# laplace.evt: Laplace approximation of a model marginal likelihood by... In lbelzile/BMAmevt: Multivariate Extremes: Bayesian Estimation of the Spectral Measure

## Description

Approximation of a model marginal likelihood by Laplace method.

## Usage

 ```1 2``` ``` laplace.evt(mode = NULL, npar = 4, likelihood, prior, Hpar, data, link, unlink, method = "L-BFGS-B") ```

## Arguments

 `mode` The parameter vector (on the “unlinked” scale, i.e. before transformation to the real line) which maximizes the posterior density, or `NULL`. `npar` The size of the parameter vector. Default to four. `likelihood` The likelihood function, e.g. `dpairbeta` or `dnestlog` `prior` The prior density (takes an “unlinked” parameter as argument and returns the density of the `linked` parameter) `Hpar` The prior hyper parameter list. `data` The angular dataset `link` The link function, from the “classical” or “unlinked” parametrization onto the real line. (e.g. `log` for the PB model, an `logit` for the NL model) `unlink` The inverse link function (e.g. `exp` for the PB model and `invlogit` for the NL model) `method` The optimization method to be used. Default to `"L-BFGS-B"`.

## Details

The posterior mode is either supplied, or approximated by numerical optimization. For an introduction about Laplace's method, see e.g. Kass and Raftery, 1995 and the references therein.

## Value

mode

the parameter (on the unlinked scale) deemed to maximize the posterior density. This is equal to the argument if the latter is not null.

value

The value of the posterior, evaluated at `mode`.

laplace.llh

The logarithm of the estimated marginal likelihood

invHess

The inverse of the estimated hessian matrix at `mode`

## References

KASS, R.E. and RAFTERY, A.E. (1995). Bayes Factors. Journal of the American Statistical Association, Vol. 90, No.430

lbelzile/BMAmevt documentation built on May 17, 2018, 12:16 p.m.