inla.sample {INLA} | R Documentation

## Generate samples, and functions thereof, from an approximated posterior of a fitted model

### Description

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

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), and optional (and by default) corrected for the estimated skewness.

The log.density report is only correct when there is no constraints. With constraints, it correct the Gaussian part of the sample for the constraints.

After the sample is (optional) skewness corrected, the log.density is is not exact for correcting for constraints, but the error is very small in most cases.

### Usage

    inla.posterior.sample(
      n = 1L,
      result,
      selection = list(),
      intern = FALSE,
      use.improved.mean = TRUE,
      skew.corr = TRUE,
      add.names = TRUE,
      seed = 0L,
      num.threads = NULL,
      parallel.configs = TRUE,
      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. NOTE THAT USING THIS ARGUMENT WILL MAKE `inla.posterior.sample.eval` FAIL.
`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))
`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.
`skew.corr` | Logical. If `TRUE` then correct samples for skewness, if `FALSE`, do not correct samples for skewness (ie use the Gaussian).
`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` | See the same argument in `?inla.qsample` for further information. In order to produce reproducible results, you ALSO need to make sure the RNG in R is in the same state, see example below. When `seed` is non-zero, `num.threads` is forced to "1:1" and parallel.configs is set to `FALSE`, since parallel sampling would not produce a reproducible sequence of pseudo-random numbers.
`num.threads` | The number of threads to use in the format 'A:B' defining the number threads in the outer (A) and inner (B) layer for nested parallelism. A '0' will be replaced intelligently. `seed!=0` requires serial comptuations.
`parallel.configs` | Logical. If `TRUE` and not on Windows, then try to run each configuration in parallel (not Windows) using `A` threads (see `num.threads`), where each of them is using `B:0` 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. To simplify usage, `fun` can also be a vector character's. In this case `fun` it is interpreted as (strict) variable names, and a function is created that return these variables: if argument `fun` equals `c("Intercept", "a[1:2]")`, then this is equivalent to pass `function() return(c(get('Intercept'), get('a[1:2]')))`.
`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`

### 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 hrue@r-inla.org and Cristian Chiuchiolo cristian.chiuchiolo@kaust.edu.sa

### Examples

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

      ## reproducible results:
      inla.seed = as.integer(runif(1)*.Machine$integer.max)
      set.seed(12345)
      x = inla.posterior.sample(10, r, seed = inla.seed, num.threads="1:1")
      set.seed(12345)
      xx = inla.posterior.sample(10, r, seed = inla.seed, num.threads="1.1")
      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(10, 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)

     ## just return samples of the intercept
     intercepts = inla.posterior.sample.eval("Intercept", r.samples)

     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)
     }

     ##
     ## Be aware that using non-clean variable names might be a little tricky
     ##
     n <- 100
     X <- matrix(rnorm(n^2), n, 2)
     x <- X[, 1]
     xx <- X[, 2]
     xxx <- x*xx

     y <- 1 + 2*x + 3*xx + 4*xxx + rnorm(n, sd = 0.01)

     r <- inla(y ~ X[, 1]*X[, 2],
               data = list(y = y, X = X),
               control.compute = list(config = TRUE))
     print(round(dig = 4, r$summary.fixed[,"mean"]))

     sam <- inla.posterior.sample(100, r)
     sam.extract <- inla.posterior.sample.eval(
         (function(...) {
             beta.1 <- get("X[, 1]")
             beta.2 <- get("X[, 2]")
             beta.12 <- get("X[, 1]:X[, 2]")
             return(c(Intercept, beta.1, beta.2, beta.12))
         }), sam)
     print(round(dig = 4, rowMeans(sam.extract)))

     ## a simpler form can also be used here, and in the examples below
     sam.extract <- inla.posterior.sample.eval(
                    c("Intercept", "X[, 1]", "X[, 2]", "X[, 1]:X[, 2]"), sam)
     print(round(dig = 4, rowMeans(sam.extract)))

     r <- inla(y ~ x + xx + xxx,
               data = list(y = y, x = x, xx = xx, xxx = xxx),
               control.compute = list(config = TRUE))

     sam <- inla.posterior.sample(100, r)
     sam.extract <- inla.posterior.sample.eval(
         (function(...) {
             return(c(Intercept, x, xx, xxx))
         }), sam)
     print(round(dig = 4, rowMeans(sam.extract)))

     sam.extract <- inla.posterior.sample.eval(c("Intercept", "x", "xx", "xxx"), sam)
     print(round(dig = 4, rowMeans(sam.extract)))

     r <- inla(y ~ x*xx,
               data = list(y = y, x = x, xx = xx),
               control.compute = list(config = TRUE))

     sam <- inla.posterior.sample(100, r)
     sam.extract <- inla.posterior.sample.eval(
         (function(...) {
             return(c(Intercept, x, xx, get("x:xx")))
         }), sam)
     print(round(dig = 4, rowMeans(sam.extract)))

     sam.extract <- inla.posterior.sample.eval(c("Intercept", "x", "xx", "x:xx"), sam)
     print(round(dig = 4, rowMeans(sam.extract)))

[Package INLA version 26.02.05 Index]