laplace.evt {BMAmevt}

Laplace approximation of a model marginal likelihood by Laplace approximation.

Description

Approximation of a model marginal likelihood by Laplace method.

Usage

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

A list made of

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