tis: Truncated importance sampling (TIS)

Description

Implementation of truncated (self-normalized) importance sampling (TIS), truncated at S^(1/2) as recommended by Ionides (2008).

Usage

tis(log_ratios, ...)
# S3 method for array
tis(log_ratios, ..., r_eff = NULL, cores = getOption("mc.cores", 1))
# S3 method for matrix
tis(log_ratios, ..., r_eff = NULL, cores = getOption("mc.cores", 1))
# S3 method for default
tis(log_ratios, ..., r_eff = NULL)

Arguments

log_ratios

An array, matrix, or vector of importance ratios on the log scale (for Importance sampling LOO, these are negative log-likelihood values). See the Methods (by class) section below for a detailed description of how to specify the inputs for each method.

...

Arguments passed on to the various methods.

r_eff

Vector of relative effective sample size estimates containing one element per observation. The values provided should be the relative effective sample sizes of 1/exp(log_ratios) (i.e., 1/ratios). This is related to the relative efficiency of estimating the normalizing term in self-normalizing importance sampling. See the relative_eff() helper function for computing r_eff. If using psis with draws of the log_ratios not obtained from MCMC then the warning message thrown when not specifying r_eff can be disabled by setting r_eff to NA.

cores

The number of cores to use for parallelization. This defaults to the option mc.cores which can be set for an entire R session by options(mc.cores = NUMBER). The old option loo.cores is now deprecated but will be given precedence over mc.cores until loo.cores is removed in a future release. As of version 2.0.0 the default is now 1 core if mc.cores is not set, but we recommend using as many (or close to as many) cores as possible.

Note for Windows 10 users: it is strongly recommended to avoid using the .Rprofile file to set mc.cores (using the cores argument or setting mc.cores interactively or in a script is fine).

Value

The tis() methods return an object of class "tis", which is a named list with the following components:

log_weights

Vector or matrix of smoothed (and truncated) but unnormalized log weights. To get normalized weights use the weights() method provided for objects of class tis.

diagnostics

A named list containing one vector:

pareto_k: Not used in tis, all set to 0.
n_eff: Effective sample size estimates.

Objects of class "tis" also have the following attributes:

norm_const_log: Vector of precomputed values of colLogSumExps(log_weights) that are used internally by the weights()method to normalize the log weights.
r_eff: If specified, the user's r_eff argument.
tail_len: Not used for tis.
dims: Integer vector of length 2 containing S (posterior sample size) and N (number of observations).
method: Method used for importance sampling, here tis.

Methods (by class)

array: An $I$ by $C$ by $N$ array, where $I$ is the number of MCMC iterations per chain, $C$ is the number of chains, and $N$ is the number of data points.
matrix: An $S$ by $N$ matrix, where $S$ is the size of the posterior sample (with all chains merged) and $N$ is the number of data points.
default: A vector of length $S$ (posterior sample size).

References

Ionides, Edward L. (2008). Truncated importance sampling. Journal of Computational and Graphical Statistics 17(2): 295--311.

Examples

Run this code

# NOT RUN {
log_ratios <- -1 * example_loglik_array()
r_eff <- relative_eff(exp(-log_ratios))
tis_result <- tis(log_ratios, r_eff = r_eff)
str(tis_result)

# extract smoothed weights
lw <- weights(tis_result) # default args are log=TRUE, normalize=TRUE
ulw <- weights(tis_result, normalize=FALSE) # unnormalized log-weights

w <- weights(tis_result, log=FALSE) # normalized weights (not log-weights)
uw <- weights(tis_result, log=FALSE, normalize = FALSE) # unnormalized weights

# }

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