# mcstrga: MCMC samples from the transformed Gaussian model In geoBayes: Analysis of Geostatistical Data using Bayes and Empirical Bayes Methods

## Description

Draw MCMC samples from the transformed Gaussian model with known link function

## Usage

 ```1 2 3 4``` ```mcstrga(formula, data, weights, subset, atsample, Nout, Nthin = 1, Nbi = 0, betm0, betQ0, ssqdf, ssqsc, tsqdf, tsqsc, phipars, omgpars, corrfcn = c("matern", "spherical", "powerexponential"), kappa, linkp, phisc, omgsc, zstart, phistart, omgstart, longlat = FALSE, test = FALSE) ```

## Arguments

 `formula` A representation of the model in the form `response ~ terms`. The response must be set to `NA`'s at the prediction locations (see the example in `mcsglmm` for how to do this using `stackdata`). At the observed locations the response is assumed to be a total of replicated measurements. The number of replications is inputted using the argument `weights`. `data` An optional data frame containing the variables in the model. `weights` An optional vector of weights. Number of replicated samples. `subset` An optional vector specifying a subset of observations to be used in the fitting process. `atsample` A formula in the form `~ x1 + x2 + ... + xd` with the coordinates of the sampled locations. `Nout` Number of MCMC samples to return. `Nthin` The thinning of the MCMC algorithm. `Nbi` The burn-in of the MCMC algorithm. `betm0` Prior mean for beta (a vector or scalar). `betQ0` Prior standardised precision (inverse variance) matrix. Can be a scalar, vector or matrix. The first two imply a diagonal with those elements. Set this to 0 to indicate a flat improper prior. `ssqdf` Degrees of freedom for the scaled inverse chi-square prior for the partial sill parameter. `ssqsc` Scale for the scaled inverse chi-square prior for the partial sill parameter. `tsqdf` Degrees of freedom for the scaled inverse chi-square prior for the measurement error parameter. `tsqsc` Scale for the scaled inverse chi-square prior for the measurement error parameter. `phipars` Parameters for the generalized inverse gamma prior for the range parameter `phi`. A four dimensional vector with parameters scale, shape, exponent, location in that order. See `mcsglmm`. `omgpars` Parameters for the generalized inverse gamma prior for the relative nugget parameter `omg`. A four dimensional vector with parameters scale, shape, exponent, location in that order. See `mcsglmm`. `corrfcn` Spatial correlation function. See `ebsglmm` for details. `kappa` Spatial correlation parameter. Smoothness parameter for Matern, exponent for the power family. `linkp` The exponent of the Box-Cox transformation. `phisc` Random walk parameter for `phi`. Smaller values increase the acceptance ratio. Set this to 0 for fixed `phi`. In this case the fixed value is given in the argument `phistart`. `omgsc` Random walk parameter for `omg`. Smaller values increase the acceptance ratio. Set this to 0 for fixed `omg`. In this case the fixed value is given in the argument `omgstart`. `zstart` Optional starting value for the MCMC for the GRF. This can be either a scalar, a vector of size n where n is the number of sampled locations. `phistart` Optional starting value for the MCMC for the spatial range parameter `phi`. Defaults to the mean of its prior. If `phisc` is 0, then this argument is required and it corresponds to the fixed value of `phi`. `omgstart` Optional starting value for the MCMC for the relative nugget parameter `omg`. Defaults to the mean of its prior. If `omgsc` is 0, then this argument is required and itcorresponds to the fixed value of `omg`. `longlat` How to compute the distance between locations. If `FALSE`, Euclidean distance, if `TRUE` Great Circle distance. See `spDists`. `test` Whether this is a trial run to monitor the acceptance ratio of the random walk for `phi` and `omg`. If set to `TRUE`, the acceptance ratio will be printed on the screen every 100 iterations of the MCMC. Tune the `phisc` and `omgsc` parameters in order to achive 20 to 30% acceptance. Set this to a positive number to change the default 100. No thinning or burn-in are done when testing.

## Details

Simulates from the posterior distribution of this model.

## Value

A list containing the MCMC samples and other variables as follows:

• `z` A matrix containing the MCMC samples for the spatial random field. Each column is one sample.

• `mu` A matrix containing the MCMC samples for the mean response (a transformation of z). Each column is one sample.

• `beta` A matrix containing the MCMC samples for the regressor coefficients. Each column is one sample.

• `ssq` A vector with the MCMC samples for the partial

• `tsq` A vector with the MCMC samples for the measurement error variance.

• `phi` A vector with the MCMC samples for the spatial range parameter.

• `omg` A vector with the MCMC samples for the relative nugget parameter.

• `nu` The link function parameter translated to numeric code used internally.

• `logLik` A vector containing the value of the log-likelihood evaluated at each sample.

• `acc_ratio` The acceptance ratio for the joint update of the parameters `phi` and `omg`.

• `sys_time` The total computing time for the MCMC sampling.

• `Nout`, `Nbi`, `Nthin` As in input. Used internally in other functions.

• `response` The average of the response variable at the observed locations, i.e. its value divided by the corresponding weight. Used internally in other functions.

• `weights` The response weights at the observed locations. Used internally in other functions.

• `modelmatrix` The model matrix at the observed locations. Used internally in other functions.

• `family` As in input. Used internally in other functions.

• `betm0`, `betQ0`, `ssqdf`, `ssqsc`, `corrfcn`, `kappa`, `tsqdf`, `tsqsc` As in input. Used internally in other functions.

• `locations` Coordinates of the observed locations. Used internally in other functions.

• `whichobs` A logical vector indicated which rows in the data and in the MCMC samples for the spatial random field correspond to the observed locations.

## 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 35 36 37 38 39 40 41 42 43 44 45 46 47``` ```## Not run: ### Load the data data(rhizoctonia) rhiz <- na.omit(rhizoctonia) rhiz\$IR <- rhiz\$Infected/rhiz\$Total # Incidence rate of the # rhizoctonia disease ### Define the model corrf <- "spherical" ssqdf <- 1 ssqsc <- 1 tsqdf <- 1 tsqsc <- 1 betm0 <- 0 betQ0 <- diag(.01, 2, 2) phiprior <- c(200, 1, 1000, 100) # U(100, 300) phisc <- 1 omgprior <- c(3, 1, 1000, 0) # U(0, 3) omgsc <- 1.3 linkp <- 1 ## MCMC parameters Nout <- 100 Nbi <- 0 Nthin <- 1 samplt <- mcstrga(Yield ~ IR, data = rhiz, atsample = ~ Xcoord + Ycoord, corrf = corrf, Nout = Nout, Nthin = Nthin, Nbi = Nbi, betm0 = betm0, betQ0 = betQ0, ssqdf = ssqdf, ssqsc = ssqsc, tsqdf = tsqdf, tsqsc = tsqsc, phipars = phiprior, omgpars = omgprior, linkp = linkp, phisc = phisc, omgsc = omgsc, test=10) sample <- mcstrga(Yield ~ IR, data = rhiz, atsample = ~ Xcoord + Ycoord, corrf = corrf, Nout = Nout, Nthin = Nthin, Nbi = Nbi, betm0 = betm0, betQ0 = betQ0, ssqdf = ssqdf, ssqsc = ssqsc, tsqdf = tsqdf, tsqsc = tsqsc, phipars = phiprior, omgpars = omgprior, linkp = linkp, phisc = phisc, omgsc = omgsc, test=FALSE) ## End(Not run) ```

geoBayes documentation built on May 30, 2017, 5:47 a.m.