optimize_theta: Obtain function information necessary for performing...

In aghq: Adaptive Gauss Hermite Quadrature for Bayesian Inference

Obtain function information necessary for performing quadrature

Description

This function computes the two pieces of information needed about the log posterior to do adaptive quadrature: the mode, and the hessian at the mode. It is designed for use within aghq::aghq, but is exported in case users need to debug the optimization process and documented in case users want to write their own optimizations.

Usage

optimize_theta(ff, startingvalue, control = default_control(), ...)

Arguments

ff	A list with three elements: fn: function taking argument theta and returning a numeric value representing the log-posterior at theta gr: function taking argument theta and returning a numeric vector representing the gradient of the log-posterior at theta he: function taking argument theta and returning a numeric matrix representing the hessian of the log-posterior at theta The user may wish to use numDeriv::grad and/or numDeriv::hessian to obtain these. Alternatively, the user may consider the TMB package. This list is deliberately formatted to match the output of TMB::MakeADFun.
startingvalue	Value to start the optimization. ff$fn(startingvalue), ff$gr(startingvalue), and ff$he(startingvalue) must all return appropriate values without error.
control	A list with elements method: optimization method to use: 'sparse_trust' (default): trustOptim::trust.optim with method = 'sparse' 'SR1' (default): trustOptim::trust.optim with method = 'SR1' 'trust': trust::trust 'BFGS': optim(...,method = "BFGS") Default is 'sparse_trust'. optcontrol: optional: a list of control parameters to pass to the internal optimizer you chose. The aghq package uses sensible defaults.
...	Additional arguments to be passed to ff$fn, ff$gr, and ff$he.

Value

A list with elements

• ff: the function list that was provided

• mode: the mode of the log posterior

• hessian: the hessian of the log posterior at the mode

• convergence: specific to the optimizer used, a message indicating whether it converged

See Also

Other quadrature: aghq(), get_hessian(), get_log_normconst(), get_mode(), get_nodesandweights(), get_numquadpoints(), get_opt_results(), get_param_dim(), laplace_approximation(), marginal_laplace_tmb(), marginal_laplace(), nested_quadrature(), normalize_logpost(), plot.aghq(), print.aghqsummary(), print.aghq(), print.laplacesummary(), print.laplace(), print.marginallaplacesummary(), summary.aghq(), summary.laplace(), summary.marginallaplace()

Examples

# Poisson/Exponential example
logfteta <- function(eta,y) {
  sum(y) * eta - (length(y) + 1) * exp(eta) - sum(lgamma(y+1)) + eta
}

y <- rpois(10,5) # Mode should be (sum(y) + 1) / (length(y) + 1)

objfunc <- function(x) logfteta(x,y)
funlist <- list(
  fn = objfunc,
  gr = function(x) numDeriv::grad(objfunc,x),
  he = function(x) numDeriv::hessian(objfunc,x)
)

optimize_theta(funlist,1.5)
optimize_theta(funlist,1.5,control = default_control(method = "trust"))
optimize_theta(funlist,1.5,control = default_control(method = "BFGS"))

aghq documentation built on June 7, 2023, 5:10 p.m.