BSL (version 0.1.1)

mgnk: The multivariate G&K example

Description

Here we provide the data and tuning parameters required to reproduce the results from the multivariate G & K (Drovandi and Pettitt, 2011) example from An et al. (2018).

The function mgnk_sim(theta_tilde,sim_options) simulates from the multivariate G & K model.

The function mgnk_sum(y) calculates the summary statistics for the multivariate G & K example.

Usage

mgnk_sim(theta_tilde, sim_options)
mgnk_sum(y)

Arguments

theta_tilde

A vector with 15 elements for the proposed model parameters.

sim_options

A list of options for simulating data from the model. For this example, the list contains

• T: The number of observations in the data.

• J: The number of variables in the data.

• bound: A matrix of boundaries for the uniform prior.

y

A T \(x\) J matrix of data.

An example dataset

We use the foreign currency exchange data available from http://www.rba.gov.au/statistics/historical-data.html as in An et al. (2018).

• data: A 1651 \(x\) 3 matrix of data.

• sim_options: Values of sim_options relevant to this example.

• start: A vector of suitable initial values of the parameters for MCMC.

• cov: Covariance matrix of the multivariate normal random walk, in the form of a \(15 x 15\) matrix.

Details

It is not practical to give a reasonable explanation of this example through R documentation given the number of equations involved. We refer the reader to the BSLasso paper (An et al., 2018) at https://eprints.qut.edu.au/102263/ for information on the model and summary statistic used in this example.

References

An, Z., South, L. F., Nott, D. J. & Drovandi, C. C. (2018). Accelerating Bayesian synthetic likelihood with the graphical lasso. https://eprints.qut.edu.au/102263/

Drovandi, C. C. and Pettitt, A. N. (2011). Likelihood-free Bayesian estimation of multivariate quantile distributions. Computational Statistics and Data Analysis, 55(9):2541-2556.

Examples

# NOT RUN {
require(doParallel) # You can use a different package to set up the parallel backend

# Loading the data for this example
data(mgnk)

# Opening up the parallel pools using doParallel
cl <- makeCluster(detectCores())
registerDoParallel(cl)

# Performing BSL
resultMgnkBSL <- bsl(mgnk$data, n = 60, M = 80000, start = mgnk$start, cov_rw = mgnk$cov,
                 fn_sim = mgnk_sim, fn_sum = mgnk_sum, sim_options = mgnk$sim_options, 
                 parallel = TRUE, parallel_packages = c('BSL', 'MASS', 'elliplot'),
                 theta_names = c('a1','b1','g1','k1','a2','b2','g2','k2','a3','b3','g3','k3'
                 ,'delta12','delta13','delta23'))
summary(resultMgnkBSL)
plot(resultMgnkBSL, thin = 20)

# Performing tuning for BSLasso
lambda_all <- list(exp(seq(-2.5,0.5,length.out=20)), exp(seq(-2.5,0.5,length.out=20)), 
                   exp(seq(-4,-0.5,length.out=20)), exp(seq(-5,-2,length.out=20)))

sp_mgnk <- selectPenalty(ssy = mgnk_sum(mgnk$data), n = c(15, 20, 30, 50), lambda_all,
                 theta = mgnk$start, M = 100, sigma = 1.5, fn_sim = mgnk_sim, 
                 fn_sum = mgnk_sum, sim_options = mgnk$sim_options, standardise = TRUE, 
                 parallel_sim = TRUE, parallel_sim_packages = c('BSL', 'MASS', 'elliplot'),
                 parallel_main = TRUE)
sp_mgnk
plot(sp_mgnk)

# Performing BSLasso with a fixed penalty
resultMgnkBSLasso <- bsl(mgnk$data, n = 20, M = 80000, start = mgnk$start, cov_rw = mgnk$cov,
                 fn_sim = mgnk_sim, fn_sum = mgnk_sum, sim_options = mgnk$sim_options,
                 penalty = 0.3, standardise = TRUE, parallel = TRUE,
                 parallel_packages = c('BSL', 'MASS', 'elliplot'),
                 theta_names = c('a1','b1','g1','k1','a2','b2','g2','k2','a3','b3','g3','k3',
                 'delta12','delta13','delta23'))
summary(resultMgnkBSLasso)
plot(resultMgnkBSLasso, thin = 20)

# Plotting the results together for comparison
combinePlotsBSL(resultMgnkBSL, resultMgnkBSLasso, thin = 20)

# Closing the parallel pools
stopCluster(cl)
# }
# NOT RUN {
# }