MCMC toolbox for Matlab-经管之家官网！

From this page you can download a set of Matlab function for some statistical MCMC analyses of mathematical models. This code might be useful to you if you are already familiar with Matlab and want to do MCMC analysis using it.

For a more comprehensive and better documented and maintained software for MCMC, see OpenBugs. There are also some MCMC functions in Mahtworks own Statistics Toolbox.

This toolbox provides tools to generate and analyse Metropolis-Hastings MCMC chain using multivariate Gaussian proposal distribution. The covariance matrix of the proposal distribution can be adapted during the simulation according to adaptive schemes described in the references.

The code can do the following

• Produce MCMC chain for user written -2*log(likelihood) and -2*log(prior) functions. These will be equal to sum-of-squares functions when using Gaussian likelihood and prior.
• In case of Gaussian error model, sample the model error variance from the conjugate inverse chi squared distribution.
• Do plots and statistical analyses based on the chain, such as basic statistics, convergence diagnostics, chain timeseries plots, 2 dimensional clouds of points, kernel densities, and histograms.
• Calculate densities, cumulative distributions, quantiles, and random variates for some useful common statistical distributions without using Mathworks own statistics toolbox.
  

The code is self consistent, no additional Matlab toolboxes are used. However, a quite recent version of Matlab is needed. The documentation might get better gradually, but in the mean while please look at the following page:

• Examples on using the toolbox for some statistical problems.
  

Code

The main functions in the toolbox are the following.

mcmcrun.mMatlab function for the MCMC run. The user provides her own Matlab function to calculate the "sum-of-squares" function for the likelihood part, e.g. a function that calculates minus twice the log likelihood, -2log(p(θ;data)). Optionally a prior "sum-of-squares" function can also be given, returning -2log(p(θ)). See the example and help mcmcrun for more details.mcmcplot.mThis function plots some useful plots of the generated chain, such as chain time series, 2 dimensional marginal plots, kernel density estimates, and histograms. See help mcmcplot.mcmcpred.mFor certain types of models is is useful to plot predictive envelopes of model functions by sampling parameter values from the generated chain. This functions calls the model function repeatedly while sampling the unknowns from the chain. It calculates probability regions with respect to a "time" variable of the model. See the examples.OtherMatlab command help mcmcstat should display the contents of the file Contents.m.

NOTE: There is a similar Matlab code described in my DRAM page. That special DRAM code has fewer options then the general MCMC toolbox function. The DRAM code might be easier to read and alter if you are interested in inner workings of the code.

Downloadsmcmcstat.zip (updated 2013-01-15)The toolbox files. Save them to a separate directory, and add the Matlab path to it.mcmcexamples.zipSome example Matlab scripts, these are described in the examples page.

Comments are welcome!

References

H. Haario, M. Laine, A. Mira and E. Saksman, 2006. DRAM: Efficient adaptive MCMC, Statistics and Computing 16, pp. 339-354. (doi:10.1007/s11222-006-9438-0)

H. Haario, E. Saksman and J. Tamminen, 2001. An adaptive Metropolis algorithm Bernoulli 7, pp. 223-242.

「经管之家」APP：经管人学习、答疑、交友，就上经管之家！
免流量费下载资料----在经管之家app可以下载论坛上的所有资源，并且不额外收取下载高峰期的论坛币。
涵盖所有经管领域的优秀内容----覆盖经济、管理、金融投资、计量统计、数据分析、国贸、财会等专业的学习宝库，各类资料应有尽有。
来自五湖四海的经管达人----已经有上千万的经管人来到这里，你可以找到任何学科方向、有共同话题的朋友。
经管之家（原人大经济论坛），跨越高校的围墙，带你走进经管知识的新世界。
扫描下方二维码下载并注册APP