MCMC sampling software

Exercise BADT

Author

Zheng Zhou

MCMC sampling software

  1. Gibbs sampling and BUGS

  • Strength: Simple coding and similar to basic Metropolis algorithm

  • Weakness: Really random walks, poor at dealing with complex problems

  1. Hamilton MC and stan

  • Strength: Uses gradient information to explore high-dimensional, correlated parameter space more efficiently

  • Weakness: Requires more coding efforts

Stan ecosystem

  1. sampler: rstan, cmdstanr, CmdStanPy, PyMC

  2. high-level utility package: rstanarm, brms, PyStan, bambi and more

Getting start with Stan

  1. Installation

If you Use R: install cmdstanr

If you Use python: install cmdstanPy

  1. install appropriate C++ toolchain based on your IDE: for R and for python

  2. install compiler for your IDE

  3. install utility package if desire

  1. Once done, run an example model to check the compiler

The beta-binomial example in stan

library(cmdstanr)
This is cmdstanr version 0.9.0
- CmdStanR documentation and vignettes: mc-stan.org/cmdstanr
- CmdStan path: C:/Users/ekol-usa/.cmdstan/cmdstan-2.38.0
- CmdStan version: 2.38.0
file <- file.path(cmdstan_path(), "examples", "bernoulli", "bernoulli.stan")
mod <- cmdstan_model(file)
# names correspond to the data block in the Stan program
data_list <- list(N = 10, y = c(0,1,0,0,0,0,0,0,0,1))

# call out the stan script
mod$print()
data {
  int<lower=0> N;
  array[N] int<lower=0, upper=1> y;
}
parameters {
  real<lower=0, upper=1> theta;
}
model {
  theta ~ beta(1, 1); // uniform prior on interval 0,1
  y ~ bernoulli(theta);
}

Sampling

fit <- mod$sample(
  data = data_list,
  seed = 123,
  chains = 4
)
Running MCMC with 4 sequential chains...

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  1. Extract model diagnostics
# install.package(c("bayesplot","tidyverse"))
library(bayesplot)
This is bayesplot version 1.15.0
- Online documentation and vignettes at mc-stan.org/bayesplot
- bayesplot theme set to bayesplot::theme_default()
   * Does _not_ affect other ggplot2 plots
   * See ?bayesplot_theme_set for details on theme setting
library(tidyverse)
── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr     1.1.4     ✔ readr     2.1.6
✔ forcats   1.0.1     ✔ stringr   1.6.0
✔ ggplot2   4.0.1     ✔ tibble    3.3.0
✔ lubridate 1.9.4     ✔ tidyr     1.3.1
✔ purrr     1.2.0     
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

Check rhat and effective sample size:

# all parameters
fit$summary()
# A tibble: 2 × 10
  variable   mean median    sd   mad      q5    q95  rhat ess_bulk ess_tail
  <chr>     <dbl>  <dbl> <dbl> <dbl>   <dbl>  <dbl> <dbl>    <dbl>    <dbl>
1 lp__     -7.27  -6.99  0.750 0.323 -8.74   -6.75   1.00    1931.    2287.
2 theta     0.252  0.239 0.120 0.122  0.0806  0.477  1.00    1368.    1664.

Rhat should be as close to 1 as possible

ESS: ideally number of sampling steps from all chains

Traceplot:

# all parameters
mcmc_trace(fit$draws())

# specific parameter
mcmc_trace(fit$draws("theta"))

Autocorrelation:

# all parameters
mcmc_acf(fit$draws())

When something goes wrong, check this