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Compute Log Randomized Predictive p-values using ISCV Method

Source: R/iscv_logrpp.R
iscv_logrpp.Rd

Calculates log randomized predictive p-values (log-RPPs) based on the Importance Sampling Cross-Validation (ISCV) method, using precomputed log cumulative distribution function (log-CDF) and log probability mass function (log-PMF) values.

Usage

iscv_logrpp(log_cdf, log_pmf)

Arguments

log_cdf

A numeric matrix of log-CDF values with dimensions \(M \times N\), where \(M\) is the number of posterior draws and \(N\) is the number of observations.

log_pmf

A numeric matrix of log-PMF values with the same dimensions as log_cdf.

Value

A numeric vector of length \(N\), giving the log randomized predictive p-values for each observation.

Details

This function implements the Importance Sampling Cross-Validation (ISCV) version of the log randomized predictive p-value (log-RPP) computation. It uses numerically stable log-sum-exp operations to avoid overflow or underflow when summing in log space.

Randomized predictive p-values (\(rpp\)) are computed using uniform random draws \(u_i \sim \text{Uniform}(0,1)\), combined with the model-predicted \(\text{CDF}\) and \(\text{PMF}\) values for each observation and posterior sample. The result is returned in log scale for numerical stability.

Internally, this function:

  • Generates uniform random values \(u_i\) for each observation.

  • Computes \(\log(u_i)\) and adds it to \(\log(\text{PMF})\).

  • Applies numerically stable log-sum-exp operations column-wise.

Values numerically equal to 0 or 1 are replaced by \(\log(1e-5)\) and \(\log(9e-5)\) respectively to keep calculations stable.

Examples

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