# Predictions of Binary Gaussian Process The function computes the predicted response and its variance as well as its confidence interval. ```r ## S3 method for class 'binaryGP' predict(object, xnew, conf.level = 0.95, sim.number = 101, ...) ``` ## Arguments - `object`: a class binaryGP object estimated by `binaryGP_fit`. - `xnew`: a testing matrix with dimension `n_new` by `d` in which each row corresponds to a predictive location. - `conf.level`: a value from 0 to 1 specifying the level of confidence interval. The default is 0.95. - `sim.number`: a positive integer specifying the simulation number for Monte-Carlo method. The default is 101. - `...`: for compatibility with generic method `predict`. ## Returns - **mean**: a matrix with dimension `n_new` by `T` displaying predicted responses at locations `xnew`. - **var**: a matrix with dimension `n_new` by `T` displaying predictive variances at locations `xnew`. - **upper.bound**: a matrix with dimension `n_new` by `T` displaying upper bounds with `conf.level` confidence level. - **lower.bound**: a matrix with dimension `n_new` by `T` displaying lower bounds with `conf.level` confidence level. - **y_pred**: a matrix with dimension `n_new` by `T` displaying predicted binary responses at locations `xnew`. ## Examples ```r library(binaryGP) ##### Testing function: cos(x1 + x2) * exp(x1*x2) with TT sequences ##### ##### Thanks to Sonja Surjanovic and Derek Bingham, Simon Fraser University ##### test_function <- function(X, TT) { x1 <- X[,1] x2 <- X[,2] eta_1 <- cos(x1 + x2) * exp(x1*x2) p_1 <- exp(eta_1)/(1+exp(eta_1)) y_1 <- rep(NA, length(p_1)) for(i in 1:length(p_1)) y_1[i] <- rbinom(1,1,p_1[i]) Y <- y_1 P <- p_1 if(TT > 1){ for(tt in 2:TT){ eta_2 <- 0.3 * y_1 + eta_1 p_2 <- exp(eta_2)/(1+exp(eta_2)) y_2 <- rep(NA, length(p_2)) for(i in 1:length(p_2)) y_2[i] <- rbinom(1,1,p_2[i]) Y <- cbind(Y, y_2) P <- cbind(P, p_2) y_1 <- y_2 } } return(list(Y = Y, P = P)) } set.seed(1) n <- 30 n.test <- 10 d <- 2 X <- matrix(runif(d * n), ncol = d) X.test <- matrix(runif(d * n.test), ncol = d) ##### without time-series ##### Y <- test_function(X, 1)$Y ## Y is a vector test.out <- test_function(X.test, 1) Y.test <- test.out$Y P.true <- test.out$P # fitting binaryGP.model <- binaryGP_fit(X = X, Y = Y) # prediction binaryGP.prediction <- predict(binaryGP.model, xnew = X.test) print(binaryGP.prediction$mean) print(binaryGP.prediction$var) print(binaryGP.prediction$upper.bound) print(binaryGP.prediction$lower.bound) ##### with time-series ##### Y <- test_function(X, 10)$Y ## Y is a matrix with 10 columns test.out <- test_function(X.test, 10) Y.test <- test.out$Y P.true <- test.out$P # fitting binaryGP.model <- binaryGP_fit(X = X, Y = Y, R = 1) # prediction binaryGP.prediction <- predict(binaryGP.model, xnew = X.test) print(binaryGP.prediction$mean) print(binaryGP.prediction$var) print(binaryGP.prediction$upper.bound) print(binaryGP.prediction$lower.bound) ``` ## Author(s) Chih-Li Sung ## See Also `binaryGP_fit` for estimation of the binary Gaussian process.

predict.binaryGP function