aghq (version 0.4.1)

nested_quadrature: Nested, sparse Gaussian quadrature in AGHQ

Description

Compute a whole sequence of log normalizing constants for 1,3,5,...,k points, using only the function evaluations from the k-point nested rule.

Usage

nested_quadrature(optresults, k, ndConstruction = "product", ...)
adaptive_nested_quadrature(optresults, k, ndConstruction = "product", ...)
get_quadtable(p, k, ndConstruction = "product", ...)

Value

For get_quadtable, a pre-computed table of nodes for the k-point rule, with weights for the points from each of the 1,3,...,k-point rules, for passing to nested_quadrature. For nested_quadrature and adaptive_nested_quadrature, a named numeric vector of optresults$fn

values for each k.

Arguments

optresults

The results of calling aghq::optimize_theta(): see return value of that function. The dimension of the parameter p will be taken from optresults$mode.

k

Integer, the number of quadrature points to use.

ndConstruction

Create a multivariate grid using a product or sparse construction? Passed directly to mvQuad::createNIGrid(), see that function for further details.

...

Additional arguments to be passed to optresults$ff, see ?optimize_theta.

p

Dimension of the variable of integration.

Details

get_quadtable currently uses mvQuad to compute the nodes and weights. This will be replaced by a manual reading of the pre-tabulated nodes and weights.

nested_quadrature and adaptive_nested_quadrature take the log function values, just like optimize_theta(), and return the log of the base/adapted quadrature rule.

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(), normalize_logpost(), optimize_theta(), plot.aghq(), print.aghqsummary(), print.aghq(), print.laplacesummary(), print.laplace(), print.marginallaplacesummary(), summary.aghq(), summary.laplace(), summary.marginallaplace()

Examples

# Same setup as optimize_theta
logfteta <- function(eta,y) {
  sum(y) * eta - (length(y) + 1) * exp(eta) - sum(lgamma(y+1)) + eta
}
set.seed(84343124)
y <- rpois(10,5) # Mode should be sum(y) / (10 + 1)
truemode <- log((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)
)
opt_sparsetrust <- optimize_theta(funlist,1.5)