This C++ version of BAT is still being maintained, but addition of new features is unlikely. Check out our new incarnation, BAT.jl, the Bayesian analysis toolkit in Julia. In addition to Metropolis-Hastings sampling, BAT.jl supports Hamiltonian Monte Carlo (HMC) with automatic differentiation, automatic prior-based parameter space transformations, and much more. See the BAT.jl documentation.
Results of performance testing for BAT version 0.4.3
Back to | overview for 0.4.3 | all versions |
Test "1d_cauchy"
| Results | |
|---|---|
| Status | good |
| CPU time | 54.99 s |
| Real time | 54.99 s |
| Plots | 1d_cauchy.ps |
| Log | 1d_cauchy.log |
| Settings | |
|---|---|
| N chains | 10 |
| N lag | 10 |
| Convergence | true |
| N iterations (pre-run) | 1000 |
| N iterations (run) | 10000000 |
 |  |  |
| Auto-correlation for the parameter. | Distribution from MCMC and analytic function. | Distribution from MCMC and analytic function in log-scale. |
 |  |  |
| Difference between the distribution from MCMC and the analytic function. The one, two and three sigma uncertainty bands are colored green, yellow and red, respectively. | Pull between the distribution from MCMC and the analytic function. The Gaussian has a mean value of 0 and a standard deviation of 1 (not fitted). | Summary of subtest values. |
| Subtest | Status | Target | Test | Uncertainty | Deviation [%] | Deviation [sigma] | Tol. (Good) | Tol. (Acceptable) | Tol. (Bad) |
|---|---|---|---|---|---|---|---|---|---|
| correlation par 0 | off | 0 | 0.06578 | 0.006563 | - | -10.02 | 0.3 | 0.5 | 0.7 |
| chi2 | good | 100 | 127.2 | 14.14 | 27.17 | -1.921 | 42.43 | 70.71 | 98.99 |
| KS | good | 1 | 0.6077 | 0.95 | -39.23 | 0.413 | 0.95 | 0.99 | 0.9999 |
| mean | good | 0 | -0.004364 | 0.003825 | - | 1.141 | 0.01147 | 0.01912 | 0.02677 |
| mode | good | -4.016e-09 | -0.5 | 0.3333 | 1.245e+10 | 1.5 | 1 | 1.667 | 2.333 |
| variance | good | 144.9 | 147.8 | 34.26 | 1.984 | -0.08391 | 102.8 | 171.3 | 239.9 |
| quantile10 | good | -12.03 | -12.03 | 0.3333 | -0.009025 | -0.003258 | 1 | 1.667 | 2.333 |
| quantile20 | good | -6.089 | -6.095 | 0.3333 | 0.0931 | 0.01701 | 1 | 1.667 | 2.333 |
| quantile30 | good | -3.358 | -3.364 | 0.3333 | 0.1802 | 0.01815 | 1 | 1.667 | 2.333 |
| quantile40 | good | -1.529 | -1.532 | 0.3333 | 0.229 | 0.0105 | 1 | 1.667 | 2.333 |
| quantile50 | good | 1.655e-15 | -0.005067 | 0.3333 | -3.062e+14 | 0.0152 | 1 | 1.667 | 2.333 |
| quantile60 | good | 1.529 | 1.524 | 0.3333 | -0.3034 | 0.01392 | 1 | 1.667 | 2.333 |
| quantile70 | good | 3.358 | 3.355 | 0.3333 | -0.06699 | 0.006748 | 1 | 1.667 | 2.333 |
| quantile80 | good | 6.089 | 6.082 | 0.3333 | -0.1154 | 0.02108 | 1 | 1.667 | 2.333 |
| quantile90 | good | 12.03 | 12.02 | 0.3333 | -0.07597 | 0.02742 | 1 | 1.667 | 2.333 |
| Subtest | Description |
|---|---|
| correlation par 0 | Calculate the auto-correlation among the points. |
| chi2 | Calculate χ2 and compare with prediction for dof=number of bins with an expectation >= 10. Tolerance good: |χ2-E[χ2]| < 3 · (2 dof)1/2, Tolerance acceptable: |χ2-E[χ2]| < 5 · (2 dof)1/2, Tolerance bad: |χ2-E[χ2]| < 7 · (2 dof)1/2. |
| KS | Calculate the Kolmogorov-Smirnov probability based on the ROOT implemention. Tolerance good: KS prob > 0.05, Tolerance acceptable: KS prob > 0.01 Tolerance bad: KS prob > 0.0001. |
| mean | Compare sample mean, <x>, with expectation value of function, E[x]. Tolerance good: |<x> -E[x]| < 3 · (V[x]/n)1/2,Tolerance acceptable: |<x> -E[x]| < 5 · (V[x]/n)1/2,Tolerance bad: |<x> -E[x]| < 7 · (V[x]/n)1/2. |
| mode | Compare mode of distribution with mode of the analytic function. Tolerance good: |x*-mode| < 3 · V[mode]1/2, Tolerance acceptable: |x*-mode| < 5 · V[mode]1/2 bin widths, Tolerance bad: |x*-mode| < 7 · V[mode]1/2. |
| variance | Compare sample variance s2 of distribution with variance of function. Tolerance good: 3 · V[s2]1/2, Tolerance acceptable: 5 · V[s2]1/2, Tolerance bad: 7 · V[s2]1/2. |
| quantile10 | Compare quantile of distribution from MCMC with the quantile of analytic function. Tolerance good: |q_{X}-E[q_{X}]|<3·V[q]1/2, Tolerance acceptable: |q_{X}-E[q_{X}]|<5·V[q]1/2, Tolerance bad: |q_{X}-E[q_{X}]|<7·V[q]1/2. |
| quantile20 | Compare quantile of distribution from MCMC with the quantile of analytic function. Tolerance good: |q_{X}-E[q_{X}]|<3·V[q]1/2, Tolerance acceptable: |q_{X}-E[q_{X}]|<5·V[q]1/2, Tolerance bad: |q_{X}-E[q_{X}]|<7·V[q]1/2. |
| quantile30 | Compare quantile of distribution from MCMC with the quantile of analytic function. Tolerance good: |q_{X}-E[q_{X}]|<3·V[q]1/2, Tolerance acceptable: |q_{X}-E[q_{X}]|<5·V[q]1/2, Tolerance bad: |q_{X}-E[q_{X}]|<7·V[q]1/2. |
| quantile40 | Compare quantile of distribution from MCMC with the quantile of analytic function. Tolerance good: |q_{X}-E[q_{X}]|<3·V[q]1/2, Tolerance acceptable: |q_{X}-E[q_{X}]|<5·V[q]1/2, Tolerance bad: |q_{X}-E[q_{X}]|<7·V[q]1/2. |
| quantile50 | Compare quantile of distribution from MCMC with the quantile of analytic function. Tolerance good: |q_{X}-E[q_{X}]|<3·V[q]1/2, Tolerance acceptable: |q_{X}-E[q_{X}]|<5·V[q]1/2, Tolerance bad: |q_{X}-E[q_{X}]|<7·V[q]1/2. |
| quantile60 | Compare quantile of distribution from MCMC with the quantile of analytic function. Tolerance good: |q_{X}-E[q_{X}]|<3·V[q]1/2, Tolerance acceptable: |q_{X}-E[q_{X}]|<5·V[q]1/2, Tolerance bad: |q_{X}-E[q_{X}]|<7·V[q]1/2. |
| quantile70 | Compare quantile of distribution from MCMC with the quantile of analytic function. Tolerance good: |q_{X}-E[q_{X}]|<3·V[q]1/2, Tolerance acceptable: |q_{X}-E[q_{X}]|<5·V[q]1/2, Tolerance bad: |q_{X}-E[q_{X}]|<7·V[q]1/2. |
| quantile80 | Compare quantile of distribution from MCMC with the quantile of analytic function. Tolerance good: |q_{X}-E[q_{X}]|<3·V[q]1/2, Tolerance acceptable: |q_{X}-E[q_{X}]|<5·V[q]1/2, Tolerance bad: |q_{X}-E[q_{X}]|<7·V[q]1/2. |
| quantile90 | Compare quantile of distribution from MCMC with the quantile of analytic function. Tolerance good: |q_{X}-E[q_{X}]|<3·V[q]1/2, Tolerance acceptable: |q_{X}-E[q_{X}]|<5·V[q]1/2, Tolerance bad: |q_{X}-E[q_{X}]|<7·V[q]1/2. |