# Predictive posterior mean and variance for DNAmf object with nonseparable kernel. The function computes the predictive posterior mean and variance for the DNAmf model using closed-form expressions based on the chosen nonseparable kernel at given new input locations. ```r ## S3 method for class 'DNAmf' predict(object, x = NULL, targett = 0, nimpute = 50, ...) ``` ## Arguments - `object`: A fitted DNAmf object. - `x`: A vector or matrix of new input locations to predict. - `targett`: A numeric value of target tuning parameter to predict. - `nimpute`: Number of imputations for non-nested designs. Default is 50. - `...`: Additional arguments for compatibility with generic method `predict`. ## Returns A list of predictive posterior mean and variance for each level and computation time containing: * `mu_1`, `sig2_1`, ..., `mu_L`, `sig2_L`: A vector of predictive posterior mean and variance at each level. * `mu`: A vector of predictive posterior mean at target tuning parameter. * `sig2`: A vector of predictive posterior variance at target tuning parameter `targett`. * `time`: Total computation time in seconds. ## Details The `predict.DNAmf` function internally calls `closed_form_DNA`, which further calls `h1_sqex`, `h2_sqex`, `h2_sqex_single` for `kernel="sqex"`, or `h1_matern`, `h2_matern`, `h2_matern_single` for `kernel="matern1.5"` or`kernel="matern2.5"`, to recursively compute the closed-form posterior mean and variance at each level. From the fitted model from `DNAmf`, the posterior mean and variance are calculated based on the closed-form expression derived by a recursive fashion. The formulas depend on its kernel choices. If the fitted model was constructed with non-nested designs (`nested=FALSE`), the function generates `nimpute` sets of imputations for pseudo outputs via `imputer_DNA`. For further details, see Heo, Boutelet, and Sung (2025+, ). ## Examples ```r ### Non-Additive example ### library(RNAmf) ### Non-Additive Function ### fl <- function(x, t){ term1 <- sin(10 * pi * x / (5+t)) term2 <- 0.2 * sin(8 * pi * x) term1 + term2 } ### training data ### n1 <- 13; n2 <- 10; n3 <- 7; n4 <- 4; n5 <- 1; m1 <- 2.5; m2 <- 2.0; m3 <- 1.5; m4 <- 1.0; m5 <- 0.5; d <- 1 eps <- sqrt(.Machine$double.eps) x <- seq(0,1,0.01) ### fix seed to reproduce the result ### set.seed(1) ### generate initial nested design ### NestDesign <- NestedX(c(n1,n2,n3,n4,n5),d) X1 <- NestDesign[[1]] X2 <- NestDesign[[2]] X3 <- NestDesign[[3]] X4 <- NestDesign[[4]] X5 <- NestDesign[[5]] y1 <- fl(X1, t=m1) y2 <- fl(X2, t=m2) y3 <- fl(X3, t=m3) y4 <- fl(X4, t=m4) y5 <- fl(X5, t=m5) ### fit a DNAmf ### fit.DNAmf <- DNAmf(X=list(X1, X2, X3, X4, X5), y=list(y1, y2, y3, y4, y5), kernel="sqex", t=c(m1,m2,m3,m4,m5), multi.start=10, constant=TRUE) ### predict ### pred.DNAmf <- predict(fit.DNAmf, x, targett=0) predydiffu <- pred.DNAmf$mu predsig2diffu <- pred.DNAmf$sig2 ### RMSE ### print(sqrt(mean((predydiffu-fl(x, t=0))^2))) # 0.1162579 ### visualize the emulation performance ### oldpar <- par(mfrow = c(2,3)) create_plot_base <- function(i, mesh_size, x, pred_mu, pred_sig2, X_points = NULL, y_points = NULL, add_points = TRUE, yylim) { lower <- pred_mu - qnorm(0.995) * sqrt(pred_sig2) upper <- pred_mu + qnorm(0.995) * sqrt(pred_sig2) plot(x, pred_mu, type = "n", ylim = c(-yylim, yylim), xlab = "", ylab = "", main = paste0("Mesh size = ", mesh_size), axes = FALSE) box() polygon(c(x, rev(x)), c(upper, rev(lower)), col = adjustcolor("blue", alpha.f = 0.2), border = NA) lines(x, pred_mu, col = "blue", lwd = 2) lines(x, fl(x, mesh_size), lty = 2, col = "black", lwd = 2) if (add_points && !is.null(X_points) && !is.null(y_points)) { points(X_points, y_points, col = "red", pch = 16, cex = 1.3) } } mesh_sizes <- c(m1, m2, m3, m4, m5, 0) mu_list <- list(pred.DNAmf$mu_1, pred.DNAmf$mu_2, pred.DNAmf$mu_3, pred.DNAmf$mu_4, pred.DNAmf$mu_5, pred.DNAmf$mu) sig2_list <- list(pred.DNAmf$sig2_1, pred.DNAmf$sig2_2, pred.DNAmf$sig2_3, pred.DNAmf$sig2_4, pred.DNAmf$sig2_5, pred.DNAmf$sig2) X_list <- list(X1, X2, X3, X4, X5, NULL) y_list <- list(y1, y2, y3, y4, y5, NULL) plots <- mapply(function(i, m, mu, sig2, X, y) { create_plot_base(i, m, x, mu, sig2, X, y, add_points = !is.null(X), yylim=1.5) }, i = 1:6, m = mesh_sizes, mu = mu_list, sig2 = sig2_list, X = X_list, y = y_list, SIMPLIFY = FALSE) par(oldpar) ``` ## See Also `DNAmf` for the user-level function.

predict function