Computation of Bayes factors at the skeleton points

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Description

Function to compute the Bayes factors from MCMC samples.

Usage

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bf1skel(runs, bfsize1 = 0.8, method = c("RL", "MW"), reference = 1,
  transf = FALSE, binwo = TRUE)

Arguments

runs

A list with outputs from the function mcsglmm or mcstrga.

bfsize1

A scalar or vector of the same length as runs with all integer values or all values in (0, 1]. How many samples (or what proportion of the sample) to use for estimating the Bayes factors at the first stage. The remaining sample will be used for estimating the Bayes factors in the second stage. Setting it to 1 will perform only the first stage.

method

Which method to use to calculate the Bayes factors: Reverse logistic or Meng-Wong.

reference

Which model goes in the denominator.

transf

Whether to use the transformed sample mu for the computations. Otherwise it uses z.

binwo

For the binomial family, if use workaround when the untransformed sample is used.

Details

Computes the Bayes factors using method with respect to reference.

Value

A list with components

  • logbf A vector containing logarithm of the Bayes factors.

  • logLik1 logLik2 Matrices with the values of the log-likelihood computed from the samples for each model at the first and second stages.

  • isweights A vector with the importance sampling weights for computing the Bayes factors at new points that will be used at the second stage. Used internally in bf2new and bf2optim.

  • controlvar A matrix with the control variates computed at the samples that will be used in the second stage.

  • sample2 The MCMC sample for mu or z that will be used in the second stage. Used internally in bf2new and bf2optim.

  • N1, N2 Vectors containing the sample sizes used in the first and second stages.

  • distmat Matrix of distances between locations.

  • betm0, betQ0, ssqdf, ssqsc, tsqdf, tsqsc, dispersion, response, weights, modelmatrix, locations, family, corrfcn, transf Model parameters used internally in. bf2new and bf2optim.

  • pnts A list containing the skeleton points. Used internally in bf2new and bf2optim.

References

Geyer, C. J. (1994). Estimating normalizing constants and reweighting mixtures. Technical report, University of Minnesota.

Meng, X. L., & Wong, W. H. (1996). Simulating ratios of normalizing constants via a simple identity: A theoretical exploration. Statistica Sinica, 6, 831-860.

Roy, V., Evangelou, E., and Zhu, Z. (2015). Efficient estimation and prediction for the Bayesian spatial generalized linear mixed model with flexible link functions. Biometrics. http://dx.doi.org/10.1111/biom.12371

Examples

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## Not run: 
data(rhizoctonia)
### Define the model
corrf <- "spherical"
kappa <- 0
ssqdf <- 1
ssqsc <- 1
betm0 <- 0
betQ0 <- .01
linkp <- "probit"
### Skeleton points
philist <- c(100, 140, 180)
omglist <- c(.5, 1)
parlist <- expand.grid(phi=philist, linkp=linkp, omg=omglist, kappa = kappa)
### MCMC sizes
Nout <- 100
Nthin <- 1
Nbi <- 0
### Take MCMC samples
runs <- list()
for (i in 1:NROW(parlist)) {
  runs[[i]] <- mcsglmm(Infected ~ 1, 'binomial', rhizoctonia, weights = Total,
                       atsample = ~ Xcoord + Ycoord,
                       Nout = Nout, Nthin = Nthin, Nbi = Nbi,
                       betm0 = betm0, betQ0 = betQ0,
                       ssqdf = ssqdf, ssqsc = ssqsc,
                       phistart = parlist$phi[i], omgstart = parlist$omg[i],
                       linkp = parlist$linkp[i], kappa = parlist$kappa[i],
                       corrfcn = corrf, phisc = 0, omgsc = 0)
}
bf <- bf1skel(runs)
bf$logbf

## End(Not run)