Bayesian econometrics


Bayesian Inference, Monte Carlo methods, Markov chain and MCMC algorithms

Bayesian ingredientsPrior, posterior, and predictive distributions, sequential Bayes.  Conjugate analysis: normal model and normal prior. Example from Box and Tiao (1973).

Bayesian inference via Monte Carlo (MC) methodsChronological advances, MCMC: a bit of history, simple Monte Carlo integration, Monte Carlo integration via importance function, rejection method and weighted resampling

Bayesian inference via Markov chain Monte Carlo (MCMC) methods

Additional Bayesian links

An incomplete list (in chronological order) of books on Bayesian Econometrics

  • Zellner (1971) An Introduction to Bayesian Inference and Econometrics, Wiley.
  • Berry, Chaloner and Geweke (1996) Bayesian Analysis in Statistics and Econometrics, Essays in Honor of Arnold Zellner, Wiley, New York.
  • West and Harrison (1997) Bayesian Forecasting and Dynamic Models. New York: Springer-Verlag.
  • Bauwens, Lubrano and Richard (1999) Bayesian Inference in Dynamic Econometric Models, Oxford UniversityPress, Oxford.
  • Congdon (2001) Bayesian Statistical Modelling,Wiley, New York.
  • Koop (2003) BayesianEconometrics, Wiley, New York.
  • Press (2003) Subjective and Objective Bayesian Statistics: Principles, Models, and Applications,2nd edn, Wiley, New York.
  • Lancaster (2004) AnIntroduction to Modern Bayesian Econometrics, Blackwell Publishing.
  • Geweke (2005) Contemporary Bayesian Econometrics andStatistics, Wiley, New York.
  • Rossi, Allenby and McCulloch (2005) Bayesian Statistics and Marketing, Wiley, New York.

A few references on the Monte Carlo method (including several seminal papers)
· Metropolisand Ulam (1949) The Monte Carlo method. JASA, 44,335-341.
· Metropolis, Rosenbluth, Rosenbluth,Teller and Teller (1953) Equation of state calculations by fast computingmachines. Journal of Chemical Physics, 21, 2087-1092.
· Hastings(1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97-109.
· Peskun (1973) Optimum Monte Carlo sampling using Markovchains. Biometrika, 60, 607-612.
· Besag (1974) Spatial Interaction and the StatisticalAnalysis of Lattice Systems. JRSS-B, 36, 192-236.
Kloek, and van Dijk (1978) Bayesian estimates of equation system parameters: anapplication of integration by Monte Carlo. Econometrica, 46, 1-19.
· Kirkpatrick, Gelatt and Vecchi (1983)Optimization by Simulated Annealing. Science, 220 (4598), 671-680.
· Geman and Geman (1984) Stochasticrelaxation, Gibbs distributions, and the Bayesian restoration of images. IEEETrans. Pattern Analysis and Machine Intelligence, 6, 721-741.
· Tannerand Wong (1987) The Calculation of Posterior Distributions by DataAugmentation. JASA, 82, 528-540.
· Eckhardt, R.(1987) Stan Ulam, John von Neumann, and theMonte Carlo Method. Los Alamos Science, Number 15, pp131-143.
· Metropolis, N. (1987) The Beginning of the Monte Carlo Method. LosAlamos Science, Number 15, 125-130 (special issue in honor of S. Ulam).
· Casellaand George (1992) Explaining the Gibbs Sampler. The American Statistician, 46,167-174.
· Pearl(1987) Evidential reasoning using stochastic simulation of causal models.Artificial intelligence, 32, 245-257.
· Geweke (1989) Bayesian Inference in Econometric ModelsUsing Monte Carlo Integration. Econometrica, 57,1317-1339.
· Gelfand and Smith (1990) Sampling-Based Approaches toCalculating Marginal Densities. JASA, 85, 398-409.
· Gilks and Wild (1992) Adaptive Rejection Sampling for GibbsSampling. Applied Statistics, 41, 337-348.
· Smithand Gelfand (1992) Bayesian Statistics without Tears:A Sampling-Resampling Perspective. The AmericanStatistician, 46, 84-88.
· Chib and Greenberg (1995) Understanding the Metropolis-Hastings algorithm. The American Statistician, 49, 327-335.
· Chib and Greenberg (1996) Markov Chain Monte CarloSimulation Methods in Econometrics, EconometricTheory, 12, 409-431.
· Gamerman, D. andLopes, H. F. (2006) Markov ChainMonte Carlo: Stochastic Simulation for Bayesian Inference (2nd edition). Boca Raton: Chapman& Hall/CRC Press.