# Bayesian Spectral Analysis Regression for Big data This function fits a Bayesian spectral analysis regression model for Big data. ```r 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. ## Returns 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 ```r # 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 ```

bsarBig function