bsarBig {bsamGP}

Bayesian Spectral Analysis Regression for Big data

Description

This function fits a Bayesian spectral analysis regression model for Big data.

Usage

bsarBig(formula, nbasis, nint, mcmc = list(), prior = list(), verbose = FALSE)

Arguments

formula

an object of class “formula”

nbasis

number of cosine basis functions.

nint

number of grid points where the unknown function is evaluated for plotting. The default is 500.

mcmc

a list giving the MCMC parameters. The list includes the following integers (with default values in parentheses): nblow (10000) giving the number of MCMC in transition period, nskip (10) giving the thinning interval, smcmc (1000) giving the number of MCMC for analysis, and ndisp (1000) giving the number of saved draws to be displayed on screen (the function reports on the screen when every ndisp iterations have been carried out).

prior

a list giving the prior information. The list includes the following parameters (default values specify the non-informative prior): sigma2_m0 and sigma2_v0 giving the prior mean and variance of the inverse gamma prior for the scale parameter of response, tau2_m0, tau2_s0 and w0 giving the prior mean and standard deviation of smoothing prior.

verbose

a logical variable. If TRUE, the iteration number and the Metropolis acceptance rate are printed to the screen.

Value

The MCMC samples of the parameters in the model are stored in the list mcmc.draws and the posterior samples of the fitted values are stored in the list fit.draws. The output list also includes the following objects:

post.est

posterior estimates for all parameters in the model.

call

the matched call.

mcmctime

running time of Markov chain from system.time().

See Also

bsar

Examples

# Ttrue function
ftrue <- function(x){
  ft <- 7*exp(-3*x) + 2*exp(-70*(x-.6)^2) - 2 + 5*x
  return(ft)
}

# Generate data
set.seed(1)

nobs <- 100000 # Number of observations
sigmat <- .5 # True sigma
nxgrid <- 500 # number of grid points: approximate likelihood & plots

xdata <- runif(nobs) # Generate x values
fobst <- ftrue(xdata) # True f at observations
ydata <- fobst + sigmat*rnorm(nobs)

# Compute grid on 0 to 1
xdelta <- 1/nxgrid
xgrid <- seq(xdelta/2, 1-xdelta/2, xdelta)
xgrid <- matrix(xgrid,nxgrid)
fxgridt <- ftrue(xgrid) # True f on xgrid

# Fit data
fout <- bsarBig(ydata ~ xdata, nbasis = 50, nint = nxgrid, verbose = TRUE)

# Plots
smcmc <- fout$mcmc$smcmc
t <- 1:smcmc
par(mfrow=c(2,2))
matplot(t, fout$mcmc.draws$theta, type = "l", main = "Theta", xlab = "Iteration", ylab = "Draw")
plot(t, fout$mcmc.draws$sigma, type = "l", main = "Sigma", xlab = "Iteration", ylab = "Draw")
matplot(t, fout$mcmc.draws$tau, type = "l", main = "Tau", xlab = "Iteration", ylab = "Draw")
matplot(t, fout$mcmc.draws$gamma, type = "l", main = "Gamma", xlab = "Iteration", ylab = "Draw")

dev.new()
matplot(fout$fit.draws$xgrid, cbind(fxgridt, fout$post.est$fhatm, fout$post.est$fhatq),
        type = "l", main = "Regression Function", xlab = "X", ylab = "Y")

# Compute RMISE for regression function
sse <- (fout$post.est$fhatm - fxgridt)^2
rmise <- intgrat(sse, 1/nxgrid)
rmise <- sqrt(rmise)
rmise