bssm (version 2.0.2)

estimate_ess: Effective Sample Size for IS-type Estimators

Description

Computes the effective sample size (ESS) based on weighted posterior samples.

Usage

estimate_ess(x, w, method = "sokal")

Value

A single numeric value of effective sample size estimate.

Arguments

x

A numeric vector of samples.

w

A numeric vector of weights. If missing, set to 1 (i.e. no weighting is assumed).

method

Method for computing the ESS. Default is "sokal", other option are "geyer" (see also asymptotic_var).

Details

The asymptotic variance MCMCSE^2 is based on Corollary 1 of Vihola et al. (2020) which is used to compute an estimate for the ESS using the identity ESS(x) = var(x) / MCMCSE^2 where var(x) is the posterior variance of x assuming independent samples.

References

Vihola, M, Helske, J, Franks, J. (2020). Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo. Scand J Statist. 1-38. https://doi.org/10.1111/sjos.12492

Sokal A. (1997). Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms. In: DeWitt-Morette C, Cartier P, Folacci A (eds) Functional Integration. NATO ASI Series (Series B: Physics), vol 361. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0319-8_6

Gelman, A, Carlin J B, Stern H S, Dunson, D B, Vehtari A, Rubin D B. (2013). Bayesian Data Analysis, Third Edition. Chapman and Hall/CRC.

Examples

set.seed(1)
n <- 1e4 
x <- numeric(n)
phi <- 0.7
for(t in 2:n) x[t] <- phi * x[t-1] + rnorm(1)
w <- rexp(n, 0.5 * exp(0.001 * x^2))
# different methods:
estimate_ess(x, w, method = "sokal")
estimate_ess(x, w, method = "geyer")