beta = 1.0000000 S = 0.0 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 h = 0.0000000 0.0000000 0.0000000 Probabilities and CDF for IID fair: [ 1 1 1 ] 0.1250000 0.1250000 [ 1 1 -1 ] 0.1250000 0.2500000 [ 1 -1 1 ] 0.1250000 0.3750000 [ 1 -1 -1 ] 0.1250000 0.5000000 [ -1 1 1 ] 0.1250000 0.6250000 [ -1 1 -1 ] 0.1250000 0.7500000 [ -1 -1 1 ] 0.1250000 0.8750000 [ -1 -1 -1 ] 0.1250000 1.0000000 sum P = 1.0000000 Shannon-Gibbs entropy = 3.0000000 volume = 8.0000000 Probabilities and CDF for IID p = 0.900000: [ 1 1 1 ] 0.7290000 0.7290000 [ 1 1 -1 ] 0.0810000 0.8100000 [ 1 -1 1 ] 0.0810000 0.8910000 [ 1 -1 -1 ] 0.0090000 0.9000000 [ -1 1 1 ] 0.0810000 0.9810000 [ -1 1 -1 ] 0.0090000 0.9900000 [ -1 -1 1 ] 0.0090000 0.9990000 [ -1 -1 -1 ] 0.0010000 1.0000000 sum P = 1.0000000 Shannon-Gibbs entropy = 1.4069868 volume = 2.6518272 Probabilities and CDF for indep. w/ varying p: [ 1 1 1 ] 0.3360000 0.3360000 [ 1 1 -1 ] 0.0840000 0.4200000 [ 1 -1 1 ] 0.1440000 0.5640000 [ 1 -1 -1 ] 0.0360000 0.6000000 [ -1 1 1 ] 0.2240000 0.8240000 [ -1 1 -1 ] 0.0560000 0.8800000 [ -1 -1 1 ] 0.0960000 0.9760000 [ -1 -1 -1 ] 0.0240000 1.0000000 sum P = 1.0000000 Shannon-Gibbs entropy = 2.5741696 volume = 5.9552810 Probabilities and CDF for Ising model: [ 1 1 1 ] 0.3879017 0.3879017 [ 1 1 -1 ] 0.0524968 0.4403985 [ 1 -1 1 ] 0.0071047 0.4475032 [ 1 -1 -1 ] 0.0524968 0.5000000 [ -1 1 1 ] 0.0524968 0.5524968 [ -1 1 -1 ] 0.0071047 0.5596015 [ -1 -1 1 ] 0.0524968 0.6120983 [ -1 -1 -1 ] 0.3879017 1.0000000 sum P = 1.0000000 Shannon-Gibbs entropy = 2.0541307 volume = 4.1529332 ---------------------------------------------------------------- P's and Q's: 10000 samples, indep. sampling, IID fair: [ 1 1 1 ] 0.1250000 0.1334000 diff = -0.0084000 [ 1 1 -1 ] 0.1250000 0.1235000 diff = 0.0015000 [ 1 -1 1 ] 0.1250000 0.1246000 diff = 0.0004000 [ 1 -1 -1 ] 0.1250000 0.1245000 diff = 0.0005000 [ -1 1 1 ] 0.1250000 0.1194000 diff = 0.0056000 [ -1 1 -1 ] 0.1250000 0.1267000 diff = -0.0017000 [ -1 -1 1 ] 0.1250000 0.1237000 diff = 0.0013000 [ -1 -1 -1 ] 0.1250000 0.1242000 diff = 0.0008000 P's and Q's: 10000 samples, indep. sampling, IID p = 0.900000: [ 1 1 1 ] 0.7290000 0.7306000 diff = -0.0016000 [ 1 1 -1 ] 0.0810000 0.0813000 diff = -0.0003000 [ 1 -1 1 ] 0.0810000 0.0798000 diff = 0.0012000 [ 1 -1 -1 ] 0.0090000 0.0081000 diff = 0.0009000 [ -1 1 1 ] 0.0810000 0.0811000 diff = -0.0001000 [ -1 1 -1 ] 0.0090000 0.0080000 diff = 0.0010000 [ -1 -1 1 ] 0.0090000 0.0097000 diff = -0.0007000 [ -1 -1 -1 ] 0.0010000 0.0014000 diff = -0.0004000 P's and Q's: 10000 samples, indep. sampling, indep. w/ varying p: [ 1 1 1 ] 0.3360000 0.3442000 diff = -0.0082000 [ 1 1 -1 ] 0.0840000 0.0847000 diff = -0.0007000 [ 1 -1 1 ] 0.1440000 0.1407000 diff = 0.0033000 [ 1 -1 -1 ] 0.0360000 0.0355000 diff = 0.0005000 [ -1 1 1 ] 0.2240000 0.2249000 diff = -0.0009000 [ -1 1 -1 ] 0.0560000 0.0567000 diff = -0.0007000 [ -1 -1 1 ] 0.0960000 0.0903000 diff = 0.0057000 [ -1 -1 -1 ] 0.0240000 0.0230000 diff = 0.0010000 ---------------------------------------------------------------- P's and Q's: 10000 samples, CDF sampling, IID fair: [ 1 1 1 ] 0.1250000 0.1309000 diff = -0.0059000 [ 1 1 -1 ] 0.1250000 0.1204000 diff = 0.0046000 [ 1 -1 1 ] 0.1250000 0.1255000 diff = -0.0005000 [ 1 -1 -1 ] 0.1250000 0.1144000 diff = 0.0106000 [ -1 1 1 ] 0.1250000 0.1292000 diff = -0.0042000 [ -1 1 -1 ] 0.1250000 0.1302000 diff = -0.0052000 [ -1 -1 1 ] 0.1250000 0.1241000 diff = 0.0009000 [ -1 -1 -1 ] 0.1250000 0.1253000 diff = -0.0003000 P's and Q's: 10000 samples, CDF sampling, IID p = 0.900000: [ 1 1 1 ] 0.7290000 0.7262000 diff = 0.0028000 [ 1 1 -1 ] 0.0810000 0.0813000 diff = -0.0003000 [ 1 -1 1 ] 0.0810000 0.0827000 diff = -0.0017000 [ 1 -1 -1 ] 0.0090000 0.0079000 diff = 0.0011000 [ -1 1 1 ] 0.0810000 0.0814000 diff = -0.0004000 [ -1 1 -1 ] 0.0090000 0.0092000 diff = -0.0002000 [ -1 -1 1 ] 0.0090000 0.0105000 diff = -0.0015000 [ -1 -1 -1 ] 0.0010000 0.0008000 diff = 0.0002000 P's and Q's: 10000 samples, CDF sampling, indep. w/ varying p: [ 1 1 1 ] 0.3360000 0.3404000 diff = -0.0044000 [ 1 1 -1 ] 0.0840000 0.0807000 diff = 0.0033000 [ 1 -1 1 ] 0.1440000 0.1441000 diff = -0.0001000 [ 1 -1 -1 ] 0.0360000 0.0368000 diff = -0.0008000 [ -1 1 1 ] 0.2240000 0.2271000 diff = -0.0031000 [ -1 1 -1 ] 0.0560000 0.0539000 diff = 0.0021000 [ -1 -1 1 ] 0.0960000 0.0936000 diff = 0.0024000 [ -1 -1 -1 ] 0.0240000 0.0234000 diff = 0.0006000 P's and Q's: 10000 samples, CDF sampling, Ising model: [ 1 1 1 ] 0.3879017 0.3943000 diff = -0.0063983 [ 1 1 -1 ] 0.0524968 0.0537000 diff = -0.0012032 [ 1 -1 1 ] 0.0071047 0.0064000 diff = 0.0007047 [ 1 -1 -1 ] 0.0524968 0.0492000 diff = 0.0032968 [ -1 1 1 ] 0.0524968 0.0517000 diff = 0.0007968 [ -1 1 -1 ] 0.0071047 0.0078000 diff = -0.0006953 [ -1 -1 1 ] 0.0524968 0.0499000 diff = 0.0025968 [ -1 -1 -1 ] 0.3879017 0.3870000 diff = 0.0009017 ---------------------------------------------------------------- P's and Q's: 10000 samples, Metro sampling, IID fair: [ 1 1 1 ] 0.1250000 0.1298000 diff = -0.0048000 [ 1 1 -1 ] 0.1250000 0.1202000 diff = 0.0048000 [ 1 -1 1 ] 0.1250000 0.1291000 diff = -0.0041000 [ 1 -1 -1 ] 0.1250000 0.1244000 diff = 0.0006000 [ -1 1 1 ] 0.1250000 0.1270000 diff = -0.0020000 [ -1 1 -1 ] 0.1250000 0.1243000 diff = 0.0007000 [ -1 -1 1 ] 0.1250000 0.1215000 diff = 0.0035000 [ -1 -1 -1 ] 0.1250000 0.1237000 diff = 0.0013000 P's and Q's: 10000 samples, Metro sampling, IID p = 0.900000: [ 1 1 1 ] 0.7290000 0.7243000 diff = 0.0047000 [ 1 1 -1 ] 0.0810000 0.0871000 diff = -0.0061000 [ 1 -1 1 ] 0.0810000 0.0830000 diff = -0.0020000 [ 1 -1 -1 ] 0.0090000 0.0084000 diff = 0.0006000 [ -1 1 1 ] 0.0810000 0.0781000 diff = 0.0029000 [ -1 1 -1 ] 0.0090000 0.0095000 diff = -0.0005000 [ -1 -1 1 ] 0.0090000 0.0083000 diff = 0.0007000 [ -1 -1 -1 ] 0.0010000 0.0013000 diff = -0.0003000 P's and Q's: 10000 samples, Metro sampling, indep. w/ varying p: [ 1 1 1 ] 0.3360000 0.3277000 diff = 0.0083000 [ 1 1 -1 ] 0.0840000 0.0836000 diff = 0.0004000 [ 1 -1 1 ] 0.1440000 0.1494000 diff = -0.0054000 [ 1 -1 -1 ] 0.0360000 0.0364000 diff = -0.0004000 [ -1 1 1 ] 0.2240000 0.2301000 diff = -0.0061000 [ -1 1 -1 ] 0.0560000 0.0551000 diff = 0.0009000 [ -1 -1 1 ] 0.0960000 0.0944000 diff = 0.0016000 [ -1 -1 -1 ] 0.0240000 0.0233000 diff = 0.0007000 P's and Q's: 10000 samples, Metro sampling, Ising model: [ 1 1 1 ] 0.3879017 0.3643000 diff = 0.0236017 [ 1 1 -1 ] 0.0524968 0.0531000 diff = -0.0006032 [ 1 -1 1 ] 0.0071047 0.0061000 diff = 0.0010047 [ 1 -1 -1 ] 0.0524968 0.0499000 diff = 0.0025968 [ -1 1 1 ] 0.0524968 0.0517000 diff = 0.0007968 [ -1 1 -1 ] 0.0071047 0.0078000 diff = -0.0006953 [ -1 -1 1 ] 0.0524968 0.0516000 diff = 0.0008968 [ -1 -1 -1 ] 0.3879017 0.4155000 diff = -0.0275983 ----------------------------------------------------------------