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Bayesian Statistics and Econometrics using Mathematica
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| Organization: | Federal Reserve Bank of Atlanta |
| Department: | Economic Advisor, Research Department |
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2007 Wolfram Technology Conference
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Champaign, IL
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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.
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http://www.wolfram.com/news/events/techconf2007/
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| BayesianStatisticsAndEconometrics.nb (7 MB) - Mathematica Notebook [for Mathematica 6.0] |
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