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Change m13.7 to NUTS(0.65)#45

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goedman merged 1 commit intoStatisticalRethinkingJulia:masterfrom
rikhuijzer:patch-2
Dec 31, 2020
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Change m13.7 to NUTS(0.65)#45
goedman merged 1 commit intoStatisticalRethinkingJulia:masterfrom
rikhuijzer:patch-2

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@rikhuijzer rikhuijzer commented Dec 31, 2020

In response to #42, for m13.7, the NUTS sampler works better as NUTS(0.65) because the effective sample size is higher.

Output on NUTS(0.95)

Summary Statistics
  parameters      mean       std   naive_se      mcse         ess      rhat
      Symbol   Float64   Float64    Float64   Float64     Float64   Float64

           a    1.3251    1.2191     0.0172    0.0677    285.9096    1.0027
          bp    0.2473    0.1182     0.0017    0.0042    911.0640    1.0017
       etasq    0.3713    0.8135     0.0115    0.0559    225.9016    1.0047
        g[1]   -0.3033    0.5156     0.0073    0.0421    139.5576    1.0031
        g[2]   -0.1511    0.5027     0.0071    0.0420    138.6363    1.0026
        g[3]   -0.1963    0.4883     0.0069    0.0412    138.1092    1.0021
        g[4]    0.2663    0.4516     0.0064    0.0380    142.4096    1.0022
        g[5]   -0.0051    0.4427     0.0063    0.0375    141.7021    1.0017
        g[6]   -0.4832    0.4510     0.0064    0.0375    147.5890    1.0015
        g[7]    0.0622    0.4411     0.0062    0.0364    151.7326    1.0016
        g[8]   -0.2909    0.4419     0.0062    0.0367    149.9415    1.0012
        g[9]    0.2042    0.4277     0.0060    0.0348    155.9834    1.0010
       g[10]   -0.1543    0.5292     0.0075    0.0296    325.4825    0.9998
       rhosq    1.4499    6.9762     0.0987    0.1572   2026.9409    1.0017

and, output on NUTS(0.65)

Summary Statistics
  parameters      mean       std   naive_se      mcse         ess      rhat
      Symbol   Float64   Float64    Float64   Float64     Float64   Float64

           a    1.2739    1.1451     0.0162    0.0406    809.0320    1.0000
          bp    0.2468    0.1148     0.0016    0.0037    962.4411    1.0000
       etasq    0.3212    0.3937     0.0056    0.0117   1280.4670    1.0016
        g[1]   -0.2444    0.4067     0.0058    0.0150    661.6162    1.0003
        g[2]   -0.0967    0.3932     0.0056    0.0157    594.1228    1.0000
        g[3]   -0.1440    0.3761     0.0053    0.0150    593.7547    0.9998
        g[4]    0.3212    0.3329     0.0047    0.0136    607.7597    0.9998
        g[5]    0.0532    0.3285     0.0046    0.0131    609.1391    1.0002
        g[6]   -0.4346    0.3349     0.0047    0.0120    672.7538    0.9999
        g[7]    0.1179    0.3239     0.0046    0.0131    657.4213    0.9998
        g[8]   -0.2378    0.3227     0.0046    0.0125    663.1502    0.9998
        g[9]    0.2554    0.3063     0.0043    0.0122    652.9160    0.9998
       g[10]   -0.0988    0.4330     0.0061    0.0134   1040.0763    0.9999
       rhosq    2.2386   21.7380     0.3074    0.7956    726.0831    1.0011

The meaning of ess (Effective Sample Size) is described by Kai Xu in Probabilistic Programming in Julia (https://www.mlmi.eng.cam.ac.uk/files/kai_xu_8224821_assignsubmission_file_xu_kai_dissertation.pdf) on page 30. There, he states that a larger value means a higher sampling efficiency. With NUTS(0.65), the mcse (Monte Carlo Standard Error) also decreases, which means that NUTS(0.65) has a bettter sampling performance.

@goedman goedman merged commit 93a7567 into StatisticalRethinkingJulia:master Dec 31, 2020
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@rikhuijzer @goedman