This is the main function for performing MCMC BSL (with a
standard or non-standard likelihood estimator) to sample from the
approximate posterior distribution. A couple of extentions to the standard
approach are available by changing the following arguments, method,
shrinkage, whitening, misspecType. Parallel computing
is supported with the R package foreach.
bsl(
y,
n,
M,
model,
covRandWalk,
theta0,
fnSim,
fnSum,
method = c("BSL", "uBSL", "semiBSL", "BSLmisspec"),
shrinkage = NULL,
penalty = NULL,
fnPrior = NULL,
simArgs = NULL,
sumArgs = NULL,
logitTransformBound = NULL,
standardise = FALSE,
GRC = FALSE,
whitening = NULL,
misspecType = NULL,
tau = 1,
parallel = FALSE,
parallelArgs = NULL,
thetaNames = NULL,
plotOnTheFly = FALSE,
verbose = 1L
)An object of class bsl is returned, see BSL
for more information of the S4 class.
The observed data. Note this should be the raw dataset NOT the set of summary statistics.
The number of simulations from the model per MCMC iteration for estimating the synthetic likelihood.
The number of MCMC iterations.
A ``MODEL'' object generated with function
newModel. See newModel.
The covariance matrix of a multivariate normal random walk proposal distribution used in the MCMC.
Deprecated, will be removed in the future, use model
instead. Initial guess of the parameter value, which is used as the
starting value for MCMC.
Deprecated, will be removed in the future, use
model instead. A function that simulates data for a given parameter
value. The first argument should be the parameters. Other necessary
arguments (optional) can be specified with simArgs.
Deprecated, will be removed in the future, use
model instead. A function for computing summary statistics of data.
The first argument should be the observed or simulated dataset. Other
necessary arguments (optional) can be specified with sumArgs.
A string argument indicating the method to be used. The default, ``BSL'', runs standard BSL. ``uBSL'' uses the unbiased estimator of a normal density of Ghurye1969;textualBSL. ``semiBSL'' runs the semi-parametric BSL algorithm and is more robust to non-normal summary statistics. ``BSLmisspec'' estimates the Gaussian synthetic likelihood whilst acknowledging that there may be incompatibility between the model and the observed summary statistic Frazier2019BSL.
A string argument indicating which shrinkage method to
be used. The default is NULL, which means no shrinkage is used.
Shrinkage estimation is only available for methods ``BSL'' and ``semiBSL''.
Current options are ``glasso'' for the graphical lasso method of
Friedman2008;textualBSL and ``Warton'' for the ridge
regularisation method of Warton2008;textualBSL.
The penalty value to be used for the specified shrinkage method. Must be between zero and one if the shrinkage method is ``Warton''.
Deprecated, will be removed in the future, use
model instead. A function that computes the log prior density for a
parameter. The default is NULL, which uses an improper flat prior
over the real line for each parameter. The function must have a single
input: a vector of parameter values.
Deprecated, will be removed in the future, use
model instead. A list of additional arguments to pass into the
simulation function. Only use when the input fnSim requires
additional arguments. The default is NULL.
Deprecated, will be removed in the future, use
model instead. A list of additional arguments to pass into the
summary statistics function. Only use when the input fnSum requires
additional arguments. The default is NULL.
A \(p\) by \(2\) numeric matrix indicating the
upper and lower bounds of parameters if a logit transformation is used on
the parameter space, where \(p\) is the number of parameters. The default
is NULL, which means no logit transformation is used. It is also
possible to define other transformations within the simulation and prior
function from model. The first column contains the lower bound of
each parameter and the second column contains the upper bound. Infinite
lower or upper bounds are also supported, eg.
matrix(c(1,Inf,0,10,-Inf,0.5),3,2,byrow=TRUE).
A logical argument that determines whether to standardise
the summary statistics before applying the graphical lasso. This is only
valid if method is ``BSL'', shrinkage is ``glasso'' and penalty is not
NULL. The diagonal elements will not be penalised if the shrinkage
method is ``glasso''. The default is FALSE.
A logical argument indicating whether the Gaussian rank
correlation matrix Boudt2012BSL should be used to estimate
the covariance matrix in ``BSL'' method. The default is FALSE, which
uses the sample covariance by default.
This argument determines whether Whitening transformation
should be used in ``BSL'' method with Warton's shrinkage. Whitening
transformation helps decorrelate the summary statistics, thus encouraging
sparsity of the synthetic likelihood covariance matrix. This might allow
heavier shrinkage to be applied without losing much accuracy, hence
allowing the number of simulations to be reduced. By default, NULL
represents no Whitening transformation. Otherwise this is enabled if a
Whitening matrix is provided. See estimateWhiteningMatrix for
the function to estimate the Whitening matrix.
A string argument indicating which type of model
misspecification to be used. The two options are "mean" and "variance".
Only used when method is ``BSLmisspec''. The default, NULL, means no
model misspecification is considered.
A numeric argument, parameter of the prior distribution
for "BSLmisspec" method. For mean adjustment, tau is the scale of
the Laplace distribution. For variance inflation, tau is the mean of
the exponential distribution. Only used when method is ``BSLmisspec''.
A logical value indicating whether parallel computing should
be used for simulation and summary statistic evaluation. The default is
FALSE. When model simulation is fast, it may be preferable to
perform serial or vectorised computations to avoid significant
communication overhead between workers. Parallel computation can only be
used if not using a vectorised simulation function, see MODEL
for options of vectorised simulation function.
A list of additional arguments to pass into the
foreach function. Only used when parallel computing is enabled,
default is NULL.
Deprecated, will be removed in the future, use model
instead. A string vector of parameter names, which must have the same
length as the parameter vector. The default is NULL.
A logical or numeric argument defining whether or by how
many iterations a posterior figure will be plotted during running. If
TRUE, a plot of approximate univariate posteriors based on the
current accepted samples will be shown every one thousand iterations.
The default is FALSE.
An integer indicating the verbose style. 0L
means no verbose messages will be printed. 1L uses a custom progress bar to
track the progress. 2L prints the iteration numbers (1:M) to track
the progress. The default is 1L.
Ziwen An, Leah F. South and Christopher Drovandi
Price2018BSL
An2019BSL
An2018BSL
ma2, cell, mgnk and
toad for examples. selectPenalty for a function
to tune the BSLasso tuning parameter and plot for functions
related to visualisation.
# \dontshow{
toy_sim <- function(n, theta) matrix(rnorm(n, theta), nrow = n)
toy_sum <- function(x) x
model <- newModel(fnSimVec = toy_sim, fnSum = toy_sum, theta0 = 0)
result_toy <- bsl(y = 1, n = 10, M = 100, model = model, covRandWalk = matrix(1),
method = "BSL", verbose = FALSE)
summary(result_toy)
plot(result_toy)
# }
if (FALSE) {
# This is just a minimal test run, please see package built-in examples for more
# comprehensive usages of the function
toy_sim <- function(n, theta) matrix(rnorm(n, theta), nrow = n)
toy_sum <- function(x) x
model <- newModel(fnSimVec = toy_sim, fnSum = toy_sum, theta0 = 0)
result_toy <- bsl(y = 1, n = 100, M = 1e4, model = model, covRandWalk = matrix(1),
method = "BSL", plotOnTheFly = TRUE)
summary(result_toy)
plot(result_toy)
}
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