safe_Laplace_approximation: Routine for computing the Laplace approximation of the...

In igbucur/MASSIVE: MASSIVE: Tractable and Robust Bayesian Learning of Many-Dimensional Instrumental Variable Models

Description

Routine for computing the Laplace approximation of the MASSIVE posterior using smart initialization points to find all the conjectured optima. This 'safe' version provides a fail-safe in case no optima are found with the smart initialization, in which case the "guess" strategy is used instead.

Usage

safe_Laplace_approximation(
  J,
  N,
  SS,
  sigma_G,
  prior_sd,
  post_fun = scaled_neg_log_posterior,
  gr_fun = scaled_neg_log_gradient,
  hess_fun = scaled_neg_log_hessian,
  opt_fun = robust_find_optimum,
  starting_points = "smart"
)

Arguments

J	Integer number of candidate instrumental variables.
N	Integer number of observations.
SS	Numeric matrix containing first- and second-order statistics.
sigma_G	Numeric vector of instrument standard deviations.
prior_sd	List of standard deviations for the parameter Gaussian priors.
post_fun	Function for computing the IV model posterior value.
gr_fun	Function for computing the IV model posterior gradient.
hess_fun	Function for computing the IV model posterior Hessian.
opt_fun	Function for finding the IV model posterior optima.
starting_points	Character vector indicating how to pick the starting points: "smart" or "guess" strategy?

Value

A list containing the Laplace approximation.

• optima - List of optima found.

• num_optima - Number of optima found on the posterior surface.

• evidence - Numeric value of total approximation model evidence.

Examples

J <- 5 # number of instruments
N <- 1000 # number of samples
parameters <- random_Gaussian_parameters(J) 
EAF <- runif(J, 0.1, 0.9) # EAF random values
dat <- generate_data_MASSIVE_model(N, 2, EAF, parameters)
safe_Laplace_approximation(
  J, N, dat$SS, binomial_sigma_G(dat$SS), 
  decode_IV_model(get_random_IV_model(J), 1, 0.01)
)

igbucur/MASSIVE documentation built on Oct. 26, 2020, 1:26 a.m.