Overview
Luke Tierney is a statistician at the University of Minnesota (School of Statistics) known for foundational work on Markov chain Monte Carlo methods. His 1994 Annals of Statistics paper is the standard mathematical reference for the unified Metropolis-Hastings framework and MCMC convergence theory, drawing on Nummelin's (1984) general state space Markov chain theory.
Key Contributions / Features
- Tierney (1994) — "Markov Chains for Exploring Posterior Distributions": unified treatment of Gibbs, Metropolis-Hastings, and hybrid algorithms; Peskun (1973) optimality of MH acceptance ratio; drift-condition framework for geometric ergodicity and CLT; variance reduction via conditioning; six types of Metropolis kernel.
- TKK (1989a) (Biometrika 76: 425–433): Laplace approximation for marginal density of any smooth nonlinear function g(θ); avoids explicit reparameterisation via constrained optimisation; saddlepoint accuracy O(n⁻¹).
- TKK (1989b) (JASA 84: 710–716): Fully exponential Laplace approximation to posterior expectations E[g(θ)|y] and variances; incorporates log b(θ) into the exponent; achieves O(n⁻²) relative error.
- Mykland, Tierney, and Yu (1995) — "Regeneration in Markov Chain Samplers": identifies embedded renewal processes in Harris recurrent chains for regenerative simulation analysis and parallel computation.
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