posteriorWeights {BMAmevt}

Posterior model weights

Description

Approximates the models' posterior weights by simple Monte Carlo integration

Usage

posteriorWeights(
  dat,
  HparList = list(get("pb.Hpar"), get("nl.Hpar")),
  lklList = list(get("dpairbeta"), get("dnestlog")),
  priorList = list(get("prior.pb"), get("prior.nl")),
  priorweights = c(0.5, 0.5),
  Nsim = 20000,
  Nsim.min = 10000,
  precision = 0.05,
  seed = 1,
  kind = "Mersenne-Twister",
  show.progress = floor(seq(1, Nsim, length.out = 10)),
  displ = FALSE
)

Arguments

dat

The angular data set relative to which the marginal model likelihood is to be computed

HparList

A list containing the hyper Parameter for the priors in each model. (list of lists).

lklList

A list containing the likelihood functions of each model

priorList

A list containing the prior definitions of each model.

priorweights

A vector of positive weights, summing to one: the prior marginal weights of each model.

Nsim

The maximum number of iterations to be performed.

Nsim.min

The minimum number of iterations to be performed.

precision

the desired relative precision. See MCpriorIntFun.

seed

The seed to be set via set.seed.

kind

The kind of random numbers generator. Default to "Mersenne-Twister". See set.seed for details.

show.progress

An vector of integers containing the times (iteration numbers) at which a message showing progression will be printed on the standard output.

displ

Logical. Should convergence monitoring plots be issued ?

Details

if J is the number of models, the posterior weights are given by

postW(i) = priorW(i)*lkl(i)/ (\sum_{j=1,\dots,J} priorW(j)*lkl(j)),

where lkl(i) stands for the Monte-Carlo estimate of the marginal likelihood of model i and priorW(i) is the prior weight defined in priorweights[i]. For more explanations, see the reference below The confidence intervals are obtained by adding/subtracting two times the estimated standard errors of the marginal likelihood estimates. The latter are only estimates, which interpretation may be misleading: See the note in section marginal.lkl

Value

A matrix of 6 columns and length(priorweights) rows. The columns contain respectively the posterior model weights (in the same order as in priorweights), the lower and the upper bound of the confidence interval (see Details), the marginal model weights, the estimated standard error of the marginal likelihood estimators, and the number of simulations performed.

References

HOETING, J., MADIGAN, D., RAFTERY, A. and VOLINSKY, C. (1999). Bayesian model averaging: A tutorial. Statistical science 14, 382-401.

Examples

data(pb.Hpar)
data(nl.Hpar)
set.seed(5)
mixDat=rbind(rpairbeta(n=10,dimData=3, par=c(0.68,3.1,0.5,0.5)),
  rnestlog(n=10,par=c(0.68,0.78, 0.3,0.5)))
posteriorWeights (dat=mixDat,
                  HparList=list(get("pb.Hpar"),get("nl.Hpar")),
                  lklList=list(get("dpairbeta"), get("dnestlog")),
                  priorList=list(get("prior.pb"), get("prior.nl")),
                  priorweights=c(0.5,0.5),
                  Nsim=1e+3,
                  Nsim.min=5e+2, precision=0.1,
                  displ=FALSE)
## Not run: posteriorWeights (dat=mixDat,
                  HparList=list(get("pb.Hpar"),get("nl.Hpar")),
                  lklList=list(get("dpairbeta"), get("dnestlog")),
                  priorList=list(get("prior.pb"), get("prior.nl")),
                  priorweights=c(0.5,0.5),
                  Nsim=20e+3,
                  Nsim.min=10e+3, precision=0.05,
                  displ=TRUE)
## End(Not run)