796043   9.34980818  17.1081857
  26.46320241]
[ 0.00126153  0.01083321  0.02542775  0.04979714  0.17760273  0.76258026]
Performing replicate 87 / 200
[  0.03948211   1.05328782   4.12304039   9.19464567  16.9815505
  26.28691147]
[ 0.00119577  0.01061199  0.02565895  0.04943264  0.17746581  0.58841538]
Performing replicate 88 / 200
[  0.03791471   1.06078185   4.12339037   9.29977958  17.15756274
  25.90687533]
[ 0.0011291   0.01123224  0.0259291   0.04924572  0.17453538  0.48963679]
Performing replicate 89 / 200
[  0.04087765   1.0605252    4.12449644   9.29654138  16.9609525
  25.24359057]
[ 0.00121727  0.01133554  0.02545894  0.05002876  0.17198602  0.36917528]
Performing replicate 90 / 200
[  0.03983795   1.04901499   4.08310429   9.31075973  16.93125085
  25.88421139]
[ 0.00120117  0.01086426  0.02603724  0.04904788  0.17449422  0.47714371]
Performing replicate 91 / 200
[  0.03896253   1.05143522   4.11418666   9.33723489  17.06327832
  25.48520278]
[ 0.00122054  0.01081596  0.0258668   0.05007231  0.17214854  0.46851934]
Performing replicate 92 / 200
[  0.04101405   1.048906     4.12878765   9.19697868  16.80726944
  25.70100635]
[ 0.00126021  0.01064219  0.02535777  0.05032234  0.17214338  0.64169694]
Performing replicate 93 / 200
[  0.03826325   1.04682516   4.13189649   9.30472316  16.77310672
  25.9488829 ]
[ 0.00115417  0.01098602  0.02581776  0.04954723  0.1732355   0.57264166]
Performing replicate 94 / 200
[  0.04008388   1.05568891   4.15699522   9.23955533  16.75516876
  25.43538515]
[ 0.00122172  0.01067529  0.02578736  0.04793826  0.17152036  0.61978994]
Performing replicate 95 / 200
[  0.03989147   1.06057191   4.12602383   9.28020459  17.1171829
  26.9770861 ]
[ 0.00121633  0.01089386  0.02586022  0.04962115  0.17986809  0.60045646]
Performing replicate 96 / 200
[  0.04018372   1.06378407   4.09540792   9.28942704  17.15932367
  26.73308559]
[ 0.0012441   0.01076856  0.02576526  0.0498375   0.17894144  0.62273269]
Performing replicate 97 / 200
[  0.04100587   1.06522803   4.13572988   9.22937296  17.25872487
  26.82197994]
[ 0.00123723  0.01083285  0.02551154  0.04993346  0.17862635  0.78778591]
Performing replicate 98 / 200
[  0.04067516   1.08158748   4.13823673   9.23741068  16.9811306
  25.23987472]
[ 0.00123256  0.01105371  0.02533448  0.04867907  0.17237308  0.40975343]
Performing replicate 99 / 200
[  0.04062395   1.05988377   4.12728124   9.27860033  16.58976787
  25.02622718]
[ 0.00125277  0.01090675  0.02603776  0.04873989  0.16872912  0.47892528]
Performing replicate 100 / 200
[  0.03972257   1.09509281   4.15950308   9.30395591  17.09624035
  25.84577678]
[ 0.00126001  0.01084742  0.02559193  0.04980253  0.17180177  0.61705271]
Performing replicate 101 / 200
[  0.04056107   1.06268142   4.14299783   9.27897378  17.25811858
  26.43393499]
[ 0.00126907  0.01101612  0.02539773  0.049318    0.17830433  0.52030066]
Performing replicate 102 / 200
[  0.03971916   1.06481619   4.1697053    9.19906996  16.8642742
  24.95901197]
[ 0.00123067  0.01087849  0.02553632  0.04840275  0.17076318  0.42680896]
Performing replicate 103 / 200
[  0.04019079   1.06933399   4.1502625    9.31834996  16.85776306
  25.29384044]
[ 0.00121923  0.01105588  0.02564125  0.04967859  0.16801638  0.58912949]
Performing replicate 104 / 200
[  0.04044161   1.07193778   4.12030397   9.23031517  17.0894128
  25.77459379]
[ 0.00119144  0.01091753  0.02562534  0.05004625  0.17423257  0.4822451 ]
Performing replicate 105 / 200
[  0.03966612   1.04732655   4.10900437   9.21560935  16.97641103
  25.28823359]
[ 0.00113239  0.01083073  0.02572284  0.04849648  0.17266307  0.41216901]
Performing replicate 106 / 200
[  0.04058305   1.06194868   4.13960165   9.28330548  16.99237878
  26.02023238]
[ 0.00121885  0.01099261  0.02627706  0.04942447  0.1745773   0.59194044]
Performing replicate 107 / 200
[  0.04016653   1.0586404    4.12374235   9.16855927  16.97353355
  25.99918498]
[ 0.00125259  0.01097261  0.02556163  0.04937959  0.17768187  0.45470523]
Performing replicate 108 / 200
[  0.03879013   1.06590004   4.14027896   9.24574505  17.14800199
  25.70161487]
[ 0.00121531  0.01092094  0.02568198  0.04976532  0.17439807  0.42686539]
Performing replicate 109 / 200
[  0.03920765   1.05489571   4.10904223   9.21155769  17.07863938
  26.96082993]
[ 0.0012491   0.01076601  0.02613833  0.04872695  0.18377979  0.50876926]
Performing replicate 110 / 200
[  0.03783798   1.06178244   4.07315509   9.26740031  17.01632652
  26.76811196]
[ 0.00114821  0.0109043   0.02578434  0.04800786  0.18239618  0.5642425 ]
Performing replicate 111 / 200
[  0.04113307   1.06937907   4.10844611   9.21849545  16.98213462
  27.69583133]
[ 0.00127659  0.01073172  0.02569224  0.04941777  0.18081823  1.10021637]
Performing replicate 112 / 200
[  0.0378916    1.06092494   4.12751179   9.2131647   16.72047501
  25.73117883]
[ 0.00117006  0.01091807  0.0254063   0.04844317  0.17340027  0.59354293]
Performing replicate 113 / 200
[  0.03879842   1.05923812   4.15028344   9.24604497  17.1040684
  25.89964035]
[ 0.00119105  0.01113864  0.02577114  0.04985394  0.17423649  0.55067381]
Performing replicate 114 / 200
[  0.03986741   1.04559998   4.09840359   9.20590113  17.03039231
  26.27680404]
[ 0.00125042  0.0108496   0.02578333  0.04871789  0.17753269  0.53927288]
Performing replicate 115 / 200
[  0.03796941   1.07580756   4.0914414    9.22499807  17.18948799
  25.9507876 ]
[ 0.00116507  0.01095556  0.02533575  0.05007476  0.17712813  0.44888495]
Performing replicate 116 / 200
[  0.04138133   1.04793324   4.10421298   9.34562954  17.40152011
  26.0026261 ]
[ 0.00128974  0.01086486  0.02601164  0.04981699  0.17563692  0.47490909]
Performing replicate 117 / 200
[  0.04028955   1.07236332   4.14659559   9.31715083  17.03785533
  26.28553595]
[ 0.00128571  0.0110412   0.0256319   0.04930334  0.17644276  0.60921994]
Performing replicate 118 / 200
[  0.0404798    1.0413664    4.11790418   9.26735945  17.34113028
  25.83928645]
[ 0.00120244  0.01088345  0.02606468  0.04985296  0.17584872  0.46738874]
Performing replicate 119 / 200
[  0.04130042   1.07092674   4.10352487   9.23831951  17.17766571
  25.96775538]
[ 0.00125836  0.01078906  0.02601971  0.04969393  0.17471911  0.58320999]
Performing replicate 120 / 200
[  0.03989094   1.06972924   4.13119807   9.22439206  17.34792591
  26.65192436]
[ 0.00124709  0.0109513   0.02583579  0.04970208  0.1816552   0.51888228]
Performing replicate 121 / 200
[  0.03886831   1.05644038   4.16189491   9.27478227  17.05671415
  26.03793544]
[ 0.0012069   0.01064922  0.02641444  0.04861642  0.17618984  0.570946  ]
Performing replicate 122 / 200
[  0.03845955   1.0692065    4.04336601   9.153531    16.97012872
  26.07238461]
[ 0.00116889  0.01083338  0.02494681  0.04991075  0.1785819   0.47401595]
Performing replicate 123 / 200
[  0.04156581   1.07785273   4.11470621   9.35139327  17.10678998
  26.07432017]
[ 0.00127914  0.01081712  0.02541242  0.05101825  0.17360648  0.53747748]
Performing replicate 124 / 200
[  0.0369523    1.06708374   4.09793758   9.2176403   17.17170717
  27.35039341]
[  1.12591222e-03   1.09168894e-02   2.56230242e-02   4.98695112e-02
   1.78652167e-01   1.13871906e+00]
Performing replicate 125 / 200
[  0.03916859   1.05790806   4.0774769    9.22638289  17.1919002
  26.92773245]
[ 0.00118327  0.01092405  0.02567421  0.04908701  0.18286606  0.54396684]
Performing replicate 126 / 200
[  0.03977586   1.04991045   4.148005     9.22468179  17.06792636
  26.30053771]
[ 0.0012626   0.01095323  0.02563349  0.04980977  0.17653974  0.67672793]
Performing replicate 127 / 200
[  0.04142095   1.0559735    4.12704262   9.23582     16.8061218
  25.95989429]
[ 0.00125754  0.01098718  0.02571506  0.04887964  0.17428845  0.55912737]
Performing replicate 128 / 200
[  0.03719678   1.04752747   4.18203517   9.23396859  17.0634186
  26.32968929]
[ 0.001157    0.01071383  0.02630357  0.04895444  0.17690081  0.60939269]
Performing replicate 129 / 200
[  0.04199611   1.06797827   4.15426835   9.19160114  16.91904166
  25.57800039]
[ 0.00127048  0.01105406  0.02589197  0.04924891  0.1746844   0.44325957]
Performing replicate 130 / 200
[  0.03810507   1.06550056   4.10015959   9.2487155   17.11834377
  25.96126425]
[ 0.0011702   0.01135679  0.02531197  0.04916234  0.17644098  0.48780892]
Performing replicate 131 / 200
[  0.03925455   1.04888968   4.09475578   9.25740188  16.76167382
  25.37098742]
[ 0.00120104  0.01103548  0.02540658  0.04888858  0.17244616  0.51280446]
Performing replicate 132 / 200
[  0.03922079   1.06169897   4.12579203   9.17781116  17.01796859
  25.45095861]
[ 0.00118245  0.01100145  0.02540074  0.049855    0.17311313  0.46057395]
Performing replicate 133 / 200
[  0.03952071   1.06816464   4.08847207   9.30036398  17.15135567
  26.31653997]
[ 0.0011987   0.01096494  0.02614188  0.04864399  0.17963335  0.492792  ]
Performing replicate 134 / 200
[  0.04166397   1.05488153   4.05895388   9.19203898  17.18184885
  26.77963559]
[ 0.00123061  0.01086966  0.02528654  0.05017073  0.18146952  0.52727654]
Performing replicate 135 / 200
[  0.04136422   1.06096963   4.11123148   9.20663531  16.67375264
  25.52112358]
[ 0.00127832  0.01088189  0.02545053  0.04918635  0.17224972  0.53498091]
Performing replicate 136 / 200
[  0.04219685   1.04388749   4.12758996   9.2469164   17.27460208
  27.39583162]
[ 0.00127735  0.01075889  0.02578018  0.04891266  0.18656228  0.51596832]
Performing replicate 137 / 200
[  0.03985634   1.06269733   4.11189872   9.25424476  17.21081873
  26.19167471]
[ 0.00121413  0.01106653  0.02546953  0.04982476  0.17848555  0.44741422]
Performing replicate 138 / 200
[  0.04013466   1.06941419   4.08422282   9.16676778  16.99451755
  26.30783196]
[ 0.00119747  0.01102637  0.02567901  0.04936201  0.17694132  0.66087289]
Performing replicate 139 / 200
[  0.03878843   1.06913422   4.07804802   9.27823834  17.10329262
  25.88496333]
[ 0.00118057  0.01080404  0.02634294  0.04955651  0.17520674  0.48367742]
Performing replicate 140 / 200
[  0.04010342   1.06048116   4.16675989   9.26194476  16.81398259
  25.07159596]
[ 0.00123591  0.01077064  0.02539761  0.04958305  0.1690769   0.49305708]
Performing replicate 141 / 200
[  0.03874465   1.05328165   4.0431712    9.27195769  16.99390768
  25.6237777 ]
[ 0.00116937  0.01065705  0.02579101  0.0484069   0.17646992  0.40229584]
Performing replicate 142 / 200
[  0.04215721   1.07142533   4.0808735    9.32323629  17.04227769
  25.17598607]
[ 0.00127759  0.01080358  0.02566303  0.05021267  0.17035356  0.4006108 ]
Performing replicate 143 / 200
[  0.04043168   1.07069117   4.10204078   9.29240237  17.14369459
  26.04797286]
[ 0.00120949  0.01053949  0.02594493  0.04934239  0.17456359  0.66125308]
Performing replicate 144 / 200
[  0.04088449   1.05318877   4.08067794   9.18244357  16.977117
  25.95323729]
[ 0.00129047  0.01072145  0.02522834  0.04993846  0.17707853  0.45108695]
Performing replicate 145 / 200
[  0.04009235   1.06843982   4.09262506   9.2638655   17.31553256
  26.89565361]
[ 0.00127346  0.01123077  0.02565637  0.04922175  0.18174126  0.61998037]
Performing replicate 146 / 200
[  0.03963124   1.07956863   4.13765331   9.20350867  17.16504076
  25.86232222]
[ 0.00114865  0.0109487   0.02540278  0.04911431  0.17617338  0.43291386]
Performing replicate 147 / 200
[  0.03985924   1.04159808   4.08316946   9.3056996   16.75991648
  26.11941344]
[ 0.00122513  0.01096303  0.0262326   0.04886815  0.17401069  0.78336073]
Performing replicate 148 / 200
[  0.03982678   1.07264906   4.10198652   9.22584286  16.81294905
  25.75419853]
[ 0.0012693   0.01063751  0.02593565  0.0479869   0.17544967  0.51410323]
Performing replicate 149 / 200
[  0.03950524   1.05342774   4.08868466   9.28111385  17.03683543
  26.26077134]
[ 0.0012436   0.01103079  0.02575514  0.04977335  0.17523492  0.66081985]
Performing replicate 150 / 200
[  0.04103854   1.06564037   4.10091067   9.24946845  16.85832655
  25.77860494]
[ 0.00123911  0.01080355  0.02570082  0.04926861  0.17414684  0.53573897]
Performing replicate 151 / 200
[  0.0421703    1.07052286   4.15591606   9.26279647  17.0148897
  26.87139248]
[ 0.00131449  0.01131113  0.02585465  0.04885976  0.17908127  0.63926408]
Performing replicate 152 / 200
[  0.04283881   1.06075603   4.0949236    9.19495223  17.11194677
  25.93971633]
[ 0.00130255  0.01102937  0.02483143  0.04947497  0.1779809   0.43927266]
Performing replicate 153 / 200
[  0.04233202   1.05904998   4.11066753   9.2909831   17.09160179
  26.4795255 ]
[ 0.0012714   0.01113896  0.02557989  0.04980546  0.17527974  0.6553202 ]
Performing replicate 154 / 200
[  0.04033525   1.06779141   4.10535313   9.30277389  16.95386003
  25.50736905]
[ 0.00122583  0.01110686  0.02513268  0.0501842   0.17232498  0.4821687 ]
Performing replicate 155 / 200
[  0.04026612   1.09644873   4.16853794   9.24726474  16.90114481
  25.24258986]
[ 0.0012139   0.01100923  0.02671356  0.04786345  0.1725853   0.3901067 ]
Performing replicate 156 / 200
[  0.03906261   1.09062096   4.14562783   9.22102642  16.81932758
  25.80535977]
[ 0.00117694  0.0111168   0.02529832  0.04911709  0.176728    0.44752374]
Performing replicate 157 / 200
[  0.04070245   1.08349564   4.087405     9.22263818  16.65246868
  25.01727819]
[ 0.0012579   0.01114315  0.02527657  0.04912778  0.17105104  0.42416007]
Performing replicate 158 / 200
[  0.038858     1.06436365   4.11346521   9.28805281  17.00700928
  25.94096547]
[ 0.00119331  0.01087144  0.025526    0.04949209  0.17435592  0.48873057]
Performing replicate 159 / 200
[  0.03863534   1.05785545   4.12211697   9.19493196  16.84859109
  26.38544488]
[ 0.00116276  0.01081988  0.02584204  0.04828893  0.1793468   0.51649675]
Performing replicate 160 / 200
[  0.04046122   1.04030794   4.11241122   9.20594922  16.65867485
  25.24791553]
[ 0.00123475  0.01059827  0.02570171  0.04948124  0.17060838  0.48291271]
Performing replicate 161 / 200
[  0.04140849   1.07138653   4.13329869   9.20288428  17.02143001
  25.99473279]
[ 0.001329    0.01092943  0.02507844  0.04961145  0.17602735  0.49470899]
Performing replicate 162 / 200
[  0.04166616   1.0709341    4.10146952   9.17054636  16.87661293
  26.45863914]
[ 0.00126014  0.01079852  0.02572087  0.0487759   0.17724193  0.71373954]
Performing replicate 163 / 200
[  0.04008722   1.05413579   4.10799876   9.26795049  16.81063176
  24.99624393]
[ 0.00125608  0.01100212  0.02566485  0.04938976  0.1703181   0.4161677 ]
Performing replicate 164 / 200
[  0.0387415    1.06646642   4.11179728   9.26236001  16.84517008
  25.10163539]
[ 0.00120862  0.01098634  0.02581575  0.04820443  0.17220011  0.40708557]
Performing replicate 165 / 200
[  0.0410829    1.05283067   4.0949469    9.27363586  17.07724205
  25.84018779]
[ 0.00125169  0.01102343  0.02632057  0.04843004  0.17503375  0.50340767]
Performing replicate 166 / 200
[  0.03964108   1.07658514   4.15483952   9.26922229  16.842489    25.5748169 ]
[ 0.00120427  0.0110258   0.02523857  0.04860376  0.17265797  0.48069811]
Performing replicate 167 / 200
[  0.04115877   1.04650405   4.09023549   9.23421001  16.84001286
  26.0646407 ]
[ 0.00123244  0.01086916  0.02530394  0.04886357  0.17471357  0.6034998 ]
Performing replicate 168 / 200
[  0.03962136   1.04880228   4.11120813   9.28817162  16.95461118
  26.0747367 ]
[ 0.00121454  0.0107909   0.02593557  0.0497015   0.1759755   0.52477491]
Performing replicate 169 / 200
[  0.03933242   1.0652405    4.13821324   9.29361812  16.94895642
  26.08980593]
[ 0.00118615  0.01101444  0.02588868  0.0496701   0.17644145  0.49070508]
Performing replicate 170 / 200
[  0.03924082   1.04870899   4.12174642   9.26434069  17.19187269
  25.53024351]
[ 0.00121825  0.01085487  0.02595499  0.05007439  0.17263563  0.4424045 ]
Performing replicate 171 / 200
[  0.04032347   1.06789577   4.09306472   9.20194451  17.26685859
  26.16562743]
[ 0.00124151  0.010981    0.02581321  0.05008271  0.17687769  0.52078582]
Performing replicate 172 / 200
[  0.0392444    1.07221821   4.1263054    9.24548735  17.05286745
  25.95925097]
[ 0.00118465  0.01116946  0.02566478  0.04890527  0.17580603  0.48896266]
Performing replicate 173 / 200
[  0.03971729   1.06171116   4.09255312   9.24492582  16.95772866
  26.12282377]
[ 0.0012028   0.01098921  0.0258358   0.04998143  0.17547126  0.54453633]
Performing replicate 174 / 200
[  0.04082981   1.05727036   4.07320823   9.32041326  17.02462864
  25.95365609]
[ 0.00124846  0.01082101  0.02537474  0.05062054  0.17437232  0.50413472]
Performing replicate 175 / 200
[  0.0391653    1.0826314    4.11553603   9.23761106  17.09492746
  25.48363107]
[ 0.00119351  0.01098443  0.02564818  0.04919253  0.17424364  0.39502371]
Performing replicate 176 / 200
[  0.04162999   1.04539376   4.13621659   9.25199983  17.22479623
  26.68295993]
[ 0.00126612  0.01073412  0.02545388  0.04960743  0.17992553  0.59287252]
Performing replicate 177 / 200
[  0.040892     1.0671822    4.11941036   9.26315538  17.12733979
  25.48019854]
[ 0.00121534  0.01087971  0.02631539  0.04951128  0.17169236  0.45976469]
Performing replicate 178 / 200
[  0.040593     1.04735719   4.11480803   9.18996328  16.91438114
  25.61631068]
[ 0.00121006  0.0105619   0.02519179  0.048928    0.17699047  0.41568978]
Performing replicate 179 / 200
[  0.03949997   1.05983624   4.1161433    9.24289668  17.07069573
  25.94581591]
[ 0.00123058  0.01101692  0.02611206  0.04851842  0.17539834  0.49882988]
Performing replicate 180 / 200
[  0.04268441   1.04306007   4.13891794   9.27704161  16.97015949
  25.93576014]
[ 0.00127801  0.01066696  0.0258331   0.04922634  0.17440892  0.55836257]
Performing replicate 181 / 200
[  0.03997153   1.0679806    4.09171679   9.31222106  17.15616892
  26.37041466]
[ 0.00123118  0.01070067  0.02609698  0.0496551   0.17606712  0.5655925 ]
Performing replicate 182 / 200
[  0.03916729   1.0462345    4.04675658   9.27222361  16.91813772
  25.68211268]
[ 0.00122488  0.01057735  0.02650417  0.04849245  0.17562164  0.42935177]
Performing replicate 183 / 200
[  0.04104305   1.08116288   4.093905     9.27785203  16.87299391
  25.6468424 ]
[ 0.00126306  0.01103343  0.02565125  0.04860066  0.17202623  0.58639778]
Performing replicate 184 / 200
[  0.04017636   1.06085919   4.09406332   9.19915067  16.79677292
  25.93005427]
[ 0.00120525  0.01083511  0.02512188  0.04932081  0.17543116  0.54611401]
Performing replicate 185 / 200
[  0.04198703   1.04706363   4.05060448   9.30064134  16.94518554
  26.03703662]
[ 0.00130929  0.01083047  0.02541583  0.04960069  0.17732444  0.47394367]
Performing replicate 186 / 200
[  0.03995719   1.0812905    4.11385805   9.34922996  17.3113262
  26.72903961]
[ 0.00123332  0.01089008  0.02645681  0.05054283  0.17738668  0.64498736]
Performing replicate 187 / 200
[  0.04178661   1.04738889   4.08764344   9.19222811  17.09856684
  27.02318802]
[ 0.00124473  0.0108632   0.02530931  0.04930682  0.18064872  0.70583336]
Performing replicate 188 / 200
[  0.03815262   1.06627266   4.1017307    9.19193494  16.92183004
  25.15194766]
[ 0.00115353  0.01122614  0.02492129  0.04904429  0.1714296   0.46277932]
Performing replicate 189 / 200
[  0.04185249   1.05044745   4.07419763   9.18283925  16.96688124
  26.25445596]
[ 0.00127318  0.01111222  0.02580958  0.04904387  0.17461487  0.82896019]
Performing replicate 190 / 200
[  0.04013031   1.05129657   4.12751049   9.29690192  17.25226686
  26.4353545 ]
[ 0.00125514  0.01080433  0.02645488  0.04910563  0.17889221  0.48625833]
Performing replicate 191 / 200
[  0.04245385   1.05526463   4.09175209   9.29643086  16.90897975
  26.12822411]
[ 0.00128934  0.01080084  0.02594365  0.04952361  0.17444127  0.63108606]
Performing replicate 192 / 200
[  0.03939741   1.06506177   4.12351384   9.31724781  17.38964044
  26.23684384]
[ 0.00125671  0.0109246   0.02568841  0.0500429   0.17853105  0.49399573]
Performing replicate 193 / 200
[  0.03998072   1.07018011   4.11376889   9.28750939  16.9131847
  25.48530037]
[ 0.00124424  0.01106459  0.02607634  0.04907463  0.1724432   0.46890669]
Performing replicate 194 / 200
[  0.03996269   1.05972543   4.11531239   9.28403013  16.62235584
  24.77307246]
[ 0.00121992  0.01089392  0.02644425  0.04882868  0.1669324   0.45633012]
Performing replicate 195 / 200
[  0.0389021    1.07285365   4.09265839   9.291044    16.68839384
  24.53532919]
[ 0.00120791  0.01105546  0.0260614   0.04977696  0.16517615  0.40374384]
Performing replicate 196 / 200
[  0.03820896   1.06562087   4.12246071   9.28038403  16.9777533
  25.60066381]
[ 0.00114809  0.0108086   0.02602538  0.04933105  0.17182912  0.50621923]
Performing replicate 197 / 200
[  0.03961265   1.05123143   4.13552453   9.29155693  17.01434371
  26.7809199 ]
[ 0.00123017  0.01086232  0.02591244  0.04999904  0.17486925  1.0911329 ]
Performing replicate 198 / 200
[  0.03889642   1.07099961   4.14408392   9.23450485  17.17766108
  26.65097084]
[ 0.00117274  0.01102282  0.02536606  0.04985116  0.1773005   0.72667978]
Performing replicate 199 / 200
[  0.04127325   1.0568403    4.10224829   9.26011535  16.65155574
  24.59976436]
[ 0.00123371  0.01066127  0.02576043  0.04933736  0.16771452  0.41132017]
Performing replicate 200 / 200
[  0.03843392   1.05559499   4.11173046   9.3156173   17.01134082
  26.14293771]
[ 0.00117839  0.01084721  0.02509163  0.05022886  0.17425602  0.54584475]
Free energies
Anderson-Darling Metrics (see README.md)
[[ 0.          1.28950265  1.22372038  1.19571806  1.29453297  1.29706093]
 [ 0.92104011  0.          1.11743234  0.38514148  0.39310714  0.7255426 ]
 [ 0.76238837  0.73065943  0.          0.38600061  0.3219965   0.27862602]
 [ 0.84943314  0.22877813  0.67881642  0.          0.37026049  1.22756765]
 [ 0.95619074  0.23467976  0.60820073  0.48639343  0.          3.21878282]
 [ 0.87460656  0.44539327  0.31457453  0.9575389   2.70933039  0.        ]]
The uncertainty estimates are tested in this section.
If the error is normally distributed, the actual error will be less than a
multiplier 'alpha' times the computed uncertainty 'sigma' a fraction of
time given by:
P(error < alpha sigma) = erf(alpha / sqrt(2))
For example, the true error should be less than 1.0 * sigma
(one standard deviation) a total of 68% of the time, and
less than 2.0 * sigma (two standard deviations) 95% of the time.
The observed fraction of the time that error < alpha sigma, and its
uncertainty, is given as 'obs' (with uncertainty 'obs err') below.
This should be compared to the column labeled 'normal'.
A weak lower bound that holds regardless of how the error is distributed is given
by Chebyshev's inequality, and is listed as 'cheby' below.
Uncertainty estimates are tested for both free energy differences and expectations.

Error vs. alpha
alpha      cheby        obs          obs err            normal
  0.1 -99.000000   0.084610 (  0.074922,  0.094823)   0.079656
  0.2 -24.000000   0.161892 (  0.148933,  0.175278)   0.158519
  0.3 -10.111111   0.232845 (  0.217899,  0.248128)   0.235823
  0.4  -5.250000   0.300133 (  0.283869,  0.316650)   0.310843
  0.5  -3.000000   0.369420 (  0.352242,  0.386764)   0.382925
  0.6  -1.777778   0.436043 (  0.418348,  0.453818)   0.451494
  0.7  -1.040816   0.500666 (  0.482784,  0.518548)   0.516073
  0.8  -0.562500   0.558294 (  0.540498,  0.576017)   0.576289
  0.9  -0.234568   0.615923 (  0.598455,  0.633244)   0.631880
  1.0  -0.000000   0.666889 (  0.649927,  0.683639)   0.682689
  1.1   0.173554   0.710526 (  0.694174,  0.726612)   0.728668
  1.2   0.305556   0.751166 (  0.735546,  0.766469)   0.769861
  1.3   0.408284   0.798468 (  0.783934,  0.812625)   0.806399
  1.4   0.489796   0.832112 (  0.818536,  0.845268)   0.838487
  1.5   0.555556   0.854430 (  0.841595,  0.866818)   0.866386
  1.6   0.609375   0.880080 (  0.868224,  0.891457)   0.890401
  1.7   0.653979   0.900733 (  0.889788,  0.911172)   0.910869
  1.8   0.691358   0.920053 (  0.910092,  0.929485)   0.928139
  1.9   0.722992   0.935376 (  0.926312,  0.943891)   0.942567
  2.0   0.750000   0.946369 (  0.938034,  0.954141)   0.954500
  2.1   0.773243   0.955363 (  0.947695,  0.962457)   0.964271
  2.2   0.793388   0.965023 (  0.958164,  0.971296)   0.972193
  2.3   0.810964   0.972019 (  0.965829,  0.977613)   0.978552
  2.4   0.826389   0.978348 (  0.972848,  0.983245)   0.983605
  2.5   0.840000   0.984011 (  0.979227,  0.988184)   0.987581
  2.6   0.852071   0.989340 (  0.985369,  0.992695)   0.990678
  2.7   0.862826   0.991672 (  0.988124,  0.994602)   0.993066
  2.8   0.872449   0.993338 (  0.990131,  0.995925)   0.994890
  2.9   0.881094   0.995003 (  0.992185,  0.997200)   0.996268
  3.0   0.888889   0.997335 (  0.995200,  0.998848)   0.997300
  3.1   0.895942   0.997668 (  0.995653,  0.999062)   0.998065
  3.2   0.902344   0.997668 (  0.995653,  0.999062)   0.998626
  3.3   0.908173   0.998334 (  0.996591,  0.999459)   0.999033
  3.4   0.913495   0.998668 (  0.997081,  0.999637)   0.999326
  3.5   0.918367   0.999001 (  0.997595,  0.999794)   0.999535
  3.6   0.922840   0.999334 (  0.998145,  0.999919)   0.999682
  3.7   0.926954   0.999334 (  0.998145,  0.999919)   0.999784
  3.8   0.930748   0.999667 (  0.998772,  0.999992)   0.999855
  3.9   0.934254   0.999667 (  0.998772,  0.999992)   0.999904
  4.0   0.937500   0.999667 (  0.998772,  0.999992)   0.999937

     i      average    bias      rms_error     stddev  ave_analyt_std
---------------------------------------------------------------------
      0     0.0000      0.0000      0.0000      0.0000     0.0000
      1    -0.2149      0.0082      0.1620      0.1618     0.1554
      2    -0.4987      0.0121      0.1856      0.1852     0.1768
      3    -0.9060      0.0103      0.1902      0.1899     0.1825
      4    -1.5992      0.0102      0.1917      0.1915     0.1838
      5    -1.5971      0.0123      0.1935      0.1931     0.1881
Totals:    -1.5971      0.0123      0.1935      0.1931     0.1881
Standard ensemble averaged observables
The uncertainty estimates are tested in this section.
If the error is normally distributed, the actual error will be less than a
multiplier 'alpha' times the computed uncertainty 'sigma' a fraction of
time given by:
P(error < alpha sigma) = erf(alpha / sqrt(2))
For example, the true error should be less than 1.0 * sigma
(one standard deviation) a total of 68% of the time, and
less than 2.0 * sigma (two standard deviations) 95% of the time.
The observed fraction of the time that error < alpha sigma, and its
uncertainty, is given as 'obs' (with uncertainty 'obs err') below.
This should be compared to the column labeled 'normal'.
A weak lower bound that holds regardless of how the error is distributed is given
by Chebyshev's inequality, and is listed as 'cheby' below.
Uncertainty estimates are tested for both free energy differences and expectations.

Error vs. alpha
alpha      cheby        obs          obs err            normal
  0.1 -99.000000   0.081836 (  0.065680,  0.099573)   0.079656
  0.2 -24.000000   0.161677 (  0.139544,  0.185088)   0.158519
  0.3 -10.111111   0.239521 (  0.213610,  0.266417)   0.235823
  0.4  -5.250000   0.305389 (  0.277262,  0.334253)   0.310843
  0.5  -3.000000   0.368263 (  0.338670,  0.398356)   0.382925
  0.6  -1.777778   0.431138 (  0.400626,  0.461910)   0.451494
  0.7  -1.040816   0.505988 (  0.475042,  0.536911)   0.516073
  0.8  -0.562500   0.563872 (  0.533068,  0.594435)   0.576289
  0.9  -0.234568   0.606786 (  0.576362,  0.636807)   0.631880
  1.0  -0.000000   0.663673 (  0.634132,  0.692594)   0.682689
  1.1   0.173554   0.711577 (  0.683148,  0.739205)   0.728668
  1.2   0.305556   0.757485 (  0.730482,  0.783514)   0.769861
  1.3   0.408284   0.796407 (  0.770937,  0.820757)   0.806399
  1.4   0.489796   0.828343 (  0.804397,  0.851048)   0.838487
  1.5   0.555556   0.865269 (  0.843462,  0.885697)   0.866386
  1.6   0.609375   0.888224 (  0.868004,  0.906975)   0.890401
  1.7   0.653979   0.915170 (  0.897159,  0.931612)   0.910869
  1.8   0.691358   0.928144 (  0.911371,  0.943298)   0.928139
  1.9   0.722992   0.945110 (  0.930195,  0.958343)   0.942567
  2.0   0.750000   0.955090 (  0.941438,  0.967024)   0.954500
  2.1   0.773243   0.964072 (  0.951706,  0.974687)   0.964271
  2.2   0.793388   0.969062 (  0.957491,  0.978863)   0.972193
  2.3   0.810964   0.973054 (  0.962172,  0.982151)   0.978552
  2.4   0.826389   0.981038 (  0.971729,  0.988534)   0.983605
  2.5   0.840000   0.985030 (  0.976645,  0.991589)   0.987581
  2.6   0.852071   0.990020 (  0.983001,  0.995199)   0.990678
  2.7   0.862826   0.993014 (  0.987000,  0.997184)   0.993066
  2.8   0.872449   0.993014 (  0.987000,  0.997184)   0.994890
  2.9   0.881094   0.994012 (  0.988382,  0.997797)   0.996268
  3.0   0.888889   0.997006 (  0.992801,  0.999382)   0.997300
  3.1   0.895942   0.997006 (  0.992801,  0.999382)   0.998065
  3.2   0.902344   0.998004 (  0.994447,  0.999758)   0.998626
  3.3   0.908173   0.998004 (  0.994447,  0.999758)   0.999033
  3.4   0.913495   0.999002 (  0.996322,  0.999975)   0.999326
  3.5   0.918367   0.999002 (  0.996322,  0.999975)   0.999535
  3.6   0.922840   0.999002 (  0.996322,  0.999975)   0.999682
  3.7   0.926954   0.999002 (  0.996322,  0.999975)   0.999784
  3.8   0.930748   0.999002 (  0.996322,  0.999975)   0.999855
  3.9   0.934254   0.999002 (  0.996322,  0.999975)   0.999904
  4.0   0.937500   0.999002 (  0.996322,  0.999975)   0.999937

     i      average    bias      rms_error     stddev  ave_analyt_std
---------------------------------------------------------------------
      0     0.0399     -0.0001      0.0013      0.0013     0.0013
      1     1.0629      0.0004      0.0116      0.0116     0.0113
      2     4.1105     -0.0006      0.0306      0.0306     0.0300
      3     9.2578      0.0078      0.0664      0.0659     0.0675
      4    16.9898     -0.0102      0.1829      0.1826     0.1816
Totals:    16.9898     -0.0102      0.1829      0.1826     0.1816
Anderson-Darling Metrics (see README.md)
[ 2.13488553  0.79787475  0.11485075  1.7653048   0.68530093]
MBAR ensemble averaged observables
The uncertainty estimates are tested in this section.
If the error is normally distributed, the actual error will be less than a
multiplier 'alpha' times the computed uncertainty 'sigma' a fraction of
time given by:
P(error < alpha sigma) = erf(alpha / sqrt(2))
For example, the true error should be less than 1.0 * sigma
(one standard deviation) a total of 68% of the time, and
less than 2.0 * sigma (two standard deviations) 95% of the time.
The observed fraction of the time that error < alpha sigma, and its
uncertainty, is given as 'obs' (with uncertainty 'obs err') below.
This should be compared to the column labeled 'normal'.
A weak lower bound that holds regardless of how the error is distributed is given
by Chebyshev's inequality, and is listed as 'cheby' below.
Uncertainty estimates are tested for both free energy differences and expectations.

Error vs. alpha
alpha      cheby        obs          obs err            normal
  0.1 -99.000000   0.077371 (  0.062952,  0.093121)   0.079656
  0.2 -24.000000   0.172213 (  0.151402,  0.194057)   0.158519
  0.3 -10.111111   0.247088 (  0.223120,  0.271853)   0.235823
  0.4  -5.250000   0.306156 (  0.280423,  0.332501)   0.310843
  0.5  -3.000000   0.375208 (  0.348050,  0.402760)   0.382925
  0.6  -1.777778   0.440932 (  0.412973,  0.469076)   0.451494
  0.7  -1.040816   0.508319 (  0.480061,  0.536552)   0.516073
  0.8  -0.562500   0.561564 (  0.533433,  0.589501)   0.576289
  0.9  -0.234568   0.613145 (  0.585450,  0.640483)   0.631880
  1.0  -0.000000   0.662230 (  0.635254,  0.688694)   0.682689
  1.1   0.173554   0.712146 (  0.686233,  0.737391)   0.728668
  1.2   0.305556   0.756240 (  0.731581,  0.780091)   0.769861
  1.3   0.408284   0.782862 (  0.759125,  0.805707)   0.806399
  1.4   0.489796   0.816972 (  0.794629,  0.838315)   0.838487
  1.5   0.555556   0.847754 (  0.826914,  0.867498)   0.866386
  1.6   0.609375   0.875208 (  0.855952,  0.893282)   0.890401
  1.7   0.653979   0.895175 (  0.877253,  0.911851)   0.910869
  1.8   0.691358   0.911814 (  0.895154,  0.927176)   0.928139
  1.9   0.722992   0.929285 (  0.914137,  0.943080)   0.942567
  2.0   0.750000   0.940932 (  0.926931,  0.953544)   0.954500
  2.1   0.773243   0.951747 (  0.938944,  0.963128)   0.964271
  2.2   0.793388   0.960899 (  0.949240,  0.971107)   0.972193
  2.3   0.810964   0.969218 (  0.958742,  0.978218)   0.978552
  2.4   0.826389   0.975042 (  0.965505,  0.983085)   0.983605
  2.5   0.840000   0.980033 (  0.971402,  0.987155)   0.987581
  2.6   0.852071   0.984193 (  0.976416,  0.990449)   0.990678
  2.7   0.862826   0.989185 (  0.982612,  0.994224)   0.993066
  2.8   0.872449   0.992512 (  0.986917,  0.996568)   0.994890
  2.9   0.881094   0.993344 (  0.988028,  0.997120)   0.996268
  3.0   0.888889   0.994176 (  0.989158,  0.997654)   0.997300
  3.1   0.895942   0.995840 (  0.991495,  0.998647)   0.998065
  3.2   0.902344   0.997504 (  0.993998,  0.999485)   0.998626
  3.3   0.908173   0.997504 (  0.993998,  0.999485)   0.999033
  3.4   0.913495   0.997504 (  0.993998,  0.999485)   0.999326
  3.5   0.918367   0.998336 (  0.995370,  0.999798)   0.999535
  3.6   0.922840   0.998336 (  0.995370,  0.999798)   0.999682
  3.7   0.926954   0.999168 (  0.996933,  0.999979)   0.999784
  3.8   0.930748   0.999168 (  0.996933,  0.999979)   0.999855
  3.9   0.934254   0.999168 (  0.996933,  0.999979)   0.999904
  4.0   0.937500   0.999168 (  0.996933,  0.999979)   0.999937

     i      average    bias      rms_error     stddev  ave_analyt_std
---------------------------------------------------------------------
      0     0.0399     -0.0001      0.0013      0.0013     0.0012
      1     1.0626      0.0001      0.0114      0.0114     0.0109
      2     4.1113      0.0002      0.0260      0.0260     0.0257
      3     9.2565      0.0065      0.0472      0.0468     0.0493
      4    16.9905     -0.0095      0.1804      0.1801     0.1751
      5    25.9544     -0.0456      0.6175      0.6158     0.5718
Totals:    25.9544     -0.0456      0.6175      0.6158     0.5718
Anderson-Darling Metrics (see README.md)
[  0.88636271   0.66578887   0.33607562   2.32717013   0.68941846
  12.15892596]

 ==== State 1 alone with MBAR ===== 
The uncertainty estimates are tested in this section.
If the error is normally distributed, the actual error will be less than a
multiplier 'alpha' times the computed uncertainty 'sigma' a fraction of
time given by:
P(error < alpha sigma) = erf(alpha / sqrt(2))
For example, the true error should be less than 1.0 * sigma
(one standard deviation) a total of 68% of the time, and
less than 2.0 * sigma (two standard deviations) 95% of the time.
The observed fraction of the time that error < alpha sigma, and its
uncertainty, is given as 'obs' (with uncertainty 'obs err') below.
This should be compared to the column labeled 'normal'.
A weak lower bound that holds regardless of how the error is distributed is given
by Chebyshev's inequality, and is listed as 'cheby' below.
Uncertainty estimates are tested for both free energy differences and expectations.

Error vs. alpha
alpha      cheby        obs          obs err            normal
  0.1 -99.000000   0.108911 (  0.069877,  0.155265)   0.079656
  0.2 -24.000000   0.153465 (  0.107260,  0.206163)   0.158519
  0.3 -10.111111   0.262376 (  0.204181,  0.325028)   0.235823
  0.4  -5.250000   0.336634 (  0.273241,  0.403090)   0.310843
  0.5  -3.000000   0.391089 (  0.325057,  0.459164)   0.382925
  0.6  -1.777778   0.475248 (  0.406855,  0.544104)   0.451494
  0.7  -1.040816   0.534653 (  0.465785,  0.602871)   0.516073
  0.8  -0.562500   0.589109 (  0.520668,  0.655878)   0.576289
  0.9  -0.234568   0.599010 (  0.530738,  0.665425)   0.631880
  1.0  -0.000000   0.623762 (  0.556038,  0.689165)   0.682689
  1.1   0.173554   0.648515 (  0.581525,  0.712719)   0.728668
  1.2   0.305556   0.698020 (  0.633092,  0.759233)   0.769861
  1.3   0.408284   0.742574 (  0.680251,  0.800349)   0.806399
  1.4   0.489796   0.792079 (  0.733624,  0.845059)   0.838487
  1.5   0.555556   0.826733 (  0.771728,  0.875614)   0.866386
  1.6   0.609375   0.881188 (  0.833262,  0.921978)   0.890401
  1.7   0.653979   0.891089 (  0.844735,  0.930123)   0.910869
  1.8   0.691358   0.905941 (  0.862162,  0.942125)   0.928139
  1.9   0.722992   0.930693 (  0.891940,  0.961400)   0.942567
  2.0   0.750000   0.945545 (  0.910411,  0.972368)   0.954500
  2.1   0.773243   0.960396 (  0.929565,  0.982663)   0.964271
  2.2   0.793388   0.965347 (  0.936163,  0.985886)   0.972193
  2.3   0.810964   0.970297 (  0.942906,  0.988968)   0.978552
  2.4   0.826389   0.970297 (  0.942906,  0.988968)   0.983605
  2.5   0.840000   0.975248 (  0.949833,  0.991875)   0.987581
  2.6   0.852071   0.995050 (  0.981815,  0.999874)   0.990678
  2.7   0.862826   0.995050 (  0.981815,  0.999874)   0.993066
  2.8   0.872449   0.995050 (  0.981815,  0.999874)   0.994890
  2.9   0.881094   0.995050 (  0.981815,  0.999874)   0.996268
  3.0   0.888889   0.995050 (  0.981815,  0.999874)   0.997300
  3.1   0.895942   0.995050 (  0.981815,  0.999874)   0.998065
  3.2   0.902344   0.995050 (  0.981815,  0.999874)   0.998626
  3.3   0.908173   0.995050 (  0.981815,  0.999874)   0.999033
  3.4   0.913495   0.995050 (  0.981815,  0.999874)   0.999326
  3.5   0.918367   0.995050 (  0.981815,  0.999874)   0.999535
  3.6   0.922840   0.995050 (  0.981815,  0.999874)   0.999682
  3.7   0.926954   0.995050 (  0.981815,  0.999874)   0.999784
  3.8   0.930748   0.995050 (  0.981815,  0.999874)   0.999855
  3.9   0.934254   0.995050 (  0.981815,  0.999874)   0.999904
  4.0   0.937500   0.995050 (  0.981815,  0.999874)   0.999937

     i      average    bias      rms_error     stddev  ave_analyt_std
---------------------------------------------------------------------
Totals:    -0.2149      0.0082      0.1620      0.1618     0.1554

 ==== State 2 alone with MBAR ===== 
The uncertainty estimates are tested in this section.
If the error is normally distributed, the actual error will be less than a
multiplier 'alpha' times the computed uncertainty 'sigma' a fraction of
time given by:
P(error < alpha sigma) = erf(alpha / sqrt(2))
For example, the true error should be less than 1.0 * sigma
(one standard deviation) a total of 68% of the time, and
less than 2.0 * sigma (two standard deviations) 95% of the time.
The observed fraction of the time that error < alpha sigma, and its
uncertainty, is given as 'obs' (with uncertainty 'obs err') below.
This should be compared to the column labeled 'normal'.
A weak lower bound that holds regardless of how the error is distributed is given
by Chebyshev's inequality, and is listed as 'cheby' below.
Uncertainty estimates are tested for both free energy differences and expectations.

Error vs. alpha
alpha      cheby        obs          obs err            normal
  0.1 -99.000000   0.069307 (  0.038600,  0.108060)   0.079656
  0.2 -24.000000   0.148515 (  0.103022,  0.200592)   0.158519
  0.3 -10.111111   0.207921 (  0.154941,  0.266376)   0.235823
  0.4  -5.250000   0.272277 (  0.213271,  0.335554)   0.310843
  0.5  -3.000000   0.351485 (  0.287281,  0.418475)   0.382925
  0.6  -1.777778   0.415842 (  0.348906,  0.484356)   0.451494
  0.7  -1.040816   0.480198 (  0.411729,  0.549038)   0.516073
  0.8  -0.562500   0.549505 (  0.480671,  0.617411)   0.576289
  0.9  -0.234568   0.628713 (  0.561121,  0.693891)   0.631880
  1.0  -0.000000   0.663366 (  0.596910,  0.726759)   0.682689
  1.1   0.173554   0.712871 (  0.648728,  0.773022)   0.728668
  1.2   0.305556   0.742574 (  0.680251,  0.800349)   0.769861
  1.3   0.408284   0.772277 (  0.712139,  0.827311)   0.806399
  1.4   0.489796   0.811881 (  0.755313,  0.862603)   0.838487
  1.5   0.555556   0.831683 (  0.777230,  0.879921)   0.866386
  1.6   0.609375   0.856436 (  0.804997,  0.901197)   0.890401
  1.7   0.653979   0.891089 (  0.844735,  0.930123)   0.910869
  1.8   0.691358   0.915842 (  0.873949,  0.949958)   0.928139
  1.9   0.722992   0.935644 (  0.898036,  0.965116)   0.942567
  2.0   0.750000   0.940594 (  0.904191,  0.968774)   0.954500
  2.1   0.773243   0.950495 (  0.916705,  0.975888)   0.964271
  2.2   0.793388   0.955446 (  0.923085,  0.979324)   0.972193
  2.3   0.810964   0.970297 (  0.942906,  0.988968)   0.978552
  2.4   0.826389   0.970297 (  0.942906,  0.988968)   0.983605
  2.5   0.840000   0.975248 (  0.949833,  0.991875)   0.987581
  2.6   0.852071   0.980198 (  0.957004,  0.994552)   0.990678
  2.7   0.862826   0.990099 (  0.972594,  0.998793)   0.993066
  2.8   0.872449   0.995050 (  0.981815,  0.999874)   0.994890
  2.9   0.881094   0.995050 (  0.981815,  0.999874)   0.996268
  3.0   0.888889   0.995050 (  0.981815,  0.999874)   0.997300
  3.1   0.895942   0.995050 (  0.981815,  0.999874)   0.998065
  3.2   0.902344   0.995050 (  0.981815,  0.999874)   0.998626
  3.3   0.908173   0.995050 (  0.981815,  0.999874)   0.999033
  3.4   0.913495   0.995050 (  0.981815,  0.999874)   0.999326
  3.5   0.918367   0.995050 (  0.981815,  0.999874)   0.999535
  3.6   0.922840   0.995050 (  0.981815,  0.999874)   0.999682
  3.7   0.926954   0.995050 (  0.981815,  0.999874)   0.999784
  3.8   0.930748   0.995050 (  0.981815,  0.999874)   0.999855
  3.9   0.934254   0.995050 (  0.981815,  0.999874)   0.999904
  4.0   0.937500   0.995050 (  0.981815,  0.999874)   0.999937

     i      average    bias      rms_error     stddev  ave_analyt_std
---------------------------------------------------------------------
Totals:    -0.4987      0.0121      0.1856      0.1852     0.1768

 ==== State 3 alone with MBAR ===== 
The uncertainty estimates are tested in this section.
If the error is normally distributed, the actual error will be less than a
multiplier 'alpha' times the computed uncertainty 'sigma' a fraction of
time given by:
P(error < alpha sigma) = erf(alpha / sqrt(2))
For example, the true error should be less than 1.0 * sigma
(one standard deviation) a total of 68% of the time, and
less than 2.0 * sigma (two standard deviations) 95% of the time.
The observed fraction of the time that error < alpha sigma, and its
uncertainty, is given as 'obs' (with uncertainty 'obs err') below.
This should be compared to the column labeled 'normal'.
A weak lower bound that holds regardless of how the error is distributed is given
by Chebyshev's inequality, and is listed as 'cheby' below.
Uncertainty estimates are tested for both free energy differences and expectations.

Error vs. alpha
alpha      cheby        obs          obs err            normal
  0.1 -99.000000   0.089109 (  0.053940,  0.131963)   0.079656
  0.2 -24.000000   0.183168 (  0.133045,  0.239230)   0.158519
  0.3 -10.111111   0.227723 (  0.172689,  0.287861)   0.235823
  0.4  -5.250000   0.277228 (  0.217831,  0.340803)   0.310843
  0.5  -3.000000   0.341584 (  0.277913,  0.408226)   0.382925
  0.6  -1.777778   0.396040 (  0.329813,  0.464217)   0.451494
  0.7  -1.040816   0.480198 (  0.411729,  0.549038)   0.516073
  0.8  -0.562500   0.544554 (  0.475702,  0.612571)   0.576289
  0.9  -0.234568   0.599010 (  0.530738,  0.665425)   0.631880
  1.0  -0.000000   0.633663 (  0.566210,  0.698609)   0.682689
  1.1   0.173554   0.688119 (  0.622712,  0.749997)   0.728668
  1.2   0.305556   0.757426 (  0.696146,  0.813878)   0.769861
  1.3   0.408284   0.797030 (  0.739027,  0.849465)   0.806399
  1.4   0.489796   0.831683 (  0.777230,  0.879921)   0.838487
  1.5   0.555556   0.861386 (  0.810607,  0.905396)   0.866386
  1.6   0.609375   0.881188 (  0.833262,  0.921978)   0.890401
  1.7   0.653979   0.896040 (  0.850513,  0.934154)   0.910869
  1.8   0.691358   0.925743 (  0.885897,  0.957632)   0.928139
  1.9   0.722992   0.935644 (  0.898036,  0.965116)   0.942567
  2.0   0.750000   0.945545 (  0.910411,  0.972368)   0.954500
  2.1   0.773243   0.945545 (  0.910411,  0.972368)   0.964271
  2.2   0.793388   0.950495 (  0.916705,  0.975888)   0.972193
  2.3   0.810964   0.960396 (  0.929565,  0.982663)   0.978552
  2.4   0.826389   0.965347 (  0.936163,  0.985886)   0.983605
  2.5   0.840000   0.975248 (  0.949833,  0.991875)   0.987581
  2.6   0.852071   0.980198 (  0.957004,  0.994552)   0.990678
  2.7   0.862826   0.985149 (  0.964520,  0.996911)   0.993066
  2.8   0.872449   0.990099 (  0.972594,  0.998793)   0.994890
  2.9   0.881094   0.990099 (  0.972594,  0.998793)   0.996268
  3.0   0.888889   0.995050 (  0.981815,  0.999874)   0.997300
  3.1   0.895942   0.995050 (  0.981815,  0.999874)   0.998065
  3.2   0.902344   0.995050 (  0.981815,  0.999874)   0.998626
  3.3   0.908173   0.995050 (  0.981815,  0.999874)   0.999033
  3.4   0.913495   0.995050 (  0.981815,  0.999874)   0.999326
  3.5   0.918367   0.995050 (  0.981815,  0.999874)   0.999535
  3.6   0.922840   0.995050 (  0.981815,  0.999874)   0.999682
  3.7   0.926954   0.995050 (  0.981815,  0.999874)   0.999784
  3.8   0.930748   0.995050 (  0.981815,  0.999874)   0.999855
  3.9   0.934254   0.995050 (  0.981815,  0.999874)   0.999904
  4.0   0.937500   0.995050 (  0.981815,  0.999874)   0.999937

     i      average    bias      rms_error     stddev  ave_analyt_std
---------------------------------------------------------------------
Totals:    -0.9060      0.0103      0.1902      0.1899     0.1825

 ==== State 4 alone with MBAR ===== 
The uncertainty estimates are tested in this section.
If the error is normally distributed, the actual error will be less than a
multiplier 'alpha' times the computed uncertainty 'sigma' a fraction of
time given by:
P(error < alpha sigma) = erf(alpha / sqrt(2))
For example, the true error should be less than 1.0 * sigma
(one standard deviation) a total of 68% of the time, and
less than 2.0 * sigma (two standard deviations) 95% of the time.
The observed fraction of the time that error < alpha sigma, and its
uncertainty, is given as 'obs' (with uncertainty 'obs err') below.
This should be compared to the column labeled 'normal'.
A weak lower bound that holds regardless of how the error is distributed is given
by Chebyshev's inequality, and is listed as 'cheby' below.
Uncertainty estimates are tested for both free energy differences and expectations.

Error vs. alpha
alpha      cheby        obs          obs err            normal
  0.1 -99.000000   0.089109 (  0.053940,  0.131963)   0.079656
  0.2 -24.000000   0.158416 (  0.111516,  0.211716)   0.158519
  0.3 -10.111111   0.222772 (  0.168234,  0.282508)   0.235823
  0.4  -5.250000   0.282178 (  0.222400,  0.346042)   0.310843
  0.5  -3.000000   0.336634 (  0.273241,  0.403090)   0.382925
  0.6  -1.777778   0.415842 (  0.348906,  0.484356)   0.451494
  0.7  -1.040816   0.480198 (  0.411729,  0.549038)   0.516073
  0.8  -0.562500   0.534653 (  0.465785,  0.602871)   0.576289
  0.9  -0.234568   0.613861 (  0.545896,  0.679691)   0.631880
  1.0  -0.000000   0.658416 (  0.591774,  0.722087)   0.682689
  1.1   0.173554   0.688119 (  0.622712,  0.749997)   0.728668
  1.2   0.305556   0.752475 (  0.690837,  0.809379)   0.769861
  1.3   0.408284   0.811881 (  0.755313,  0.862603)   0.806399
  1.4   0.489796   0.836634 (  0.782749,  0.884211)   0.838487
  1.5   0.555556   0.866337 (  0.816237,  0.909575)   0.866386
  1.6   0.609375   0.886139 (  0.838985,  0.926064)   0.890401
  1.7   0.653979   0.910891 (  0.868037,  0.946060)   0.910869
  1.8   0.691358   0.910891 (  0.868037,  0.946060)   0.928139
  1.9   0.722992   0.925743 (  0.885897,  0.957632)   0.942567
  2.0   0.750000   0.930693 (  0.891940,  0.961400)   0.954500
  2.1   0.773243   0.945545 (  0.910411,  0.972368)   0.964271
  2.2   0.793388   0.950495 (  0.916705,  0.975888)   0.972193
  2.3   0.810964   0.960396 (  0.929565,  0.982663)   0.978552
  2.4   0.826389   0.965347 (  0.936163,  0.985886)   0.983605
  2.5   0.840000   0.970297 (  0.942906,  0.988968)   0.987581
  2.6   0.852071   0.985149 (  0.964520,  0.996911)   0.990678
  2.7   0.862826   0.990099 (  0.972594,  0.998793)   0.993066
  2.8   0.872449   0.995050 (  0.981815,  0.999874)   0.994890
  2.9   0.881094   0.995050 (  0.981815,  0.999874)   0.996268
  3.0   0.888889   0.995050 (  0.981815,  0.999874)   0.997300
  3.1   0.895942   0.995050 (  0.981815,  0.999874)   0.998065
  3.2   0.902344   0.995050 (  0.981815,  0.999874)   0.998626
  3.3   0.908173   0.995050 (  0.981815,  0.999874)   0.999033
  3.4   0.913495   0.995050 (  0.981815,  0.999874)   0.999326
  3.5   0.918367   0.995050 (  0.981815,  0.999874)   0.999535
  3.6   0.922840   0.995050 (  0.981815,  0.999874)   0.999682
  3.7   0.926954   0.995050 (  0.981815,  0.999874)   0.999784
  3.8   0.930748   0.995050 (  0.981815,  0.999874)   0.999855
  3.9   0.934254   0.995050 (  0.981815,  0.999874)   0.999904
  4.0   0.937500   0.995050 (  0.981815,  0.999874)   0.999937

     i      average    bias      rms_error     stddev  ave_analyt_std
---------------------------------------------------------------------
Totals:    -1.5992      0.0102      0.1917      0.1915     0.1838

 ==== State 5 alone with MBAR ===== 
The uncertainty estimates are tested in this section.
If the error is normally distributed, the actual error will be less than a
multiplier 'alpha' times the computed uncertainty 'sigma' a fraction of
time given by:
P(error < alpha sigma) = erf(alpha / sqrt(2))
For example, the true error should be less than 1.0 * sigma
(one standard deviation) a total of 68% of the time, and
less than 2.0 * sigma (two standard deviations) 95% of the time.
The observed fraction of the time that error < alpha sigma, and its
uncertainty, is given as 'obs' (with uncertainty 'obs err') below.
This should be compared to the column labeled 'normal'.
A weak lower bound that holds regardless of how the error is distributed is given
by Chebyshev's inequality, and is listed as 'cheby' below.
Uncertainty estimates are tested for both free energy differences and expectations.

Error vs. alpha
alpha      cheby        obs          obs err            normal
  0.1 -99.000000   0.079208 (  0.046183,  0.120099)   0.079656
  0.2 -24.000000   0.118812 (  0.078022,  0.166738)   0.158519
  0.3 -10.111111   0.207921 (  0.154941,  0.266376)   0.235823
  0.4  -5.250000   0.277228 (  0.217831,  0.340803)   0.310843
  0.5  -3.000000   0.331683 (  0.268577,  0.397946)   0.382925
  0.6  -1.777778   0.410891 (  0.344122,  0.479332)   0.451494
  0.7  -1.040816   0.495050 (  0.426391,  0.563801)   0.516073
  0.8  -0.562500   0.534653 (  0.465785,  0.602871)   0.576289
  0.9  -0.234568   0.608911 (  0.540836,  0.674943)   0.631880
  1.0  -0.000000   0.678218 (  0.612367,  0.740726)   0.682689
  1.1   0.173554   0.707921 (  0.643507,  0.768435)   0.728668
  1.2   0.305556   0.752475 (  0.690837,  0.809379)   0.769861
  1.3   0.408284   0.801980 (  0.744442,  0.853858)   0.806399
  1.4   0.489796   0.841584 (  0.788284,  0.888484)   0.838487
  1.5   0.555556   0.856436 (  0.804997,  0.901197)   0.866386
  1.6   0.609375   0.876238 (  0.827563,  0.917867)   0.890401
  1.7   0.653979   0.891089 (  0.844735,  0.930123)   0.910869
  1.8   0.691358   0.905941 (  0.862162,  0.942125)   0.928139
  1.9   0.722992   0.915842 (  0.873949,  0.949958)   0.942567
  2.0   0.750000   0.940594 (  0.904191,  0.968774)   0.954500
  2.1   0.773243   0.950495 (  0.916705,  0.975888)   0.964271
  2.2   0.793388   0.960396 (  0.929565,  0.982663)   0.972193
  2.3   0.810964   0.960396 (  0.929565,  0.982663)   0.978552
  2.4   0.826389   0.980198 (  0.957004,  0.994552)   0.983605
  2.5   0.840000   0.990099 (  0.972594,  0.998793)   0.987581
  2.6   0.852071   0.995050 (  0.981815,  0.999874)   0.990678
  2.7   0.862826   0.995050 (  0.981815,  0.999874)   0.993066
  2.8   0.872449   0.995050 (  0.981815,  0.999874)   0.994890
  2.9   0.881094   0.995050 (  0.981815,  0.999874)   0.996268
  3.0   0.888889   0.995050 (  0.981815,  0.999874)   0.997300
  3.1   0.895942   0.995050 (  0.981815,  0.999874)   0.998065
  3.2   0.902344   0.995050 (  0.981815,  0.999874)   0.998626
  3.3   0.908173   0.995050 (  0.981815,  0.999874)   0.999033
  3.4   0.913495   0.995050 (  0.981815,  0.999874)   0.999326
  3.5   0.918367   0.995050 (  0.981815,  0.999874)   0.999535
  3.6   0.922840   0.995050 (  0.981815,  0.999874)   0.999682
  3.7   0.926954   0.995050 (  0.981815,  0.999874)   0.999784
  3.8   0.930748   0.995050 (  0.981815,  0.999874)   0.999855
  3.9   0.934254   0.995050 (  0.981815,  0.999874)   0.999904
  4.0   0.937500   0.995050 (  0.981815,  0.999874)   0.999937

     i      average    bias      rms_error     stddev  ave_analyt_std
---------------------------------------------------------------------
Totals:    -1.5971      0.0123      0.1935      0.1931     0.1881
