Bayesian Prediction with Covariates Subject to Detection Limits

TL;DR

This paper introduces a Bayesian method with an efficient MCMC algorithm for predicting outcomes when covariates are censored, improving accuracy and computational efficiency in industrial and telecom applications.

Contribution

It presents a joint covariate imputation approach using a Gibbs sampler that significantly enhances efficiency over univariate methods for real-time prediction tasks.

Findings

Joint updating of covariates is two orders of magnitude more efficient.

Bayesian imputation yields more accurate predictions than naive methods.

Auxiliary variables further improve predictive performance.

Abstract

Missing values in covariates due to censoring by signal interference or lack of sensitivity in the measuring devices are common in industrial problems. We propose a full Bayesian solution to the prediction problem with an efficient Markov Chain Monte Carlo (MCMC) algorithm that updates all the censored covariate values jointly in a random scan Gibbs sampler. We show that the joint updating of missing covariate values can be at least two orders of magnitude more efficient than univariate updating. This increased efficiency is shown to be crucial for quickly learning the missing covariate values and their uncertainty in a real-time decision making context, in particular when there is substantial correlation in the posterior for the missing values. The approach is evaluated on simulated data and on data from the telecom sector. Our results show that the proposed Bayesian imputation gives substantially more accurate predictions than na\"ive imputation, and that the use of auxiliary variables in the imputation gives additional predictive power.