Create Samples for BAMLSS by Multivariate Normal Approximation

This sampler function for BAMLSS uses estimated parameters and the Hessian information to create samples from a multivariate normal distribution. Note that smoothing variance uncertainty is not accounted for, therefore, the resulting credible intervals are most likely too narrow.

sam_MVNORM(x, y = NULL, family = NULL, start = NULL,
  n.samples = 500, hessian = NULL, ...)

MVNORM(x, y = NULL, family = NULL, start = NULL,
  n.samples = 500, hessian = NULL, ...)

Arguments

x

The x list, as returned from function bamlss.frame, holding all model matrices and other information that is used for fitting the model. Or an object returned from function bamlss.

y

The model response, as returned from function bamlss.frame.

family

A bamlss family object, see family.bamlss.

start

A named numeric vector containing possible starting values, the names are based on function parameters.

n.samples

Sets the number of samples that should be generated.

hessian

The Hessian matrix that should be used. Note that the row and column names must be the same as the names of the parameters. If hessian = NULL the function uses optim to compute the Hessian if it is not provided within x.

...

Arguments passed to function optim.

Value

Function MVNORM() returns samples of parameters. The samples are provided as a

mcmc matrix.

Examples

## Simulated data example illustrating
## how to call the sampler function.
## This is done internally within
## the setup of function bamlss().
d <- GAMart()
f <- num ~ s(x1, bs = "ps")
bf <- bamlss.frame(f, data = d, family = "gaussian")

## First, find starting values with optimizer.
o <- with(bf, opt_bfit(x, y, family))
#> AICc 319.2483 logPost -171.078 logLik -149.306 edf 10.088 eps 9.3381 iteration   1
#> AICc 318.9038 logPost -171.536 logLik -148.922 edf 10.292 eps 0.2440 iteration   2
#> AICc 318.9028 logPost -171.603 logLik -148.896 edf 10.316 eps 0.0123 iteration   3
#> AICc 318.9028 logPost -171.604 logLik -148.895 edf 10.316 eps 0.0002 iteration   4
#> AICc 318.9028 logPost -171.604 logLik -148.895 edf 10.316 eps 0.0000 iteration   5
#> AICc 318.9028 logPost -171.604 logLik -148.895 edf 10.316 eps 0.0000 iteration   5
#> elapsed time:  0.03sec

## Sample.
samps <- with(bf, sam_MVNORM(x, y, family, start = o$parameters))
#> 
plot(samps)