Coupling-based convergence assessment of some Gibbs samplers for high-dimensional Bayesian regression with shrinkage priors

Understand

We consider Markov chain Monte Carlo (MCMC) algorithms for Bayesian high-dimensional regression with continuous shrinkage priors.

• A common challenge with these algorithms is the choice of the number of iterations to perform.
• This is critical when each iteration is expensive, as is the case when dealing with modern data sets, such as genome-wide association studies with thousands of rows and up to hundred of thousands of columns.
• We develop coupling techniques tailored to the setting of high-dimensional regression with shrinkage priors, which enable practical, non-asymptotic diagnostics of convergence without relying on traceplots or long-run asymptotics.