/
sampling.R
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sampling.R
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#' Run a stage of the PMwG sampler
#'
#' Run one of burnin, adaptation or sampling phase from the PMwG
#' sampler. Each stage involves slightly different processes, so for the
#' full PMwG sampling we need to run this three times.
#'
#' The \strong{burnin} stage by default selects 50% of particles from the model
#' parameter sample (selected through a Gibbs step) and 50% of particles from
#' the previous random effect of each subject. It assesses each particle with
#' the log-likelihood function and samples from all particles weighted by their
#' log-likelihood.
#'
#' The \strong{adaptation} stage selects and assesses particle in the same was
#' as burnin, however on each iteration it also checks whether each subject has
#' enough unique random effect samples to attempt to create a conditional
#' distribution for efficient sampling in the next stage. If the attempt at
#' creating a conditional distribution fails, then the number of unique samples
#' is increased and sampling continues. If the attempt succeeds then the stage
#' is finished early.
#'
#' The \strong{final} stage (sampling) by default samples predominantly from the
#' conditional distribution created at the end of adaptation. This is more
#' efficient and allows the number of particles to be reduced whilst still
#' getting a high enough acceptance rate of new samples.
#'
#' Once complete each stage will return a sampler object with the new samples
#' stored within it.
#'
#' The progress bar (which is displayed by default) shows the number of
#' iterations out of those requested which have been completed. It also contains
#' additional information at the end about the number of newly generated
#' particles that have been accepted. This is show as New(XXX%), and is the
#' average across subjects of newly sampled random effects accept rate. See
#' \code{\link{accept_rate}} for more detail on getting individual accept rate
#' values per subject.
#'
#' @param pmwgs A Particle Metropolis within Gibbs sampler which has been set
#' up and initialised
#' @param stage The sampling stage to run. Must be one of \code{'burn'},
#' \code{'adapt'} or \code{'sample'}.
#' @param iter The number of iterations to run for the sampler. For
#' \code{'burn'} and \code{'sample'} all iterations will run. However for
#' \code{'adapt'} if all subjects have enough unique samples to create the
#' conditional distribution then the stage will finish early.
#' @param particles The default here is 1000 particles to be generated for each
#' iteration, however during the sample phase this should be reduced.
#' @param display_progress Display a progress bar during sampling.
#' @param n_cores Set to more than 1 to use \code{mclapply}. Setting
#' \code{n_cores} greater than 1 is only permitted on Linux and Mac OS X
#' machines.
#' @param n_unique A number representing the number of unique samples to check
#' for on each iteration of the sampler (An initial test for the generation
#' of the proposal distribution). Only used during the \code{'adapt'} stage.
#' @param epsilon A value between 0 and 1 that controls the extent to which the
#' covariance matrix is scaled when generating particles from the previous
#' random effect. The default will be chosen based on the number of random
#' effects in the model.
#' @param p_accept A value between 0 and 1 that will flexibly tune epsilon to
#' achieve an acceptance ratio close to what you set p_accept to. The default
#' is set at 0.8.
#' @param mix A vector of floats that controls the mixture of different sources
#' for particles. The function \code{\link{numbers_from_proportion}} is
#' passed this value and includes extra details on what is accepted.
#' @param pdist_update_n The number of iterations in the sample stage after
#' which the proposal distribution will be recomputed.
#' @return A pmwgs object with the newly generated samples in place.
#' @examples
#' library(rtdists)
#' sampled_forstmann$data <- forstmann
#' run_stage(sampled_forstmann, "sample", iter = 1, particles = 10)
#' @export
run_stage <- function(pmwgs,
stage,
iter = 1000,
particles = 100,
display_progress = TRUE,
n_cores = 1,
n_unique = ifelse(stage == "adapt", 100, NA),
epsilon = NULL,
p_accept = .8,
mix = NULL,
pdist_update_n = ifelse(stage == "sample", 50, NA)) {
# Set defaults for NULL values
subj_epsilon <- pmwgs$samples$epsilon[, pmwgs$samples$idx]
if (is.null(subj_epsilon)) {
message("ERROR: no subject specific epsilon values found in sampler object")
stop("Try running augment_sampler_epsilon(sampler) first")
}
if (is.na(subj_epsilon[1])) {
epsilon <- set_epsilon(pmwgs$n_pars, epsilon)
subj_epsilon <- rep(epsilon, pmwgs$n_subjects)
}
mix <- set_mix(stage, mix)
# Test passed arguments/defaults for correctness
do.call(check_run_stage_args, as.list(environment()))
# Hyper parameters for epsilon tuning.
# See Garthwaite, P. H., Fan, Y., & Sisson, S. A. (2016).
alpha_star <- -stats::qnorm(p_accept / 2)
n0 <- round(5 / (p_accept * (1 - p_accept)))
# Set necessary local variables
.unique_inc <- 20
apply_fn <- lapply
# Set stable (fixed) new_sample argument for this run
stable_args <- list(
X = 1:pmwgs$n_subjects,
FUN = new_sample,
data = pmwgs$data,
num_particles = particles,
# parameters argument will be generated each iteration below
# efficient arguments will be generated if needed below
mix_proportion = mix,
likelihood_func = pmwgs$ll_func,
subjects = pmwgs$subjects
)
if (n_cores > 1) {
apply_fn <- parallel::mclapply
stable_args$mc.cores <- n_cores # nolint
}
# Display stage to screen
msgs <- list(
burn = "Phase 1: Burn in\n",
adapt = "Phase 2: Adaptation\n",
sample = "Phase 3: Sampling\n"
)
cat(msgs[[stage]])
# Build new sample storage
pmwgs <- extend_sampler(pmwgs, iter, stage)
# create progress bar
if (display_progress) {
pb <- accept_progress_bar(min = 0, max = iter)
}
start_iter <- pmwgs$samples$idx
collected_msgs <- list()
# Main iteration loop
for (i in 1:iter) {
if (display_progress) {
update_progress_bar(pb, i, extra = mean(accept_rate(pmwgs)))
}
# Create/update efficient proposal distribution if we are in sampling phase.
stable_args <- utils::modifyList(
stable_args,
set_proposal(i, stage, pmwgs, pdist_update_n)
)
tryCatch(
pars <- gibbs_step(pmwgs),
error = function(err_cond) {
gibbs_step_err(pmwgs, err_cond)
}
)
iter_args <- list(
parameters = pars,
epsilon = subj_epsilon
)
tmp <- do.call(apply_fn, c(stable_args, iter_args))
lapply(tmp, function(x) {
if (inherits(x, "try-error")) {
new_sample_err(pmwgs, parent.env(environment()), x)
}
})
ll <- unlist(lapply(tmp, attr, "ll"))
alpha <- array(unlist(tmp), dim = dim(pars$alpha))
# Store results locally.
j <- start_iter + i
pmwgs$samples$theta_mu[, j] <- pars$tmu
pmwgs$samples$theta_sig[, , j] <- pars$tsig
pmwgs$samples$last_theta_sig_inv <- pars$tsinv
pmwgs$samples$alpha[, , j] <- alpha
pmwgs$samples$idx <- j
pmwgs$samples$subj_ll[, j] <- ll
pmwgs$samples$a_half[, j] <- pars$a_half
pmwgs$samples$epsilon[, j] <- subj_epsilon
# Epsilon tuning. See Garthwaite, P. H., Fan, Y., & Sisson, S. A. (2016).
if (!is.null(p_accept)) {
if (j > n0) {
acc <- pmwgs$samples$alpha[1, , j] != pmwgs$samples$alpha[1, , (j - 1)]
subj_epsilon <- update_epsilon(subj_epsilon, acc, p_accept, j,
pmwgs$n_pars, alpha_star)
}
}
if (stage == "adapt") {
res <- test_sampler_adapted(pmwgs, n_unique, i)
if (res[1] == "success") {
collected_msgs <- c(collected_msgs, res[2])
break
} else if (res[1] == "increase") {
n_unique <- n_unique + .unique_inc
collected_msgs <- c(collected_msgs, res[2])
}
}
}
if (display_progress) close(pb)
if (length(collected_msgs) > 0) lapply(collected_msgs, cat)
if (stage == "adapt") {
if (i == iter) {
message(paste(
"WARNING:",
"Particle Metropolis within Gibbs Sampler did not",
"finish adaptation phase early (all", i, "iterations were",
"run).\nYou should examine your samples and perhaps start",
"a longer adaptation run."
))
} else {
pmwgs <- trim_na(pmwgs)
}
}
pmwgs
}
#' Generate particles and select one to be the new sample
#'
#' Generate a new sample for a particular subject given their data and the
#' new model parameter estimates. This should not be called directly, rather it
#' is used internally to run_stage.
#'
#' The function that controls the generation of new samples for the Particle
#' Metropolis within Gibbs sampler. It generates samples from either the initial
#' proposal or from the last iteration of the sampler. This function should not
#' usually need to be called, as the \code{run_stage} function uses this
#' internally.
#'
#' The way it selects a new sample is by generating proposal particles from up
#' to three different distributions (according to a mixing proportion).
#'
#' The first distribution is based on the current model parameter sample values.
#' The second distribution is based on the last random effects for the subject.
#' The third distribution is only used in the final sampling phase and is based
#' on the conditional distribution built from accepted particles in the adapt
#' phase of the sampler.
#'
#' @param s A number - the index of the subject. For \code{s == 1} The first
#' subject ID from the \code{data} subject column will be selected. For
#' \code{s == 2} the second unique value for subject id will be used.
#' @param data A data.frame (or similar object) which contains the data against
#' which the particles are assessed. The only strict requirement is that
#' it contains a subject column named as such to allow for the splitting
#' of the data by unique subject id. The provided log likelihood function
#' is the only other contact with the data.
#' @param parameters A list containing:
#' \describe{
#' \item{\code{tmu}}{The vector of means for the multivariate normal}
#' \item{\code{tsig}}{A covariate matrix for the multivariate normal}
#' \item{\code{alpha}}{An array of individual subject random effects}
#' }
#' @inheritParams numbers_from_proportion
#' @inheritParams check_efficient
#' @param likelihood_func A likelihood function for calculating log likelihood
#' of samples. Usually provided internally in \code{run_stage} from the pmwgs
#' object.
#' @param epsilon A scaling factor to reduce the variance on the distribution
#' based on subject random effects when generating particles.
#' @param subjects A list of unique subject ids in the order they appear in
#' the data.frame
#'
#' @return A single sample from the new proposals
#' @keywords internal
new_sample <- function(s, data, num_particles, parameters,
efficient_mu = NULL, efficient_sig2 = NULL,
mix_proportion = c(0.5, 0.5, 0.0),
likelihood_func = NULL,
epsilon = 1, subjects = NULL) {
# Check for efficient proposal values if necessary
check_efficient(mix_proportion, efficient_mu, efficient_sig2)
e_mu <- efficient_mu[, s]
e_sig2 <- efficient_sig2[, , s]
mu <- parameters$tmu
sig2 <- parameters$tsig
subj_mu <- parameters$alpha[, s]
subj_epsilon <- epsilon[s]
if (is.null(likelihood_func)) stop("likelihood_func is a required argument")
# Create proposals for new particles
proposals <- gen_particles(
num_particles, mu, sig2, subj_mu,
mix_proportion = mix_proportion,
prop_mu = e_mu,
prop_sig2 = e_sig2,
epsilon = subj_epsilon
)
# Put the current particle in slot 1.
proposals[1, ] <- subj_mu
# Density of data given random effects proposal.
lw <- apply(
proposals,
1,
likelihood_func,
data = data[data$subject == subjects[s], ]
)
# Density of random effects proposal given population-level distribution.
lp <- mvtnorm::dmvnorm(x = proposals, mean = mu, sigma = sig2, log = TRUE)
# Density of proposals given proposal distribution.
prop_density <- mvtnorm::dmvnorm(
x = proposals,
mean = subj_mu,
sigma = sig2 * (subj_epsilon^2)
)
# Density of efficient proposals
if (mix_proportion[3] != 0) {
eff_density <- mvtnorm::dmvnorm(
x = proposals,
mean = e_mu,
sigma = e_sig2
)
} else {
eff_density <- 0
}
lm <- log(mix_proportion[1] * exp(lp) +
(mix_proportion[2] * prop_density) +
(mix_proportion[3] * eff_density))
# log of importance weights.
l <- lw + lp - lm
weights <- exp(l - max(l))
tryCatch(
idx <- sample(x = num_particles, size = 1, prob = weights),
error = function(err_cond) {
particle_select_err(s, parent.env(environment()), err_cond)
}
)
winner <- proposals[idx, ]
attr(winner, "ll") <- lw[idx]
winner
}
#' Generate proposal particles
#'
#' Generates particles for the \code{new_sample} function
#'
#' Generate particles for a particular subject from a mix of population level
#' (hierarchical) distribution, from the particles (containing individual level
#' distribution) and/or from the conditional on accepted individual level
#' particles, a more efficient proposal method.
#'
#' This function is used in burnin, adaptation and sampling using various
#' combinations of the arguments.
#'
#' @param mu A vector of means for the multivariate normal
#' @param sig2 A covariate matrix for the multivariate normal
#' @param particle A particle (re proposals for latent variables)
#' @inheritParams numbers_from_proportion
#' @param epsilon Reduce the variance for the individual level samples by this
#' factor
#'
#' @return The new proposals
#' @keywords internal
gen_particles <- function(num_particles,
mu,
sig2,
particle,
...,
mix_proportion = c(0.5, 0.5, 0.0),
prop_mu = NULL,
prop_sig2 = NULL,
epsilon = 1) {
particle_numbers <- numbers_from_proportion(mix_proportion, num_particles)
# Generate proposal particles
pop_particles <- particle_draws(particle_numbers[1], mu, sig2)
ind_particles <- particle_draws(
particle_numbers[2],
particle,
sig2 * epsilon^2
)
eff_particles <- particle_draws(particle_numbers[3], prop_mu, prop_sig2)
particles <- rbind(pop_particles, ind_particles, eff_particles)
colnames(particles) <- names(mu) # stripped otherwise.
particles
}
#' Check and normalise the number of each particle type from the mix_proportion
#'
#' Takes a mix proportion vector (3 x float) and a number of particles to
#' generate and returns a vector containing the number of each particle type to
#' generate.
#'
#' @param mix_proportion A vector of floats between 0 and 1 and summing to 1
#' which give the proportion of particles to generate from the population
#' level parameters, the individual random effects and the conditional
#' parameters respectively
#' @param num_particles The total number of particles to generate using a
#' combination of the three methods.
#'
#' @return The wound vector as a matrix
#' @keywords internal
numbers_from_proportion <- function(mix_proportion, num_particles = 1000) {
numbers <- stats::rbinom(n = 2, size = num_particles, prob = mix_proportion)
if (mix_proportion[3] == 0) {
numbers[3] <- 0
numbers[2] <- num_particles - numbers[1]
} else {
numbers[3] <- num_particles - sum(numbers)
}
numbers
}
#' Generate a cloud of particles from a multivariate normal distribution
#'
#' Takes the mean and variance for a multivariate normal distribution, as well
#' as the number of particles to generate and return random draws from the
#' multivariate normal if the numbers of particles is > 0, otherwise return
#' NULL. At least one of mean or sigma must be provided.
#'
#' @param n number of observations
#' @param mu mean vector
#' @param covar covariance matrix
#'
#' @return If n > 0 returns n draws from the multivariate normal with mean and
#' sigma, otherwise returns NULL
#' @keywords internal
particle_draws <- function(n, mu, covar) {
if (n <= 0) {
return(NULL)
}
mvtnorm::rmvnorm(n, mean = mu, sigma = covar)
}
#' Set default values for epsilon
#'
#' Takes the number of parameters and the epsilon arg value and sets a default
#' if necessary.
#'
#' @param n_pars The number of parameters for the model
#' @param epsilon The value of epsilon set in the call to `run_stage` or NULL.
#'
#' @keywords internal
set_epsilon <- function(n_pars, epsilon) {
if (checkmate::test_null(epsilon)) {
if (n_pars > 15) {
epsilon <- 0.1
} else if (n_pars > 10) {
epsilon <- 0.3
} else {
epsilon <- 0.5
}
message(
sprintf(
"MESSAGE: Epsilon has been set to %.1f based on number of parameters",
epsilon
)
)
}
epsilon
}
#' Set default values for mix
#'
#' Takes the current stage and the mix arg value and sets a default if
#' necessary.
#'
#' @param stage The stage being run by the sampler.
#' @param mix The value of mix set in the call to `run_stage` or NULL.
#'
#' @keywords internal
set_mix <- function(stage, mix) {
if (checkmate::test_null(mix)) {
if (stage == "sample") {
mix <- c(0.1, 0.2, 0.7)
} else {
mix <- c(0.5, 0.5, 0.0)
}
message(
sprintf(
"MESSAGE: mix has been set to c(%s) based on the stage being run",
paste(mix, collapse = ", ")
)
)
}
mix
}
#' Setup the proposal distribution arguments (if in sample stage)
#'
#' Takes the current stage and the mix arg value and sets a default if
#' necessary.
#'
#' @param i The current iteration of the stage being run.
#' @param stage The stage being run by the sampler.
#' @param pmwgs The pmwgs object from which to attempt to create the proposal
#' distribution
#' @param pdist_update_n The number of iterations to run before recomputing the
#' proposal distribution (NA to never update or for burnin/adaptation stages)
#'
#' @keywords internal
set_proposal <- function(i, stage, pmwgs, pdist_update_n) {
if (stage != "sample") {
return(list())
}
if (is.na(i %% pdist_update_n) && (i != 1)) {
return(list())
}
if ((i != 1) && ((i %% pdist_update_n) != 0)) {
return(list())
}
tryCatch(
prop_args <- create_efficient(pmwgs),
error = function(err_cond) {
outfile <- tempfile(
pattern = "PMwG_err_",
tmpdir = ".",
fileext = ".RData"
)
msg <- paste(
"ERROR: Unrecoverable error in conditional distribution creation.\n",
err_cond,
"MESSAGE: Saving current state of environment in file:", outfile
)
save.image(outfile)
message(msg)
stop("Quitting")
}
)
prop_args
}
#' Test the arguments to the run_stage function for correctness
#'
#' Takes the arguments to run_stage and checks them for completeness and
#' correctness. Returns a list of cleaned/checked arguments to the caller.
#'
#' @import checkmate
#' @inheritParams run_stage
#'
#' @keywords internal
check_run_stage_args <- function(pmwgs,
stage,
iter,
particles,
display_progress,
n_cores,
n_unique,
epsilon,
subj_epsilon,
p_accept,
mix,
pdist_update_n) {
asserts <- makeAssertCollection()
assert_class(pmwgs, "pmwgs", add = asserts)
assert_true(pmwgs$init, .var.name = "pmwgs$init", add = asserts)
assert_choice(stage, stages[2:length(stages)], add = asserts)
assert_count(iter, positive = TRUE, add = asserts)
assert_count(particles, positive = TRUE, add = asserts)
assert_logical(display_progress, add = asserts)
assert_count(n_cores, positive = TRUE, add = asserts)
check_cores <- function(x) {
if (test_os("windows") && test_true(x != 1)) {
return("`n_cores` cannot be greater than 1 on Windows systems.")
}
check_count(x, positive = TRUE)
}
assert_cores <- makeAssertionFunction(check_cores)
assert_cores(n_cores, add = asserts)
if (stage == "adapt") {
assert_count(n_unique, positive = TRUE, add = asserts)
} else {
assert_scalar_na(n_unique, add = asserts)
}
assert_double(epsilon, lower = 0.0, upper = 1.0, len = 1, add = asserts)
assert_double(subj_epsilon, lower = 0.0, upper = 1.0, len = 1, add = asserts)
assert_double(p_accept, lower = 0.0, upper = 1.0, len = 1, add = asserts)
assert_double(mix, lower = 0.0, upper = 1.0, len = 3, add = asserts)
assert_true(all.equal(sum(mix), 1), add = asserts)
if (stage == "sample") {
assert_count(pdist_update_n, positive = TRUE, add = asserts)
} else {
assert_scalar_na(pdist_update_n, add = asserts)
}
}
#' Return the acceptance rate for new particles across all subjects
#'
#' Here the acceptance rate is defined as the rate of accepting newly generated
#' particles for individuals random effects. That is the number of samples where
#' a newly generated particle was accepted / the number of samples.
#'
#' @param pmwgs The sampler object (containing random effects) with which we are
#' working
#' @param window_size The size of the window to calculate acceptance rate over
#'
#' @return A vector with the acceptance rate for each subject for the last X
#' samples
#' @keywords internal
accept_rate <- function(pmwgs, window_size = 200) {
n_samples <- pmwgs$samples$idx
if (is.null(n_samples) || n_samples < 3) {
return(array(0, dim(pmwgs$samples$alpha)[2]))
}
if (n_samples <= window_size) {
start <- 1
end <- n_samples
} else {
start <- n_samples - window_size + 1
end <- n_samples
}
vals <- pmwgs$samples$alpha[1, , start:end]
apply(
apply(vals, 1, diff) != 0, # If diff != 0
2,
mean
)
}
#' Update the subject specific scaling parameters (epsilon)
#'
#' Update the subject specific scaling parameter according to procedures
#' outlined in P. H. Garthwaite, Y. Fan & S. A. Sisson (2016) Adaptive optimal
#' scaling of Metropolis–Hastings algorithms using the Robbins–Monro process,
#' Communications in Statistics - Theory and Methods, 45:17, 5098-5111,
#' DOI: 10.1080/03610926.2014.936562
#'
#' @param epsilon The scaling parameter for all subjects
#' @param acc A boolean vector, TRUE if current sample != last sample
#' @param p The target sample acceptance rate (0-1)
#' @param i The current iteration for sampling
#' @param d The number of parameters for the model
#' @param alpha A hyperparameter for the epsilon tuning
#'
#' @return A vector with the new subject specific epsilon values
#'
#' @keywords internal
update_epsilon <- function(epsilon, acc, p, i, d, alpha) {
# optimal steplength constant (Proposition 5)
opt_step_const <- sqrt(2 * pi) * exp(alpha^2 / 2) / (2 * alpha)
# Linear function of 1/d (where d is size of multivariate dimension)
# Eqn (7)
c <- (1 - 1 / d) * opt_step_const + 1 / (d * p * (1 - p))
theta <- log(epsilon)
# Robbins-Monro process - Eqn 1
theta <- theta + c * (acc - p) / max(200, i / d)
return(exp(theta))
}