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stanfunc.R
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stanfunc.R
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# stanfunc.R
# Note re data.table:
# ... trailing [] to prevent "doesn't print first time" bug:
# https://stackoverflow.com/questions/32988099/data-table-objects-not-printed-after-returned-from-function
# https://github.com/Rdatatable/data.table/blob/master/NEWS.md#bug-fixes-5
library(bridgesampling)
library(coda)
library(ggplot2)
library(matrixStats)
library(parallel)
library(reshape)
library(rstan)
library(stringr)
#==============================================================================
# Namespace-like method: http://stackoverflow.com/questions/1266279/#1319786
#==============================================================================
stanfunc = new.env()
#==============================================================================
# Core functions for e.g. rstan 2.16.2:
#==============================================================================
stanfunc$load_or_run_stan <- function(
data,
model_code,
fit_filename,
model_name,
save_code_filename = NULL,
forcerun = FALSE,
chains = 8,
iter = 2000,
init = "0", # the default, "random", uses the range -2 to +2
seed = 1234, # for consistency across runs
cache_filetype=c("rds", "rda"),
...)
{
# Other potential common parameters:
# control = list(
# adapt_delta = 0.99
# # http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
# # https://www.rdocumentation.org/packages/rstanarm/versions/2.14.1/topics/adapt_delta
# )
cache_filetype <- match.arg(cache_filetype)
if (!forcerun && file.exists(fit_filename)) {
if (cache_filetype == "rds") {
# .Rds
cat("Loading Stan model fit from RDS file: ",
fit_filename, "...\n", sep="")
fit <- readRDS(fit_filename)
} else {
# .Rda, .Rdata
cat("Loading Stan model fit from RDA file: ",
fit_filename, "...\n", sep="")
fit <- NULL # so we can detect the change when we load
load(fit_filename) # assumes it will be called 'fit'
if (class(fit) != "stanfit") {
stop(paste("No stanfit object called 'fit' in file",
fit_filename))
}
}
cat("... loaded\n")
} else {
n_cores_stan <- options("mc.cores")
n_cores_available <- parallel::detectCores()
if (n_cores_stan < n_cores_available) {
warning(paste(
"Stan is not set to use all available CPU cores; using ",
n_cores_stan, " when ", n_cores_available,
" are available; retry after issuing the command\n",
" options(mc.cores = parallel::detectCores())",
sep=""))
}
if (n_cores_stan == 1) {
warning("Running with a single CPU core; Stan may be slow")
}
cat(paste("--- Running Stan, starting at", Sys.time(), "...\n"))
# Stan now supports parallel operation directly
fit <- rstan::stan(
model_name = model_name,
model_code = model_code,
data = data,
chains = chains,
iter = iter,
init = init,
seed = seed,
...
)
cat(paste("... Finished Stan run at", Sys.time(), "\n"))
if (cache_filetype == "rds") {
# .Rds
cat("--- Saving Stan model fit to RDS file: ",
fit_filename, "...\n", sep="")
saveRDS(fit, file=fit_filename) # load with readRDS()
} else {
# .Rda, .Rdata
cat("--- Saving Stan model fit to RDA file: ",
fit_filename, "...\n", sep="")
save(list = c("fit"), file=fit_filename)
}
cat("... saved\n")
}
if (!is.null(save_code_filename) &&
(forcerun || !file.exists(save_code_filename))) {
cat("--- Generating C++ code to save...\n")
stanc_result <- rstan::stanc(model_code = model_code)
cpp_code <- stanc_result$cppcode
cat("--- Saving C++ code to file: ",
save_code_filename, "...\n", sep="")
cppfile <- file(save_code_filename)
writeLines(cpp_code, cppfile)
close(cppfile)
cat("... saved\n")
}
return(fit)
}
stanfunc$load_or_run_bridge_sampler <- function(
stanfit,
filename,
assume_stanfit_from_this_R_session = FALSE,
model_code = NULL,
data = NULL,
cores = parallel::detectCores(),
forcerun = FALSE,
...)
{
if (!forcerun && file.exists(filename)) {
cat("Loading bridge_sampler() fit from RDS file: ",
filename, "...\n", sep="")
b <- readRDS(filename)
cat("... loaded\n")
} else {
# POTENTIAL PROBLEM:
# Error in .local(object, ...) :
# the model object is not created or not valid
# This is a message from rstan::log_prob(stanfit).
# https://groups.google.com/forum/#!topic/stan-users/uu1p9oGIMhU
# The FIX is to specify a new stanfit_model, like this.
if (assume_stanfit_from_this_R_session) {
cat("Using existing Stan fit as stanfit_model; will crash if the",
"Stan model was created within a different R session\n")
stanfit_model <- stanfit
} else {
cat("Creating dummy compiled Stan model...\n")
if (is.null(model_code)) {
stop("model_code not specified")
}
if (is.null(data)) {
stop("data not specified")
}
stanfit_model <- rstan::stan(
model_code=model_code,
data=data, # if you use data=list(), it segfaults
chains=1,
iter=1 # despite the bridgesampling help, iter=0 causes an error
)
cat("... done\n")
}
cat(paste("--- Running bridge_sampler, starting at",
Sys.time(), "...\n"))
b <- bridgesampling::bridge_sampler(
samples=stanfit,
stanfit_model=stanfit_model,
cores=cores,
...
)
cat(paste("... Finished bridge_sampler run at", Sys.time(), "\n"))
cat("--- Saving bridge_sampler() fit to RDS file: ",
filename, "...\n", sep="")
saveRDS(b, file=filename) # load with readRDS()
cat("... saved\n")
}
return(b)
}
stanfunc$compare_model_evidence <- function(bridgesample_list_list,
priors = NULL,
detail = FALSE,
rhat_warning_threshold = 1.1)
{
# bridgesample_list_list
# A list of lists. Each item is a list with names:
# name: the model name
# bridgesample: the output from the
# bridgesampling::bridge_sampler() function (an item of
# class bridge_list)
# stanfit (optional): a corresponding Stan fit
# ... useful to show e.g. maximum R-hat summaries
# (R note: if x is a list, then if x *doesn't* have item y, x$y == NULL.)
#
# priors:
# optional, but can be a vector containing prior probabilities for
# each model
#
# detail:
# keep the details used for intermediate calculations
#
# stanfit_list:
# NULL, or a list of stanfits whose order must match bridgesample_list;
# if present, summary statistics (such as maximum R-hat) are included
#
# Note:
# - "marginal likelihood" is the same as "evidence" (e.g. Kruschke 2011
# p57-58)
# https://stackoverflow.com/questions/9950144/access-lapply-index-names-inside-fun
# https://stackoverflow.com/questions/4227223/r-list-to-data-frame
d <- data.table(
t(
vapply(
X=seq_along(bridgesample_list_list),
FUN=function(y, i) {
item <- y[[i]]
if (is.null(item$stanfit)) {
max_rhat <- NA_real_
} else {
fit <- item$stanfit
max_rhat <- stanfunc$max_rhat(fit)
}
return(c(
i, # index
item$name, # model_name
item$bridgesample$logml, # log_marginal_likelihood
max_rhat # max_rhat
))
},
FUN.VALUE=c("index"=NA_integer_,
"model_name"=NA_character_,
"log_marginal_likelihood"=NA_real_,
"max_rhat"=NA_real_),
y=bridgesample_list_list
)
)
)
d[, index := as.numeric(index)]
d[, log_marginal_likelihood := as.numeric(log_marginal_likelihood)]
d[, rhat_warning := ifelse(
is.na(max_rhat),
NA_character_,
ifelse(max_rhat > rhat_warning_threshold, "WARNING: HIGH R-HAT", "OK")
)]
d[, model_rank := frank(-log_marginal_likelihood,
ties.method="min")] # "sports method"
# ... bigger (less negative) is better
# ... and rank() ranks from smallest (-> 1) to biggest, so want the reverse
# ... and data.table::frank is quicker than rank (not that we care here!)
n_models <- nrow(d)
if (is.null(priors)) {
# Flat priors
d[, prior_p_model := 1/n_models]
} else {
# User-specified priors
if (length(priors) != n_models) {
stop("priors: wrong length")
}
if (sum(priors) != 1) {
warning("priors sum to ", sum(priors), ", not 1")
}
d[, prior_p_model := priors]
}
# Work with logs or everything will overflow.
d[, log_prior_p_model := log(prior_p_model)]
# e.g. Grounau 2017 eq 2:
# marginal_likelihood[i] * prior[i]
# posterior_p_model[i] = ---------------------------------------------------
# sum_over_all_j( marginal_likelihood[j] * prior[j] )
#
# Taking logs:
#
# log(posterior_p_model[i]) = log(marginal_likelihood[i]) + log(prior[i]) -
# log(sum_over_all_j( marginal_likelihood[j] * prior[j] ))
#
# and note the helpful R function matrixStats::logSumExp, where
#
# logSumExp(lx) == log(sum(exp(lx))
#
# which, for lx == log(x), means
#
# logSumExp(lx) == log(sum(x))
#
# so we will use
#
# log(marginal_likelihood[j] * prior[j]) = log(marginal_likelihood[j]) +
# log(prior[j])
d[, log_prior_times_lik :=
log_marginal_likelihood + log_prior_p_model]
d[, log_sum_prior_times_lik_all_models :=
matrixStats::logSumExp(d$log_prior_times_lik)]
d[, log_posterior_p_model :=
log_prior_times_lik - log_sum_prior_times_lik_all_models]
d[, posterior_p_model := exp(log_posterior_p_model)][]
if (!detail) {
# Remove working unless the user wants it
d[, log_prior_p_model := NULL]
d[, log_prior_times_lik := NULL]
d[, log_sum_prior_times_lik_all_models := NULL]
# d[, log_posterior_p_model := NULL][]
}
# print(d)
return(d)
}
stanfunc$sampled_values_from_stanfit <- function(
fit,
parname,
method = c("extract", "manual", "as.matrix"))
{
method <- match.arg(method)
if (method == "manual") {
# 1. Laborious hand-crafted way.
n_chains <- slot(fit, "sim")$chains
n_warmup <- slot(fit, "sim")$warmup
sampled_values <- NULL
for (c in 1:n_chains) {
n_save <- slot(fit, "sim")$n_save[c]
new_values <- slot(fit, "sim")$samples[[c]][parname][[1]][(n_warmup+1):n_save]
sampled_values <- c(sampled_values, new_values)
}
} else if (method == "extract") {
# 2. The way it's meant to be done.
ex <- rstan::extract(fit, permuted=TRUE)
# Now, slightly tricky. For a plain-text parameter like "xyz", this
# is simple. For something like "subject_k[1]", it isn't so simple,
# because rstan::extract gives us proper structure.
# Can also be e.g. parname[1,1], etc.
# Grep with capture: https://stackoverflow.com/questions/952275/regex-group-capture-in-r-with-multiple-capture-groups
PARAM_WITH_INDEX_REGEX = "^(\\w+)\\[((?:\\d+,)*\\d+)\\]$" # e.g. "somevar[3]", "blah[1,2]"
# matches <- stringr::str_match("blah", PARAM_WITH_INDEX_REGEX)
# matches <- stringr::str_match("blah[1]", PARAM_WITH_INDEX_REGEX)
# matches <- stringr::str_match("blah[2,3]", PARAM_WITH_INDEX_REGEX)
matches <- stringr::str_match(parname, PARAM_WITH_INDEX_REGEX)
if (!is.na(matches[1])) {
# parameter with index/indices e.g. "subject_k[3]", "blah[1,1]"
parname_par <- matches[2]
index_csv_numbers <- matches[3]
indices <- as.integer(unlist(strsplit(index_csv_numbers, ",")))
if (!(parname_par %in% names(ex))) {
stop("No such parameter: ", parname)
}
sampled_array <- ex[[parname_par]]
# ... for one index, sampled_array has indices [samplenum, parnum]
# so one can use sampled_values <- sampled_array[, parname_num]
# ... but for two, dim(sampled_array) is e.g. c(8000, 3, 3); this
# means 8000 samples of a 3x3 array.
# To retrieve them... see http://r.789695.n4.nabble.com/array-slice-notation-td902486.html
arraydims <- dim(sampled_array)
if (length(indices) != length(arraydims) - 1) {
stop("Bad indices for parameter: ", parname,
". Indices were: ", indices,
" and dimensions were: ", arraydims)
}
n_samples <- arraydims[1]
slicelist <- c(list(1:n_samples), as.list(indices))
# e.g. for param[3, 3], slicelist should be a list whose first
# element is 1:8000 (for 8000 samples), whose second element is 3,
# and whose third element is 3.
sampled_values <- do.call("[", c(list(sampled_array), slicelist))
} else {
# e.g. "somevar"
if (!(parname %in% names(ex))) {
stop("No such parameter: ", parname)
}
sampled_values <- ex[[parname]]
}
} else if (method == "as.matrix") {
# 3. Another...
m <- as.matrix(fit)
if (!(parname %in% colnames(m))) {
stop("No such parameter: ", parname)
}
sampled_values <- m[,parname]
} else {
stop("Bad method")
}
return(sampled_values)
}
stanfunc$summary_data_table <- function(fit, ...)
{
# help("summary,stanfit-method")
s <- rstan::summary(fit, ...)
# This summary object, s, has members:
# summary = overall summary
# c_summary = per-chain summary
ss <- s$summary
parnames <- rownames(ss)
ss <- data.table(ss)
ss$parameter <- parnames
# Move the "parameters" column so it's first:
setcolorder(ss, c(ncol(ss), 1:(ncol(ss) - 1))) # make last move to first
return(ss)
}
stanfunc$params_with_high_rhat <- function(fit, threshold = 1.1)
{
s <- stanfunc$summary_data_table(fit)
return(s[Rhat >= threshold])
}
stanfunc$max_rhat <- function(fit)
{
s <- stanfunc$summary_data_table(fit)
return(max(s$Rhat))
}
stanfunc$summary_by_par_regex <- function(fit, pars=NULL, par_regex=NULL, ...)
{
if (is.null(pars)) {
s <- stanfunc$summary_data_table(fit, ...)
} else {
s <- stanfunc$summary_data_table(fit, pars=pars, ...)
}
# Optionally, filter on a regex
if (!is.null(par_regex)) {
s <- s[grepl(par_regex, s$parameter), ]
}
return(s)
}
stanfunc$annotated_parameters <- function(
fit,
pars = NULL,
ci = c(0.025, 0.975), # for the "nonzero" column
probs = c(0.025, 0.25, 0.50, 0.75, 0.975),
par_regex = NULL,
annotate = TRUE,
nonzero_as_hdi = TRUE,
hdi_proportion = 0.95,
hdi_method = "kruschke_mcmc",
...
)
{
if (length(ci) != 2) {
stop("Bad ci parameter")
}
if (!ci[1] %in% probs || !ci[2] %in% probs) {
stop("Elements of ci must be in probs")
}
initial_probs <- probs
if (annotate) {
probs <- c(probs, c(0.0005, 0.9995, # p < 0.001 two-tailed
0.005, 0.995, # for "**", p < 0.01 two-tailed
0.025, 0.975, # for "*", p < 0.05 two-tailed
0.05, 0.95)) # for ".", p < 0.1 two-tailed
} else {
probs <- initial_probs
}
probs <- sort(unique(probs))
s <- stanfunc$summary_by_par_regex(fit, pars=pars, probs=probs,
par_regex=par_regex)
# Find nonzero parameters (credible interval excludes zero)
get_colname <- function(prob) {
return(paste(prob * 100, "%", sep=""))
}
nonzero_at <- function(lower, upper) {
lower_name = get_colname(lower)
upper_name = get_colname(upper)
return(
0 < s[, lower_name, with=FALSE] | s[, upper_name, with=FALSE] < 0
)
}
if (annotate) {
p_001 <- nonzero_at(0.0005, 0.9995)
p_01 <- nonzero_at(0.005, 0.995)
p_05 <- nonzero_at(0.025, 0.975)
p_1 <- nonzero_at(0.05, 0.95)
s[
,
annotation := ifelse(p_001, "***",
ifelse(p_01, "**",
ifelse(p_05, "*",
ifelse(p_1, ".", ""))))
]
}
if (nonzero_as_hdi) {
s[, hdi_lower := NA_real_]
s[, hdi_upper := NA_real_]
for (rownum in 1:nrow(s)) {
parname <- s[rownum, parameter]
values <- stanfunc$sampled_values_from_stanfit(fit, parname)
hdi_pair <- hdi(values, hdi_proportion=hdi_proportion,
method=hdi_method)
s[rownum, hdi_lower := hdi_pair[1]]
s[rownum, hdi_upper := hdi_pair[2]]
}
s[, nonzero := (0 < hdi_lower | hdi_upper < 0)]
} else {
s[, nonzero := nonzero_at(ci[1], ci[2])]
}
hidden_probs <- setdiff(probs, initial_probs) # in former, not latter
for (remove_prob in hidden_probs) {
remove_colname <- get_colname(remove_prob)
# cat(paste("Removing column", remove_colname, "\n"))
s[, (remove_colname) := NULL]
}
s <- s[] # fix nonprinting bug; see above
return(s)
}
stanfunc$nonzero_parameters <- function(fit, annotate=FALSE, ...)
{
s <- stanfunc$annotated_parameters(fit=fit, annotate=annotate, ...)
s <- s[nonzero == TRUE][] # restrict
return(s)
}
#==============================================================================
# Running in parallel
#==============================================================================
stanfunc$parallel_stan <- function(
file = NULL,
code = "",
data,
cores = parallel:detectCores(),
chains = 8,
iter = 2000,
warmup = floor(iter/2),
seed = 1234)
{
warning("stanfunc$parallel_stan: DEPRECATED; superseded by developments to rstan")
cat("parallel_stan: cores=", cores,
", chains=", chains,
", iter=", iter,
", seed=", seed,
"\n",
sep="")
cat("--- Step 1: compile the model (and run it once, very briefly, ignoring its output)\n")
f1 <- stan(file = file,
model_code = code,
data = data,
chains = 1,
iter = 1,
seed = seed,
chain_id = 1)
# sflist1 = list(f1)
cat("--- Step 2: run more chains in parallel\n")
sflist2 <- mclapply(
1:chains,
mc.cores = cores,
function(i) {
stan(fit = f1,
data = data,
chains = 1,
iter = iter,
warmup = warmup,
seed = seed,
chain_id = i)
}
# , refresh = -1
)
# ... passing the same seed to all chains follows example(sflist2stanfit)
# ... important to use the same seed but different chain_id when executing in parallel: http://stackoverflow.com/questions/12848168/will-rstan-run-on-a-supercomputer
sflist <- sflist2
cat("--- Finished.\n")
return(sflist2stanfit(sflist))
}
stanfunc$load_or_run_stan_old <- function(data, code, file, forcerun = FALSE)
{
warning("stanfunc$load_or_run_stan_old: DEPRECATED; superseded by developments to rstan")
if (!forcerun && file.exists(file)) {
cat("Loading Stan model from file:", file, "\n")
load(file)
} else {
cat("Running Stan model\n")
fit = stanfunc$parallel_stan(code, data)
cat("--- Saving Stan model to file:", file, "\n")
save(fit, file=file)
}
return(fit)
}
stanfunc$parallel_stan_reuse_fit <- function(f1, data,
cores = detectCores(),
chains = 8,
iter = 2000, seed = 1234)
{
warning("stanfunc$parallel_stan_reuse_fit: DEPRECATED; superseded by developments to rstan")
cat("parallel_stan_reuse_fit: cores=", cores,
", chains=", chains,
", iter=", iter,
", seed=", seed,
"\n",
sep="")
cat("--- Reusing existing model\n")
sflist2 <- mclapply(
1:chains,
mc.cores = cores,
function(i) {
stan(fit = f1, data = data,
iter = iter, seed = seed, chains = 1, chain_id = i)
}
)
sflist <- sflist2
cat("--- Finished.\n")
return(sflist2stanfit(sflist))
}
#==============================================================================
# LOOKING AT OUTPUT
#==============================================================================
stanfunc$save_plots_from_stanfit <- function(
fit,
parfile = "teststan_parameters.pdf",
tracefile = "teststan_trace.pdf",
pairfile = "teststan_pairs.pdf")
{
cat("Plotting parameters to", parfile, "\n")
pdf(file = parfile)
plot(fit)
dev.off()
cat("Plotting trace to", tracefile, "\n")
pdf(file = tracefile)
traceplot(fit) # options include: pars, inc_warmup
dev.off()
cat("Plotting pairs to", pairfile, "\n")
pdf(file = pairfile)
pairs(fit)
dev.off()
}
stanfunc$quick_summary_stanfit <- function(
fit, probs = c(0.025, 0.25, 0.5, 0.75, 0.975))
{
print(fit, digits_summary = 5, probs = probs)
}
stanfunc$calculate_mode <- function(sampled_values)
{
my_density <- density(sampled_values)
max_density <- max(my_density$y)
my_density$x[which(my_density$y == max_density)]
}
stanfunc$density_at_sub <- function(my_density, value)
{
# Known exactly?
if (value %in% my_density$x) {
# cat("density_at: exact\n")
return( my_density$y[ my_density$x == value ] )
}
# Out of range?
if (value < min(my_density$x) || value > max(my_density$x) ) {
cat("density_at: out of range\n")
return(NA)
}
# Otherwise, interpolate:
# cat("density_at: interpolating\n")
lower_x <- max(my_density$x[my_density$x < value])
upper_x <- min(my_density$x[my_density$x > value])
lower_d <- my_density$y[my_density$x == lower_x]
upper_d <- my_density$y[my_density$x == upper_x]
proportion <- (value - lower_x) / (upper_x - lower_x)
return(lower_d + proportion * (upper_d - lower_d))
}
stanfunc$density_at <- function(sampled_values, values)
{
my_density <- density(sampled_values)
result <- NULL
for (v in values) {
result <- c(result, density_at_sub(my_density, v))
}
return(result)
}
stanfunc$cum_density_between_two_values <- function(sampled_values,
lower, upper)
{
my_ecdf <- ecdf(sampled_values)
my_ecdf(upper) - my_ecdf(lower)
}
stanfunc$find_value_giving_density <- function(sampled_values, target_density)
{
dens <- density(sampled_values)
finder <- function(x) {
density_at_sub(dens, x) - target_density
}
uniroot()
}
stanfunc$find_value_giving_cum_density <- function(sampled_values, cum_density)
{
cdf <- ecdf(sampled_values)
find_root <- function(x) {
cdf(x) - cum_density
}
search_range <- c(min(sampled_values), max(sampled_values))
value <- uniroot(find_root, interval = search_range)$root
}
stanfunc$JUNK1 = "
calculate_hdi_from_sample_interpolating <- function(x, hdi_proportion = 0.95)
{
# INCOMPLETE
# x contains sampled values
dens = density(x)
cdf = ecdf(x)
finder_density_between_values_equals <- function(lower, upper, target_cum_density) {
# 0 when CDF(upper) - CDF(lower) = target_cum_density
cdf(upper) - cdf(lower) - target_cum_density
}
finder_density_equal_at_upper_and_lower <- function(lower, upper) {
density_at_upper = density_at_sub(dens, upper)
density_at_lower = density_at_sub(dens, lower)
density_at_upper - density_at_lower
}
# https://stat.ethz.ch/pipermail/r-help/2007-November/146688.html
density_diff <- function(lower, level=0.95) {
plower = density_at_sub(dens, lower)
pupper = plower + level
# ...
}
# ...
}
"
stanfunc$calculate_hdi_from_sample_piecewise <- function(x, hdi_proportion = 0.95)
{
# WORKS, BUT USE coda::HPDinterval instead
# x contains sampled values
# ... the shortest interval for which the difference in the empirical cumulative density function values of the endpoints is the nominal probability
# http://stats.stackexchange.com/questions/18533/find-probability-density-intervals
x <- sort(x)
# http://www.sumsar.net/best_online/js/js_mcmc.js
n <- length(x)
ci_nbr_of_points <- floor(n * hdi_proportion) # want this many samples in the HDI
min_width_ci <- c(min(x), max(x)) # initialize
for (i in 1:(n - ci_nbr_of_points)) {
ci_width <- x[i + ci_nbr_of_points] - x[i]
if (ci_width < min_width_ci[2] - min_width_ci[1]) {
min_width_ci <- c( x[i], x[i + ci_nbr_of_points] )
}
}
return(min_width_ci)
# We want an HDI such that
# CDF(upper) - CDF(lower) = hdi_proportion
# and PDF(upper) = PDF(lower)
}
stanfunc$HDIofMCMC <- function(sampleVec, credMass = 0.95)
{
# Krushke, p628, HDIofMCMC.R
# Computes highest density interval from a sample of representative values,
# estimated as shortest credible interval.
# Arguments:
# sampleVec
# is a vector of representative values from a probability distribution.
# credMass
# is a scalar between 0 and 1, indicating the mass within the credible
# interval that is to be estimated.
# Value:
# HDIlim is a vector containing the limits of the HDI
sortedPts <- sort( sampleVec )
ciIdxInc <- floor( credMass * length( sortedPts ) )
nCIs <- length( sortedPts ) - ciIdxInc
ciWidth <- rep( 0 , nCIs )
for (i in 1:nCIs) {
ciWidth[i] <- sortedPts[i + ciIdxInc] - sortedPts[i]
}
HDImin <- sortedPts[which.min(ciWidth)]
HDImax <- sortedPts[which.min(ciWidth) + ciIdxInc]
HDIlim <- c(HDImin, HDImax)
return(HDIlim)
}
TEST_HDI_OF_MCMC <- '
# See Kruschke (2011) p41, p628
set.seed(1234)
n = 20000
symmetric_y <- rnorm(n, mean=0, sd=1)
symmetric_d <- density(symmetric_y)
symmetric_hdi <- stanfunc$HDIofMCMC(symmetric_y) # -1.975671 1.904936
plot(symmetric_d)
abline(v=symmetric_hdi[1])
abline(v=symmetric_hdi[2])
asymmetric_y <- rgamma(n, shape=2, scale=2)
asymmetric_d <- density(asymmetric_y)
asymmetric_hdi <- stanfunc$HDIofMCMC(asymmetric_y) #
plot(asymmetric_d)
abline(v=asymmetric_hdi[1])
abline(v=asymmetric_hdi[2])
'
stanfunc$hdi_via_coda <- function(sampled_values, hdi_proportion = 0.95)
{
hdi_limits_matrix <- coda::HPDinterval(as.mcmc(sampled_values),
prob = hdi_proportion)
# ... Sometimes crashes with
# "Error in dimnames(x)[[2]] : subscript out of bounds"
# for perfectly valid-looking data that works with other methods.
return(c(hdi_limits_matrix[1, "lower"], hdi_limits_matrix[1, "upper"]))
}
stanfunc$hdi_via_lme4 <- function(sampled_values, hdi_proportion = 0.95)
{
hdi_limits_matrix <- lme4::HPDinterval(as.matrix(sampled_values),
prob = hdi_proportion)
return(c( hdi_limits_matrix[1, "lower"], hdi_limits_matrix[1, "upper"]))
}
stanfunc$compare_hdi_methods <- function(sampled_values, hdi_proportion)
{
cat("Bååth:\n")
print(calculate_hdi_from_sample_piecewise(sampled_values, hdi_proportion))
cat("Kruschke:\n")
print(HDIofMCMC(sampled_values, hdi_proportion))
cat("coda:\n")
print(hdi_via_coda(sampled_values, hdi_proportion))
cat("lme4:\n")
print(hdi_via_lme4(sampled_values, hdi_proportion))
}
stanfunc$hdi <- function(sampled_values, hdi_proportion = 0.95,
method=c("kruschke_mcmc",
"coda",
"baath",
"lme4"))
{
# Method chooser!
method <- match.arg(method)
if (method == "kruschke_mcmc") {
return(HDIofMCMC(sampled_values, hdi_proportion))
} else if (method == "coda") {
return(hdi_via_coda(sampled_values, hdi_proportion))
} else if (method == "baath") {
return(calculate_hdi_from_sample_piecewise(sampled_values, hdi_proportion))
} else if (method == "lme4") {
return(hdi_via_lme4(sampled_values, hdi_proportion))
} else {
stop("Bad method")
}
}
stanfunc$interval_includes <- function(interval, testval,
lower_inclusive = TRUE,
upper_inclusive = TRUE)
{
# Ensure ordered from low to high:
if (interval[2] < interval[1]) {
interval <- c(interval[2], interval[1])
}
lowertest <- ifelse(lower_inclusive,
interval[1] <= testval,
interval[1] < testval)
uppertest <- ifelse(upper_inclusive,
testval <= interval[2],
testval < interval[2])
return(lowertest && uppertest)
}
stanfunc$interval_excludes <- function(interval, testval,
lower_inclusive = TRUE,
upper_inclusive = TRUE)
{
!stanfunc$interval_includes(interval, testval,
lower_inclusive = lower_inclusive,
upper_inclusive = upper_inclusive)
}
stanfunc$hdi_proportion_excluding_test_value <- function(
x, test_value = 0, largest_such_interval = TRUE, debug = FALSE)
{
# cruddy method!
# NOTE ALSO: neither the lower bound nor the upper bound of an HDI
# move monotonically as the HDI proportion is changed (because the
# distribution can be asymmetrical).
width_accuracy <- 0.001 # 0.1%
if (largest_such_interval) {
startval <- 1
endval <- 0
width_accuracy <- -width_accuracy
stoptest <- interval_excludes
}
else {
startval <- 0
endval <- 1
stoptest <- interval_includes
}
prev_width <- startval
for (width in seq(startval, endval, width_accuracy)) {
if (width == 1) next # or HDI will be invalid (infinite)
interval <- hdi(x, width)
current_interval_fails <- stoptest(interval, test_value)
if (debug) cat("testing proportion ", width,
", interval: ", interval,
", fails? ", current_interval_fails,
"\n", sep="")
if (current_interval_fails) {
# current interval fails, so return the previous
return(prev_width)
}
prev_width <- width
}
return(endval)
}
stanfunc$plot_density_function <- function(
sampled_values,
parname,
test_value = 0,
quantile_probs = c(0.025, 0.5, 0.975),
hdi_proportion = 0.95,
histogram_breaks = 50,
digits = 3,
colour_quantiles = "gray",
colour_mean = "black",
colour_mode = "lightgrey",
colour_hdi = "darkgreen",
lty_quantiles = 3,
lty_mean = 1,
lty_mode = 1,
lty_hdi = 1,
colour_density = "blue",
show_hdi_proportion_excluding_test_value = FALSE,
show_quantiles = TRUE,
show_mean = TRUE,
show_mode = TRUE,
show_hdi = TRUE,
ypos_quantiles = 1.15,
ypos_mean = 0.6,
ypos_mode = 0.4)
{
my_density <- density(sampled_values)
max_density <- max(my_density$y)
q <- quantile(sampled_values, probs=quantile_probs)
my_mean <- mean(sampled_values)
my_mode <- calculate_mode(sampled_values)
my_ecdf <- ecdf(sampled_values)
hdi_percent <- hdi_proportion * 100
#debug_quantity(sampled_values)
hdi_limits <- hdi(sampled_values, hdi_proportion)
central_proportion_excluding_test_value <- 1 - 2 * my_ecdf(test_value)
cat("\nParameter:", parname, "\n")
cat("Mean:", my_mean, "\n")
cat("Mode:", my_mode, "\n")
cat("Quantiles:\n")
print(q)
cat("Central proportion excluding test value of", test_value, ":",