Dynamic quantile linear models: a Bayesian approach

TL;DR

This paper introduces dynamic quantile linear models that combine Bayesian dynamic linear models with quantile regression, enabling robust, high-dimensional, and time-varying predictive analysis with efficient inference algorithms.

Contribution

It presents a novel Bayesian framework for dynamic quantile linear models, including an efficient MCMC algorithm and a fast sequential procedure for high-dimensional data.

Findings

Effective in modeling changing distributions over time.

Accurate predictions of tuberculosis incidence in Rio de Janeiro.

Outperforms traditional models in robustness and adaptability.

Abstract

A new class of models, named dynamic quantile linear models, is presented. It combines dynamic linear models with distribution free quantile regression producing a robust statistical method. Bayesian inference for dynamic quantile linear models can be performed using an efficient Markov chain Monte Carlo algorithm. A fast sequential procedure suited for high-dimensional predictive modeling applications with massive data, in which the generating process is itself changing overtime, is also proposed. The proposed model is evaluated using synthetic and well-known time series data. The model is also applied to predict annual incidence of tuberculosis in Rio de Janeiro state for future years and compared with global strategy targets set by the World Health Organization.