posterior.predictive3D {BMAmevt} R Documentation

## Posterior predictive density on the simplex, for three-dimensional extreme value models.

### Description

Computes an approximation of the predictive density based on a posterior parameters sample. Only allowed in the three-dimensional case.

### Usage

```posterior.predictive3D(
post.sample,
densityGrid,
from = post.sample\$Nbin + 1,
to = post.sample\$Nsim,
thin = 40,
npoints = 40,
eps = 10^(-3),
equi = T,
displ = T,
...
)
```

### Arguments

 `post.sample` A posterior sample as returned by `posteriorMCMC` `densityGrid` A function returning a `npoints*npoints` matrix, representing a discretized version of the spectral density on the two dimensional simplex. The function should be compatible with `dgridplot`. In particular, it must use `discretize` to produce the discretization grid. It must be of type ```function(par, npoints, eps, equi, displ,invisible, ... )```. See Details below. `from` Integer or `NULL`. If `NULL`, the default value is used. Otherwise, should be greater than `post.sample\$Nbin`. Indicates the index where the averaging process should start. Default to `post.sample\$Nbin +1` `to` Integer or `NULL`. If `NULL`, the default value is used. Otherwise, must be lower than `Nsim+1`. Indicates where the averaging process should stop. Default to `post.sample\$Nsim`. `thin` Thinning interval. `npoints` The number of grid nodes on the squared grid containing the desired triangle. `eps` Positive number: minimum distance from any node inside the simplex to the simplex boundary `equi` logical. Is the simplex represented as an equilateral triangle (if `TRUE`) or a right triangle (if `FALSE`) ? `displ` logical. Should a plot be produced ? `...` Additional graphical parameters and arguments to be passed to `contour` and `image`.

### Details

The posterior predictive density is approximated by averaging the densities produced by the function `densityGrid(par, npoints, eps, equi, displ,invisible, ...)` for `par` in a subset of the parameters sample stored in `post.sample`. The arguments of `densityGrid` must be

• `par`: A vector containing the parameters.

• `npoints, eps, equi`: Discretization parameters to be passed to `dgridplot`.

• `displ`: logical. Should a plot be produced ?

• `invisible`: logical. Should the result be returned as `invisible` ?

• `...` additional arguments to be passed to `dgridplot`

Only a sub-sample is used: one out of `thin` parameters is used (thinning). Further, only the parameters produced between time `from` and time `to` (included) are kept.

### Value

A `npoints*npoints` matrix: the posterior predictive density.

### Note

The computational burden may be high: it is proportional to `npoints^2`. Therefore, the function assigned to `densityGridplot` should be optimized, typically by calling `.C` with an internal, user defined `C` function.

Anne Sabourin

### See Also

`dgridplot`, `posteriorMCMC`.

[Package BMAmevt version 1.0.4 Index]