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Bayesian Statistics and Econometrics using Mathematica
Author

Mark Fisher
Organization: Federal Reserve Bank of Atlanta
Department: Economic Advisor, Research Department
Conference

2007 Wolfram Technology Conference
Conference location

Champaign, IL
Description

Abstract

This talk will illustrate how I use Mathematica for Bayesian statistical and econometric analysis.

Bayesian statistical techniques are numerically intensive
  • Extensive use of Compile
  • Problems with running out of RAM
  • Parallelization and gridMathematica
Review and illustration of some Markov chain Monte Carlo (MCMC) techniques
  • Random-walk Metropolis algorithm
  • Gibbs sampling
  • Reversible Jump MCMC (for model averaging)
  • Particle filters (for dynamic models with latent state variables)
  • Using "bridge estimator" to compute the likelihood of a model from MCMC output
Applications
  • Inferring probabilities of the target fed funds rate from options on fed funds futures contracts (illustrates Reversible Jump MCMC and particle filters)
  • Unit root tests of Purchasing Power Parity (illustrates Bayesian hypothesis testing and maximum entropy priors)
  • Batting averages and hitting streaks in baseball (illustrates hierarchical models and Markov-switching models)
Alternative software
  • More or less dedicated: WinBUGS, R (umacs and rv), BACC (WinR)
  • Nondedicated competitors: Matlab (main one for economists), C, and fortran
  • Possible connectivity via J/Link and .NET/Link
Wish list
  • Bayesian statistical techniques use probability distributions that are not included. Need more built in. Dirichlet. t-distribution with scale and location parameters.
  • Need to compile NormalDistribution, GammaDistribution, etc.
Subjects

*Business and Economics
*Mathematica Technology
*Mathematics > Probability and Statistics
URL

http://www.wolfram.com/news/events/techconf2007/
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BayesianStatisticsAndEconometrics.nb (7 MB) - Mathematica Notebook [for Mathematica 6.0]