Generate Uncertainty Intervals for Transition Probabilities
Source:R/generate_uncertainty.R
generate_uncertainty.RdEstimates uncertainty around transition probabilities using a Beta distribution assumption derived from the binomial variance of the sample size. It generates correlated Monte Carlo samples (using a Gaussian Copula) to preserve the relationship between age/cohort groups across iterations.
The process follows these steps: 1. Standard Error: Calculates SE based on the effective sample size (\(SE = \sqrt{p(1-p)/n}\)). 2. Beta Parameters: Converts the Mean (p) and Variance (SE^2) into Beta shape parameters (\(\alpha, \beta\)). 3. Correlated Sampling: Generates a matrix of correlated uniform probabilities using a Gaussian Copula.
Common factor \(Z_{shared}\) accounts for systematic uncertainty.
Idiosyncratic factor \(Z_{indiv}\) accounts for random noise.
4. Inverse CDF: Maps these probabilities through the qbeta function to get the final samples.
Arguments
- data
Data table. Must contain the probability column.
- prob_col
Character. Name of the column containing the point estimate probabilities (e.g., "p_start").
- n_eff
Numeric. The effective sample size used to calculate variance. Higher
nimplies narrower confidence intervals.- n_samp
Integer. Number of Monte Carlo samples to generate (e.g., 100 or 1000).
- correlation
Numeric (0-1). The correlation coefficient (\(R\)) between rows in a single sample iteration. High correlation implies that if one age group is overestimated, others likely are too.