# Find Scale Parameter for Gamma (Half-Normal) Hyperprior This function implements a optimisation routine that computes the scale parameter $\theta$ of the gamma prior for $\tau^2$ (corresponding to a half-normal prior for $\tau$) for a given design matrix and prior precision matrix such that approximately $P(|f(x_{k}|\le c,k=1,\ldots,p)\ge 1-\alpha$ ```r get_theta_ga(alpha = 0.01, method = "integrate", Z, c = 3, eps = .Machine$double.eps, Kinv) ``` ## Arguments - `alpha`: denotes the 1-$\alpha$ level. - `method`: with `integrate` as default. Currently no further method implemented. - `Z`: the design matrix. - `c`: denotes the expected range of the function. - `eps`: denotes the error tolerance of the result, default is `.Machine$double.eps`. - `Kinv`: the generalised inverse of K. ## Returns an object of class `list` with values from `uniroot`. ## Examples ```r set.seed(123) require(MASS) # prior precision matrix (second order differences) # of a spline of degree l=3 and with m=20 inner knots # yielding dim(K)=m+l-1=22 K <- t(diff(diag(22), differences=2))%*%diff(diag(22), differences=2) # generalised inverse of K Kinv <- ginv(K) # covariate x x <- runif(1) Z <- matrix(DesignM(x)$Z_B,nrow=1) theta <- get_theta_ga(alpha = 0.01, method = "integrate", Z = Z, c = 3, eps = .Machine$double.eps, Kinv = Kinv)$root ## Not run: set.seed(91179) library(BayesX) library(MASS) # prior precision matrix to zambia data set K <- read.gra(system.file("examples/zambia.gra", package="sdPrior")) # generalised inverse of K Kinv <- ginv(K) # read data dat <- read.table(system.file("examples/zambia_height92.raw", package="sdPrior"), header = TRUE) # design matrix for spatial component Z <- t(sapply(dat$district, FUN=function(x){1*(x==rownames(K))})) # get scale parameter theta <- get_theta_ga(alpha = 0.01, method = "integrate", Z = Z, c = 3, eps = .Machine$double.eps, Kinv = Kinv)$root ## End(Not run) ``` ## References Nadja Klein and Thomas Kneib (2015). Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression. **Working Paper**. Andrew Gelman (2006). Prior Distributions for Variance Parameters in Hierarchical Models. **Bayesian Analysis**, 1 (3), 515--533. ## Author(s) Nadja Klein

get_theta_ga function