MultiGHQuad (version 1.2.0)

init.quad: Q-dimensional grid of quadrature points.

Description

Creates a flattened, rotated grid that incorporates correlation through an eigenvalue decomposition of the covariance matrix.

Usage

init.quad(Q = 2, prior = list(mu = rep(0, Q), Sigma = diag(Q)), adapt = NULL, ip = 6, prune = FALSE, forcePD = FALSE, debug = FALSE)

Arguments

Q

Number of dimensions. Defaults to 2. Only required when mu and Sigma are not provided.

prior

List of prior mean mu, = vector, and covariance matrix Sigma = matrix, defaults to zero vector and identity matrix respectively.

adapt

List of adaptive mean mu, = vector, and covariance matrix Sigma = matrix, if NULL no adaptation is used. Defaults to NULL.

ip

Number of quadrature points per dimension. Defaults to 6. Note that the total number of quadrature points is ip^Q.

prune

Logical, should quadrature points with a very low weight be removed? Defaults to false. See details.

forcePD

Logical, should adapt and prior arguments be forced to the neares positive definite matrix - if not already PD? If TRUE (Default: FALSE), nearPD is used to arrive at the closest PD matrix.

debug

Logical, draws debugging plots when true.

Value

A list with a matrix X of ip^Q by Q quadrature points and a vector W of length ip^Q associated weights.

Details

Creates a Q-dimensional grid by calling expand.grid on Q vectors of unidimensional quadrature points obtained with gaussHermiteData. The grid is then corrected for a prior distribution, and can optionally be adapted around a previous estimate. The resultant grid can be pruned to remove quadrature points that are unlikely to add information.

See Also

gaussHermiteData, used to create unidimensional quadrature points, and eval.quad for evaluating the integral.

Examples

### basic quadrature grid /w pruning.
mu <- c(0,0)
sigma <- matrix(c(1,.5,.5,1),2,2)
grid <- init.quad(Q = 2, prior = list(mu = mu, Sigma = sigma), ip = 10, prune = FALSE)
grid2 <- init.quad(Q = 2, prior = list(mu = mu, Sigma = sigma), ip = 10, prune = TRUE)
library(mvtnorm)
normal <- rmvnorm(1000, mu, sigma)
# noise
plot(normal, xlim = c(-6,6), ylim = c(-6,6), pch = 19, col = rgb(0,0,0,.5))
# full quad grid
points(grid$X, cex = exp(grid$W)/max(exp(grid$W))*4, col = 'red', pch = 20)
# pruned quad grid
points(grid2$X, cex = exp(grid2$W)/max(exp(grid2$W))*4, col = 'green', pch = 20)


### Adaptive quadrature grid
prior <- list(mu = c(0,0), Sigma = matrix(c(1,.5,.5,1),2,2))
adapt <- list(mu = c(-2,2), Sigma = prior$Sigma / 2)
grid <- init.quad(Q = 2, prior, ip = 10, prune = FALSE)
library(mvtnorm)
normal <- rmvnorm(1000, adapt$mu, adapt$Sigma)
# noise, centered at (-2, 2)
plot(normal, xlim = c(-6,6), ylim = c(-6,6), pch = 19, col = rgb(0,0,0,.5))
# initial quad grid, centered at (0, 0)
points(grid$X, cex = exp(grid$W)/max(exp(grid$W))*4, col = 'red', pch = 20)
# adapted grid
grid2 <- init.quad(Q =2, prior, adapt = adapt, ip = 10, prune = TRUE)
points(grid2$X, cex = exp(grid2$W)/max(exp(grid2$W))*4, col = 'green', pch = 20)
# the grid is adapted to the latest estimate, but weighted towards the prior