MCMC-recover: Compare MCMC estimates to "true" parameter values

Description

Plots comparing MCMC estimates to "true" parameter values. Before fitting a model to real data it is useful to simulate data according to the model using known (fixed) parameter values and to check that these "true" parameter values are (approximately) recovered by fitting the model to the simulated data. See the Plot Descriptions section, below, for details on the available plots.

Usage

mcmc_recover_intervals(x, true, batch = rep(1, length(true)),
  facet_args = list(), ..., prob = 0.5, prob_outer = 0.9,
  point_est = c("median", "mean", "none"), size = 4, alpha = 1)
mcmc_recover_scatter(x, true, batch = rep(1, length(true)),
  facet_args = list(), ..., point_est = c("median", "mean"), size = 3,
  alpha = 1)
mcmc_recover_hist(x, true, facet_args = list(), ..., binwidth = NULL)

Arguments

A 3-D array, matrix, list of matrices, or data frame of MCMC draws. The MCMC-overview page provides details on how to specify each these allowed inputs.

true

A numeric vector of "true" values of the parameters in x. There should be one value in true for each parameter included in x and the order of the parameters in true should be the same as the order of the parameters in x.

batch

Optionally, a vector-like object (numeric, character, integer, factor) used to split the parameters into batches. If batch is specified, it must have the same length as true and be in the same order as true. Parameters in the same batch will be grouped together in the same facet in the plot (see the Examples section, below). The default is to group all parameters together into a single batch. Changing the default is most useful when parameters are on very different scales, in which case batch can be used to group them into batches within which it makes sense to use the same $y$ -axis.

facet_args

A named list of arguments (other than facets) passed to facet_wrap or facet_grid to control faceting.

...

Currently unused.

prob

The probability mass to include in the inner interval. The default is 0.5 (50% interval).

prob_outer

The probability mass to include in the outer interval. The default is 0.9 (90% interval).

point_est

The point estimate to show. Either "median" (the default), "mean", or "none".

size, alpha

Passed to geom_point to control the appearance of plotted points.

binwidth

An optional value used as the binwidth argument to geom_histogram to override the default binwidth.

Value

A ggplot object that can be further customized using the ggplot2 package.

Plot Descriptions

mcmc_recover_intervals: Central intervals and point estimates computed from MCMC draws, with "true" values plotted using a different shape.
mcmc_recover_scatter: Scatterplot of posterior means (or medians) against "true" values.
mcmc_recover_hist: Histograms of the draws for each parameter with the "true" value overlaid as a vertical line.

Examples

Run this code

# NOT RUN {
library(rstanarm)
alpha <- 1; beta <- rnorm(10, 0, 3); sigma <- 2
X <- matrix(rnorm(1000), 100, 10)
y <- rnorm(100, mean = c(alpha + X %*% beta), sd = sigma)
fit <- stan_glm(y ~ ., data = data.frame(y, X))
draws <- as.matrix(fit)
print(colnames(draws))
true <- c(alpha, beta, sigma)

mcmc_recover_intervals(draws, true)

# put the coefficients on X into the same batch
mcmc_recover_intervals(draws, true, batch = c(1, rep(2, 10), 1))
# equivalent
mcmc_recover_intervals(draws, true, batch = grepl("X", colnames(draws)))
# same but facets stacked vertically
mcmc_recover_intervals(draws, true,
                       batch = grepl("X", colnames(draws)),
                       facet_args = list(ncol = 1),
                       size = 3)

# each parameter in its own facet
mcmc_recover_intervals(draws, true, batch = 1:ncol(draws))
# same but in a different order
mcmc_recover_intervals(draws, true, batch = c(1, 3, 4, 2, 5:12))
# present as bias by centering with true values
mcmc_recover_intervals(sweep(draws, 2, true), rep(0, ncol(draws))) + hline_0()


# scatterplot of posterior means vs true values
mcmc_recover_scatter(draws, true, point_est = "mean")


# histograms of parameter draws with true value added as vertical line
color_scheme_set("brightblue")
mcmc_recover_hist(draws[, 1:4], true[1:4])
# }
# NOT RUN {
# }

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