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 258.2817 logPost -119.943 logLik -122.265 edf 6.7683 eps 1.1731 iteration   1
#> AICc 257.9515 logPost -119.641 logLik -121.862 edf 6.9996 eps 0.0160 iteration   2
#> AICc 257.9901 logPost -119.640 logLik -121.841 edf 7.0389 eps 0.0014 iteration   3
#> AICc 257.9911 logPost -119.640 logLik -121.840 edf 7.0400 eps 0.0000 iteration   4
#> AICc 257.9911 logPost -119.640 logLik -121.840 edf 7.0400 eps 0.0000 iteration   4
#> elapsed time:  0.05sec

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