On Sat, 25 Aug 2012, Allin Cottrell wrote: I'm no specialist on this, so I may be not entirely correct, but basically MCMC is a family of methods for drawing pseudo-random numbers from given (conditional) distributions. A good starting point is Chib and Greenberg(1995), "Understanding the Metropolis-Hastings Algorithm", The American Statistician, Vol. 49(4), pp. 327-335 or its predecessor, Casella and George(1992), "Explaining the Gibbs sampler", The American Statistician, Vol. 46(3), pp. 167-174. Once you've got a steady supply of pseudo-random draws, you may use them to simulate several useful object. Bayesians, for example, use them a lot to explore the posterior distribution of a parameter. In a frequentist context, you may use those draws to compute a simulated log-likelihood and then maximise it. See eg Gourieroux and Monfort(1996), Simulation-based econometric methods, Oxford UP This said, I think Lee is much more knowledgeable than me on this. Over to you, Prof. Adkins :) -------------------------------------------------- Riccardo (Jack) Lucchetti Dipartimento di Economia Università Politecnica delle Marche (formerly known as Università di Ancona) r.lucchetti(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti --------------------------------------------------

Allin et al, "Anyway, does anyone have a recommendation for a sort of "Markov Chain Monte Carlo for dummies" -- a useful book, article or website?" Gary Koop's "Bayesian Econometrics" has a good discussion of Gibbs sampling and MCMC more generally, starting in section 4.2 (p. 60). He also covers convergence diagnostics and importance sampling, and provides some further references. There's matlab code available on his website. Tony Lancaster's book ("An introduction to modern Bayesian econometrics") is also pretty clear and has examples in R & Bugs. " That is, if we start from some econometric problem, and we assume some relevant data are available -- and maybe we also assume that I have some prior beliefs about the problem in question that could be quantified to some extent, in some way -- how exactly could I use MCMC to arrive at "better" (in what sense?) parameter estimates, confidence intervals for these estimates, forecasts, and confidence intervals for the forecasts, than I could obtain via regular OLS, GLS, MLE, or GMM?" Well, as (primarily) a Bayesian, I'd mention the general argument that the posterior distribution takes parameter uncertainty into account in an explicit way (via the prior), that the other methods don't. Also, Bayesian estimators often have attractive frequentist properties (I can't think of any references off the top of my head though). Specifically regarding MCMC methods, it can be much easier to explore the likelihood surface by simulation rather than trying to find a global maximum. MCMC can also make it much easier conceptually (and computationally) to deal with latent-variable models like probits or Markov-switching models. The unobservable 'states' are treated just like any other data. Finally, using Bayes factors marginal likelihoods (often computed via MCMC) to compare models can deal with various frequentist problems like non-nested models or parameters that aren't identified under the null. I've been working on a function package to do Bayesian VARs via MCMC, but it's not ready yet. I've also ported some gauss code that does MCMC for unit root tests with multiple structural breaks at unknown dates. I'd be glad to share that if there's interest. HTH, PS -----Original Message----- From: gretl-users-bounces(a)lists.wfu.edu [mailto:gretl-users-bounces@lists.wfu.edu] On Behalf Of Allin Cottrell Sent: Saturday, August 25, 2012 8:05 PM To: Gretl users Subject: [Gretl-users] MCMC for dummies? This may appear to be totally off-topic but it's not entirely so, given that we've had a "feature request" at sourceforge for a Gibbs sampler implementation. Anyway, does anyone have a recommendation for a sort of "Markov Chain Monte Carlo for dummies" -- a useful book, article or website? I understand the principles of Monte Carlo analysis pretty well; I've read some interesting arguments in favour of a Bayesian approach in statistics (though I'm basically a frequentist); and I have some notion of what Markov chains are; but I'm having trouble putting the whole picture together. That is, if we start from some econometric problem, and we assume some relevant data are available -- and maybe we also assume that I have some prior beliefs about the problem in question that could be quantified to some extent, in some way -- how exactly could I use MCMC to arrive at "better" (in what sense?) parameter estimates, confidence intervals for these estimates, forecasts, and confidence intervals for the forecasts, than I could obtain via regular OLS, GLS, MLE, or GMM? I'm not asking people to explain this to me here, just to give any references that they have found particularly useful. Thanks. Allin Cottrell _______________________________________________ Gretl-users mailing list Gretl-users(a)lists.wfu.edu http://lists.wfu.edu/mailman/listinfo/gretl-users

On 08/26/2012 02:05 AM, Allin Cottrell wrote: Well I'm not sure if it is for dummies, but the Koop/Korobilis half-textbook/half-survey "Bayesian Multivariate Time Series Methods for Empirical Macroeconomics" could also be useful and is downloadable at: http://personal.strath.ac.uk/gary.koop/koop_korobilis_Foundations_and_Tre... See especially section 3.2. On Koop's website (see URL beginning above) there's also some code. cheers, sven

On Mon, Aug 27, 2012 at 3:27 PM, Allin Cottrell <cottrell(a)wfu.edu&gt; wrote: While you're doing timings, you might be interested to check out Julia, if you haven't. New, fast high-level language that is promising for these kinds of simulations. http://timsalimans.com/gibbs-sampling-with-julia/ http://julialang.org/ Skipper