beta = 1.0000000 S = 0.0 -1.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 h = 0.2000000 0.2000000 0.2000000 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 ] 0.0038136 0.0038136 [ 1 1 -1 ] 0.0420384 0.0458520 [ 1 -1 1 ] 0.3106238 0.3564758 [ 1 -1 -1 ] 0.0627139 0.4191897 [ -1 1 1 ] 0.0420384 0.4612281 [ -1 1 -1 ] 0.4633963 0.9246244 [ -1 -1 1 ] 0.0627139 0.9873383 [ -1 -1 -1 ] 0.0126617 1.0000000 sum P = 1.0000000 Shannon-Gibbs entropy = 2.0341270 volume = 4.0957481 ---------------------------------------------------------------- P's and Q's: 10000 samples, indep. sampling, IID fair: [ 1 1 1 ] 0.1250000 0.1219000 diff = 0.0031000 [ 1 1 -1 ] 0.1250000 0.1297000 diff = -0.0047000 [ 1 -1 1 ] 0.1250000 0.1255000 diff = -0.0005000 [ 1 -1 -1 ] 0.1250000 0.1236000 diff = 0.0014000 [ -1 1 1 ] 0.1250000 0.1233000 diff = 0.0017000 [ -1 1 -1 ] 0.1250000 0.1261000 diff = -0.0011000 [ -1 -1 1 ] 0.1250000 0.1249000 diff = 0.0001000 [ -1 -1 -1 ] 0.1250000 0.1250000 diff = 0.0000000 P's and Q's: 10000 samples, indep. sampling, IID p = 0.900000: [ 1 1 1 ] 0.7290000 0.7278000 diff = 0.0012000 [ 1 1 -1 ] 0.0810000 0.0810000 diff = -0.0000000 [ 1 -1 1 ] 0.0810000 0.0826000 diff = -0.0016000 [ 1 -1 -1 ] 0.0090000 0.0095000 diff = -0.0005000 [ -1 1 1 ] 0.0810000 0.0810000 diff = -0.0000000 [ -1 1 -1 ] 0.0090000 0.0091000 diff = -0.0001000 [ -1 -1 1 ] 0.0090000 0.0085000 diff = 0.0005000 [ -1 -1 -1 ] 0.0010000 0.0005000 diff = 0.0005000 P's and Q's: 10000 samples, indep. sampling, indep. w/ varying p: [ 1 1 1 ] 0.3360000 0.3402000 diff = -0.0042000 [ 1 1 -1 ] 0.0840000 0.0849000 diff = -0.0009000 [ 1 -1 1 ] 0.1440000 0.1450000 diff = -0.0010000 [ 1 -1 -1 ] 0.0360000 0.0368000 diff = -0.0008000 [ -1 1 1 ] 0.2240000 0.2229000 diff = 0.0011000 [ -1 1 -1 ] 0.0560000 0.0547000 diff = 0.0013000 [ -1 -1 1 ] 0.0960000 0.0909000 diff = 0.0051000 [ -1 -1 -1 ] 0.0240000 0.0246000 diff = -0.0006000 ---------------------------------------------------------------- P's and Q's: 10000 samples, CDF sampling, IID fair: [ 1 1 1 ] 0.1250000 0.1246000 diff = 0.0004000 [ 1 1 -1 ] 0.1250000 0.1285000 diff = -0.0035000 [ 1 -1 1 ] 0.1250000 0.1275000 diff = -0.0025000 [ 1 -1 -1 ] 0.1250000 0.1233000 diff = 0.0017000 [ -1 1 1 ] 0.1250000 0.1231000 diff = 0.0019000 [ -1 1 -1 ] 0.1250000 0.1244000 diff = 0.0006000 [ -1 -1 1 ] 0.1250000 0.1236000 diff = 0.0014000 [ -1 -1 -1 ] 0.1250000 0.1250000 diff = 0.0000000 P's and Q's: 10000 samples, CDF sampling, IID p = 0.900000: [ 1 1 1 ] 0.7290000 0.7195000 diff = 0.0095000 [ 1 1 -1 ] 0.0810000 0.0829000 diff = -0.0019000 [ 1 -1 1 ] 0.0810000 0.0828000 diff = -0.0018000 [ 1 -1 -1 ] 0.0090000 0.0096000 diff = -0.0006000 [ -1 1 1 ] 0.0810000 0.0860000 diff = -0.0050000 [ -1 1 -1 ] 0.0090000 0.0082000 diff = 0.0008000 [ -1 -1 1 ] 0.0090000 0.0102000 diff = -0.0012000 [ -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 0.3340000 diff = 0.0020000 [ 1 1 -1 ] 0.0840000 0.0826000 diff = 0.0014000 [ 1 -1 1 ] 0.1440000 0.1473000 diff = -0.0033000 [ 1 -1 -1 ] 0.0360000 0.0365000 diff = -0.0005000 [ -1 1 1 ] 0.2240000 0.2321000 diff = -0.0081000 [ -1 1 -1 ] 0.0560000 0.0526000 diff = 0.0034000 [ -1 -1 1 ] 0.0960000 0.0902000 diff = 0.0058000 [ -1 -1 -1 ] 0.0240000 0.0247000 diff = -0.0007000 P's and Q's: 10000 samples, CDF sampling, Ising model: [ 1 1 1 ] 0.0038136 0.0035000 diff = 0.0003136 [ 1 1 -1 ] 0.0420384 0.0418000 diff = 0.0002384 [ 1 -1 1 ] 0.3106238 0.3156000 diff = -0.0049762 [ 1 -1 -1 ] 0.0627139 0.0606000 diff = 0.0021139 [ -1 1 1 ] 0.0420384 0.0402000 diff = 0.0018384 [ -1 1 -1 ] 0.4633963 0.4653000 diff = -0.0019037 [ -1 -1 1 ] 0.0627139 0.0614000 diff = 0.0013139 [ -1 -1 -1 ] 0.0126617 0.0116000 diff = 0.0010617 ---------------------------------------------------------------- P's and Q's: 10000 samples, Metro sampling, Ising model: [ 1 1 1 ] 0.0038136 0.0045000 diff = -0.0006864 [ 1 1 -1 ] 0.0420384 0.0458000 diff = -0.0037616 [ 1 -1 1 ] 0.3106238 0.2843000 diff = 0.0263238 [ 1 -1 -1 ] 0.0627139 0.0592000 diff = 0.0035139 [ -1 1 1 ] 0.0420384 0.0423000 diff = -0.0002616 [ -1 1 -1 ] 0.4633963 0.4914000 diff = -0.0280037 [ -1 -1 1 ] 0.0627139 0.0605000 diff = 0.0022139 [ -1 -1 -1 ] 0.0126617 0.0120000 diff = 0.0006617 ----------------------------------------------------------------