thames {thames}

THAMES estimator of the (reciprocal) log marginal likelihood

Description

This function computes the THAMES estimate of the reciprocal log marginal likelihood using posterior samples and unnormalized log posterior values.

Usage

thames(
  lps = NULL,
  params,
  n_samples = NULL,
  d = NULL,
  radius = NULL,
  p = 0.025,
  q = 1 - p,
  lp_func = NULL,
  bound = NULL,
  n_simuls = 1e+05
)

Arguments

lps

vector of unnormalized log posterior values of length n_samples (sum of the log prior and the log likelihood)

params

matrix of parameter posterior samples of dimension n_samples * d

n_samples

integer, number of posterior samples

d

integer, dimension of parameter space

radius

positive number, radius to use for defining the ellipsoid A

p

percentile, used for lower bound of confidence interval

q

percentile, used for upper bound of confidence interval

lp_func

function to compute unnormalized log posterior values

bound

function calculating membership of a point in the posterior support

n_simuls

integer, number of Monte Carlo simulations to use in the bounded parameter correction calculation.

Value

Returns a named list with the following elements:

References

Metodiev M, Perrot-Dockès M, Ouadah S, Irons N. J., Raftery A. E. (2023) Easily Computed Marginal Likelihoods from Posterior Simulation Using the THAMES Estimator. arXiv preprint.

Examples

mu_star = 1
n <- 50
Y = rnorm(n, mu_star, 1)
sig2 <- 1
sig2_n <- 1/(n+1/sig2)
mn <- sum(Y)/(n + 1/sig2)
params <- rnorm(20, mean=mn,  (sig2_n))
lps <-  sapply(params, function(i){
sum(dnorm(Y,i,1,log = TRUE)) + dnorm(i,0,sig2, log = TRUE)})
thames(lps, params)