quantile: Posterior Quantiles from a Fitted BKP or DKP Model

Description

Compute posterior quantiles from a fitted BKP or DKP model. For a BKP object, this returns the posterior quantiles of the positive class probability. For a DKP object, this returns posterior quantiles for each class probability.

Usage

# S3 method for BKP
quantile(x, probs = c(0.025, 0.5, 0.975), ...)
# S3 method for DKP
quantile(x, probs = c(0.025, 0.5, 0.975), ...)

Value

For BKP: a numeric vector (if length(probs) = 1) or a numeric matrix (if length(probs) > 1) of posterior quantiles. Rows correspond to observations, and columns correspond to the requested probabilities.

For DKP: a numeric matrix (if length(probs) = 1) or a 3D array (if length(probs) > 1) of posterior quantiles. Dimensions correspond to observations × classes × probabilities.

Arguments

x: An object of class BKP or DKP, typically the result of a call to fit_BKP or fit_DKP.
probs: Numeric vector of probabilities specifying which posterior quantiles to return. Defaults to c(0.025, 0.5, 0.975).
...: Additional arguments (currently unused).

Details

For a BKP model, posterior quantiles are computed from the Beta Kernel Process for the positive class probability. For a DKP model, posterior quantiles for each class are approximated using the Beta approximation of the marginal distributions of the posterior Dirichlet distribution.

Examples

Run this code

# -------------------------- BKP ---------------------------
set.seed(123)

# Define true success probability function
true_pi_fun <- function(x) {
  (1 + exp(-x^2) * cos(10 * (1 - exp(-x)) / (1 + exp(-x)))) / 2
}

n <- 30
Xbounds <- matrix(c(-2, 2), nrow = 1)
X <- tgp::lhs(n = n, rect = Xbounds)
true_pi <- true_pi_fun(X)
m <- sample(100, n, replace = TRUE)
y <- rbinom(n, size = m, prob = true_pi)

# Fit BKP model
model <- fit_BKP(X, y, m, Xbounds = Xbounds)

# Extract posterior quantiles
quantile(model)

# -------------------------- DKP ---------------------------
#' set.seed(123)

# Define true class probability function (3-class)
true_pi_fun <- function(X) {
  p1 <- 1/(1+exp(-3*X))
  p2 <- (1 + exp(-X^2) * cos(10 * (1 - exp(-X)) / (1 + exp(-X)))) / 2
  return(matrix(c(p1/2, p2/2, 1 - (p1+p2)/2), nrow = length(p1)))
}

n <- 30
Xbounds <- matrix(c(-2, 2), nrow = 1)
X <- tgp::lhs(n = n, rect = Xbounds)
true_pi <- true_pi_fun(X)
m <- sample(100, n, replace = TRUE)

# Generate multinomial responses
Y <- t(sapply(1:n, function(i) rmultinom(1, size = m[i], prob = true_pi[i, ])))

# Fit DKP model
model <- fit_DKP(X, Y, Xbounds = Xbounds)

# Extract posterior quantiles
quantile(model)