posterior.sample: Generate samples, and functions thereof, from an approximated...

In INBO-BMK/INLA: Full Bayesian Analysis of Latent Gaussian Models using Integrated Nested Laplace Approximations

Description

This function generate samples, and functions of those, from an approximated posterior of a fitted model (an inla-object)

Usage

     inla.posterior.sample(n = 1L, result, selection = list(),
                           intern = FALSE, use.improved.mean = TRUE,
                           add.names = TRUE, seed = 0L, num.threads = NULL,
                           verbose = FALSE)
     inla.posterior.sample.eval(fun, samples, return.matrix = TRUE, ...)
 

Arguments

n	Number of samples.
result	The inla-object, ie the output from an inla-call. The inla-object must be created with control.compute=list(config=TRUE).
selection	Select what part of the sample to return. By default, the whole sample is returned. selection is a named list with the name of the components of the sample, and what indices of them to return. Names include APredictor, Predictor, (Intercept), and otherwise names in the formula. The values of the list, is interpreted as indices. If they are negative, they are interpreted as 'not', a zero is interpreted as 'all', and positive indices are interpreted as 'only'. The names of elements of each samples refer to the indices in the full sample.
use.improved.mean	Logical. If TRUE then use the marginal mean values when constructing samples. If FALSE then use the mean in the Gaussian approximations.
intern	Logical. If TRUE then produce samples in the internal scale for the hyperparmater, if FALSE then produce samples in the user-scale. (For example log-precision (intern) and precision (user-scale))
add.names	Logical. If TRUE then add name for each elements of each sample. If FALSE, only add name for the first sample. (This save space.)
seed	Control the RNG of inla.qsample, see ?inla.qsample for further information. If seed=0L then GMRFLib will set the seed intelligently/at 'random'. If seed < 0L then the saved state of the RNG will be reused if possible, otherwise, GMRFLib will set the seed intelligently/at 'random'. If seed > 0L then this value is used as the seed for the RNG. If you want reproducible results, you ALSO need to control the seed for the RNG in R by controlling the variable .Random.seed or using the function set.seed, the example for how this can be done.
num.threads	The number of threads that can be used. num.threads>1L requires seed = 0L. Default value is controlled by inla.getOption("num.threads")
verbose	Logical. Run in verbose mode or not.
fun	The function to evaluate for each sample. Upon entry, the variable names defined in the model are defined as the value of the sample. The list of names are defined in result$misc$configs$contents where result is an inla-object. This includes predefined names for for the linear predictor (Predictor and APredictor), and the intercept ((Intercept) or Intercept). The hyperparameters are defined as theta, no matter if they are in the internal scale or not. The function fun can also return a vector.
samples	samples is the output from inla.posterior.sample()
return.matrix	Logical. If TRUE, then return the samples of fun as matrix, otherwise, as a list.
...	Additional arguments to fun

Details

The hyperparameters are sampled from the configurations used to do the numerical integration, hence if you want a higher resolution, you need to to change the int.stratey variable and friends. The latent field is sampled from the Gaussian approximation conditioned on the hyperparameters, but with a correction for the mean (default).

Set sparse-matrix library with inla.setOption(smtp=...) and number of threads by inla.setOption(num.threads=...).

Value

inla.posterior.sample returns a list of the samples, where each sample is a list with names hyperpar and latent, and with their marginal densities in logdens$hyperpar and logdens$latent and the joint density is in logdens$joint. inla.posterior.sample.eval return a list or a matrix of fun applied to each sample.

Author(s)

Havard Rue [e-mail]

Examples

  r = inla(y ~ 1 ,data = data.frame(y=rnorm(1)), control.compute = list(config=TRUE))
  samples = inla.posterior.sample(2,r)

  ## reproducible results:
  set.seed(1234)
  inla.seed = as.integer(runif(1)*.Machine$integer.max)
  x = inla.posterior.sample(100, r, seed = inla.seed)
  set.seed(1234)
  xx = inla.posterior.sample(100, r, seed = inla.seed)
  all.equal(x, xx)

 set.seed(1234)
 n = 25
 xx = rnorm(n)
 yy = rev(xx)
 z = runif(n)
 y = rnorm(n)
 r = inla(y ~ 1 + z + f(xx) + f(yy, copy="xx"),
         data = data.frame(y, z, xx, yy), 
         control.compute = list(config=TRUE),
         family = "gaussian")
 r.samples = inla.posterior.sample(100, r)
 
 fun = function(...) {
     mean(xx) - mean(yy)
 }
 f1 = inla.posterior.sample.eval(fun, r.samples)
 
 fun = function(...) {
     c(exp(Intercept), exp(Intercept + z))
 }
 f2 = inla.posterior.sample.eval(fun, r.samples)
 
 fun = function(...) {
     return (theta[1]/(theta[1] + theta[2]))
 }
 f3 = inla.posterior.sample.eval(fun, r.samples)

 ## Predicting nz new observations, and
 ## comparing the estimated one with the true one
 set.seed(1234)
 n = 100
 alpha = beta = s = 1
 z = rnorm(n)
 y = alpha + beta * z + rnorm(n, sd = s)
 r = inla(y ~ 1 + z, 
         data = data.frame(y, z), 
         control.compute = list(config=TRUE),
         family = "gaussian")
 r.samples = inla.posterior.sample(10^3, r)
 nz = 3
 znew = rnorm(nz)
 fun = function(zz = NA) {
     ## theta[1] is the precision
     return (Intercept + z * zz +
             rnorm(length(zz), sd = sqrt(1/theta[1])))
 }
 par(mfrow=c(1, nz))
 f1 = inla.posterior.sample.eval(fun, r.samples, zz = znew)
 for(i in 1:nz) {
     hist(f1[i, ], n = 100, prob = TRUE)
     m = alpha + beta * znew[i]
     xx = seq(m-4*s, m+4*s, by = s/100)
     lines(xx, dnorm(xx, mean=m, sd = s), lwd=2)
 }

INBO-BMK/INLA documentation built on Dec. 4, 2019, 11:43 p.m.