Package 'diagis'

Title: Diagnostic Plot and Multivariate Summary Statistics of Weighted Samples from Importance Sampling
Description: Fast functions for effective sample size, weighted multivariate mean, variance, and quantile computation, and weight diagnostic plot for generic importance sampling type or other probability weighted samples.
Authors: Jouni Helske [aut, cre]
Maintainer: Jouni Helske <[email protected]>
License: GPL (>= 2)
Version: 0.2.3
Built: 2024-11-06 03:57:36 UTC
Source: https://github.com/helske/diagis

Help Index

Auxiliary functions and diagnostic plots for importance sampling

Description

This package contains functions computing weighted (running) summaries and diagonostic plots for importance sampling problems.

Examples

# simple importance sampling example
# true distribution is a standard normal:
p <- function(x) dnorm(x)
# proposal distribution is normal with sd s
q <- function(x, s) dnorm(x, 0, s)

# IS weights have finite variance only if s^2 > 1/2
# variance is s/(2-1/s^2)^(3/2)

#optimal case
set.seed(42)
s_opt <- sqrt(2)
x_opt <- rnorm(1000, sd = s_opt)
w_opt <- p(x_opt) / q(x_opt, s_opt) 
weighted_mean(x_opt, w_opt)
weighted_var(x_opt, w_opt)
s_inf <- 0.25
x_inf <- rnorm(1000, sd = s_inf)
w_inf <- p(x_inf) / q(x_inf, s_inf)
weighted_mean(x_inf, w_inf) #!!
weighted_var(x_inf, w_inf) #!!
# diagnostic plots
weight_plot(w_inf)
weight_plot(w_opt)

Effective sample size

Description

Computes the effective sample size (ESS) of importance sampling estimator.

Usage

ess(w, f, x)

Arguments

w

A numeric vector of non-negative weights.
f

A function used in computing f-specific ESS.
x

A numeric vector of samples used to generate w. Used for computing f(x).

Value

An effective sample size estimate.

Running effective sample size

Description

Computes and returns the running estimate of effective sample size (ESS) of importance sampling estimator.

Usage

running_ess(w, f, x)

Arguments

w

A numeric vector of non-negative weights.
f

A function used in computing f-specific ESS.
x

A numeric vector of samples used to generate w. Used for computing f(x).

Value

An effective sample size estimate.

Running mean

Description

Computes running mean of a vector or matrix, returning the values from each step.

Usage

running_mean(x, na.rm)

Arguments

x

A numeric vector, matrix, three dimensional array, or an mcmc object from the coda package. For matrix, the mean is computed for each column, and for array the sweep is done over the third dimension.
na.rm

If TRUE, NA values in x are omitted from the computation. Default is FALSE.

Value

A vector containing the recursive mean estimates.

Running variance of a vector

Description

Computes running variance of a vector, returning the values from each step.

Usage

running_var(x, method = c("moment", "unbiased"), na.rm = FALSE)

Arguments

x

A numeric vector or object that can be coerced to such.
method

Estimator type, either "moment" (default) or "unbiased", which is unbiased only in case of frequency weights.
na.rm

If TRUE, NA values in x are omitted from the computation. Default is FALSE.

Value

A vector containing the recursive variance estimates.

Running weighted mean

Description

Computes running weighted mean of a vector or matrix, returning the values from each step.

Usage

running_weighted_mean(x, w, na.rm)

Arguments

x

A numeric vector, matrix, three dimensional array, or an mcmc object from the coda package. For matrix, the mean is computed for each column, and for array the sweep is done over the third dimension.
w

A numeric vector of non-negative weights. Will be automatically normalised to sum to one.
na.rm

If TRUE, NA values in x (and corresponding weights in w) are omitted from the computation. Default is FALSE. Only used in vector methods.

Value

A vector containing the recursive weighted mean estimates.

Running weighted variance of a vector

Description

Computes running weighted variance of a vector, returning the values from each step.

Usage

running_weighted_var(x, w, method = c("moment", "unbiased"), na.rm = FALSE)

Arguments

x

A numeric vector or object that can be coerced to such.
w

A numeric vector of non-negative weights. Will be automatically normalised to sum to one.
method

Estimator type, either "moment" (default) or "unbiased", which is unbiased only in case of frequency weights.
na.rm

If TRUE, NA values in x (and corresponding weights in w) are omitted from the computation. Default is FALSE.

Value

A vector containing the recursive weighted variance estimates.

Diagnostic plot of importance sampling weights

Description

Function weight_plot plots four figures given the weight vector w: Plot of largest weights, sorted graph of all weights, running variance estimate of weights, and running effective sample size estimate of weights.

Usage

weight_plot(w)

Arguments

w

Vector of weights.

Examples

#' importance sampling from too narrow distribution
#' weights have infinite variance
set.seed(1)
x_inf <- rnorm(1000, sd = 0.1)
w_inf <- dnorm(x_inf) / dnorm(x_inf, 0, 0.1)
weight_plot(w_inf)
x_opt <- rnorm(1000, sd = sqrt(2))
w_opt <- dnorm(x_opt) / dnorm(x_opt, 0, sqrt(2))
weight_plot(w_opt)

Weighted mean

Description

Computes a weighted mean of a vector, matrix, or a three dimensional array.

Usage

weighted_mean(x, w, na.rm)

Arguments

x

A numeric vector, matrix, three dimensional array, or an mcmc object from the coda package. For matrix, the mean is computed for each column, and for array the sweep is done over the third dimension.
w

A numeric vector of non-negative weights. Will be automatically normalised to sum to one.
na.rm

If TRUE, NA values in x (and corresponding weights in w) are omitted from the computation. Default is FALSE. Only used in vector methods.

Value

A weighted mean.

Weighted quantiles

Description

Computes a weighted quantiles of a vector or matrix. Based on the formula in Wikipedia (see the vignette) which is one of many ways to compute weighted quantiles.

Usage

weighted_quantile(x, w, probs = probs, na.rm)

Arguments

x

A numeric vector or matrix. For matrix, the quantiles are computed for each column.
w

A numeric vector of non-negative weights. Will be automatically normalised to sum to one.
probs

A numeric vector of probabilities with values between 0 and 1.
na.rm

If TRUE, NA and NaN values in x (and corresponding weights in w) are omitted from the computation. Default is FALSE. Additional missing values in w are not allowed.

Value

A weighted variance.

Note

Compared to some other R functions, here the weights are regarded as probability weights, not frequency weights.

Weighted standard error

Description

Computes a weighted standard error of a vector or matrix.

Usage

weighted_se(x, w, na.rm)

Arguments

x

A numeric vector or matrix. For matrix, standard errors are computed for each column
w

A numeric vector of non-negative weights. Will be automatically normalised to sum to one.
na.rm

If TRUE, NA values in x (and corresponding weights in w) are omitted from the computation. Default is FALSE.

Value

A weighted variance.

Note

Compared to some other R functions, here the weights are regarded as probability weights, not frequency weights.

Weighted covariance

Description

Computes a weighted variance/covariance of a vector, matrix or a three dimensional array.

Usage

weighted_var(x, w, method, na.rm)

Arguments

x

A numeric vector, matrix or three dimensional array. For matrix, covariances are computed between columns. For array, marginal covariances are computed for each column, i.e. for $m x n x k$ array function returns $m x m x n$ array.
w

A numeric vector of non-negative weights. Will be automatically normalised to sum to one.
method

Estimator type, either "moment" (default) or "unbiased", which is unbiased only in case of frequency weights.
na.rm

If TRUE, NA values in x (and corresponding weights in w) are omitted from the computation. Default is FALSE.

Value

A weighted variance.

Note

Compared to some other R functions, here the weights are regarded as probability weights, not frequency weights.