| title | author | date | bibliography |
|---|---|---|---|
MCMC notes |
Ben Bolker |
6 October 2021 |
mcmc.bib |
This is a very broad outline/brain dump.
[@gilks_markov_1995; @van_ravenzwaaij_simple_2018; @bolker_ecological_2008]
- need to construct a Markov chain on the parameter space
- stationarity, ergodicity, irreducibility
-
detailed balance/reversibility:
$\pi_i P_{ij} = \pi_j P_{ji}$
- Metropolis-Hastings
- Gibbs (conditional conjugate sampling)
- slice
- 'generalized Gibbs' (x-within-Gibbs)
- hybrid/Hamiltonian MCMC (uses gradient info)
- reversible-jump MCMC (variable dimensionality)
- sequential MC (time series etc.)
- Metropolis-coupled MCMC (MC^3) (tempering) [@altekar_parallel_2004]
- BUGS/JAGS
- Stan (+
rethinking::ulam) - Nimble
- PyMC3
- TMB +
tmbstan - greta
- special-case front ends (
MCMCglmm,brms,rstanarm, ...)
(1) Which samplers are available? (2) Simplicity vs flexiblity (2) Procedural or graphical model definition?
- trace plots
- R-hat, improved R-hat, effective sample size, ... [@vehtari_rank-normalization_2019; @lambert_r_2020]
- simulation-based calibration [@talts_validating_2020]
- tuning/adaptation [@rosenthal_optimal_2011]
- shape of candidate distribution should match shape of posterior
- acceptance probability 0.1 to 0.6, approx 0.24 in high dim
- change samplers
- reparameterize
- make priors stronger
- run longer!
See @gelman_bayesian_2020
- @betancourt_markov_2020: long blog post with geometry, examples, etc.; semi-technical
- @kery_introduction_2010: what it sounds like. Various standard models implemented and explained in WinBUGS
- @kery_bayesian_2011: as previous, but focusing on models for ecologists; state-space models for population counts, capture-mark-recapture data, occupancy models, etc.
- @liang_advanced_2010: haven't read it but looks interesting??