Autoregressive (AR) models are some of the most widely used models in applied economics, among other disciplines, because of their generality and simplicity. However, the dynamic characteristics of real economic and financial data can change from one time period to another, limiting the applicability of linear time-series models. For example, the change of unemployment rate is a function of the state of the economy, whether it is expanding or contracting. A variety of models have been developed that allow time-series dynamics to depend on the regime of the system they are part of. The class of regime-dependent models include Markov-switching, smooth transition, and threshold autoregressive (TAR) models. Read more…

Monitoring lineages of the Omicron variant of the SARS-CoV-2 virus continues to be an important health consideration. The World Health Organization identifies BA.1, BA.1.1, and the most recent BA.2 as the most common sublineages. A recent study from Japan, Yamasoba et al. (2022), compares, among other characteristics, the transmissibility of these three Omicron lineages with the latest Delta variant. It identifies BA.2 to have the highest transmissibility of the four. Preprint of the study is available at bioarxiv.org. One interesting aspect of the study is the application of Bayesian multilevel models for representing lineage growth dynamics. In this post, I demonstrate how to use Stata’s bayesmh and bayesstats summary commands to perform similar analysis. Read more…

Overview

Markov chain Monte Carlo (MCMC) is the principal tool for performing Bayesian inference. MCMC is a stochastic procedure that utilizes Markov chains simulated from the posterior distribution of model parameters to compute posterior summaries and make predictions. Given its stochastic nature and dependence on initial values, verifying Markov chain convergence can be difficult—visual inspection of the trace and autocorrelation plots are often used. A more formal method for checking convergence relies on simulating and comparing results from multiple Markov chains; see, for example, Gelman and Rubin (1992) and Gelman et al. (2013). Using multiple chains, rather than a single chain, makes diagnosing convergence easier.

As of Stata 16, bayesmh and its bayes prefix commands support a new option, nchains(), for simulating multiple Markov chains. There is also a new convergence diagnostic command, bayesstats grubin. All Bayesian postestimation commands now support multiple chains. In this blog post, I show you how to check MCMC convergence and improve your Bayesian inference using multiple chains through a series of examples. I also show you how to speed up your sampling by running multiple Markov chains in parallel. Read more…