marginal.lkl: Marginal model likelihood In lbelzile/BMAmevt: Multivariate Extremes: Bayesian Estimation of the Spectral Measure

Description

Estimates the marginal likelihood of a model, proceeding by simple Monte-Carlo integration under the prior distribution.

Usage

 ```1 2 3``` ```marginal.lkl(dat, likelihood, prior, Nsim = 300, displ = TRUE, Hpar, Nsim.min = Nsim, precision = 0, show.progress = floor(seq(1, Nsim, length.out = 20))) ```

Arguments

 `dat` The angular data set relative to which the marginal model likelihood is to be computed `likelihood` The likelihood function of the model. See `posteriorMCMC` for the required format. `prior` The prior distribution: of type ```function(type=c("r","d"), n ,par, Hpar, log, dimData )```, where `dimData` is the dimension of the sample space (e.g., for the two-dimensional simplex (triangle), `dimData=3`. Should return either a matrix with `n` rows containing a random parameter sample generated under the prior (if `type == "d"`), or the density of the parameter `par` (the logarithm of the density if `log==TRUE`. See `prior.pb` and `prior.nl` for templates. `Nsim` Total number of iterations to perform. `displ` logical. If `TRUE`, a plot is produced, showing the temporal evolution of the cumulative mean, with approximate confidence intervals of +/-2 estimated standard errors. `Hpar` A list containing Hyper-parameters to be passed to `prior`. `Nsim.min` The minimum number of iterations to be performed. `precision` the desired relative precision. See `MCpriorIntFun`. `show.progress` An vector of integers containing the times (iteration numbers) at which a message showing progression will be printed on the standard output.

Details

The function is a wrapper calling `MCpriorIntFun` with parameter `FUN` set to `likelihood`.

Value

The list returned by `MCpriorIntFun`. The estimate is the list's element named `emp.mean`.

Note

The estimated standard deviations of the estimates produced by this function should be handled with care:For "larger" models than the Pairwise Beta or the NL models, the likelihood may have infinite second moment under the prior distribution. In such a case, it is recommended to resort to more sophisticated integration methods, e.g. by sampling from a mixture of the prior and the posterior distributions. See the reference below for more details.

References

KASS, R. and RAFTERY, A. (1995). Bayes factors. Journal of the american statistical association , 773-795.

`marginal.lkl.pb`, `marginal.lkl.nl` for direct use with the implemented models.
 ``` 1 2 3 4 5 6 7 8 9 10``` ```## Not run: lklNL= marginal.lkl(dat=Leeds, likelihood=dnestlog, prior=prior.nl, Nsim=20e+3, displ=TRUE, Hpar=nl.Hpar, ) ## End(Not run) ```