# bf1skel: Computation of Bayes factors at the skeleton points In geoBayes: Analysis of Geostatistical Data using Bayes and Empirical Bayes Methods

## Description

Function to compute the Bayes factors from MCMC samples.

## Usage

 ```1 2``` ```bf1skel(runs, bfsize1 = 0.8, method = c("RL", "MW"), reference = 1, transf = c("no", "mu", "wo")) ```

## 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 a transformed sample for the computations. If `"no"` or `FALSE`, it doesn't. If `"mu"` or `TRUE`, it uses the samples for the mean. If `"wo"` it uses an alternative transformation. The latter can be used only for the families indicated by `.geoBayes_models\$haswo`.

## 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, 72(1), 289-298.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34``` ```## 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) ```

geoBayes documentation built on May 14, 2018, 1:03 a.m.