MCMC swMATH ID: 3488 Software Authors: Marko Laine Description: 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. Homepage: http://helios.fmi.fi/~lainema/mcmc/ Programming Languages: None Operating Systems: None Dependencies: Matlab Keywords: adaptive algorithm; Markov chain Monte Carlo; ergodicity; random walk Metropolis algorithms; convergence; numerical tests; Metropolis-Hastings algorithms Related Software: NUTS; GPstuff; TOMS659; EGO; energy; MCSim; BayesDA; RODAS Cited in: 9 Publications all top 5 Cited by 28 Authors 2 Haario, Heikki 1 Airaksinen, Manu 1 Alku, Paavo 1 Auvinen, Harri 1 Bleyer, Ismael Rodrigo 1 Campos-Knupp, Diego 1 da Silva Neto, Antônio José 1 Huo, Hai-Feng 1 Husmeier, Dirk 1 Jing, Shuanglin 1 Kalachev, Leonid V. 1 Kumar, Kundan 1 Laine, Marko 1 Lewis, Allison L. 1 Lybeck, Lasse 1 Mesa, Mirtha Irizar 1 Paun, L. Mihaela 1 Pisarenco, Maxim 1 Rudnaya, Maria 1 Saksman, Eero 1 Savcenco, Valeriu 1 Siltanen, Samuli 1 Smith, Ralph C. 1 Tamminen, Johanna 1 Tavares Câmara, Leôncio D. 1 Vu, Phuong Nam 1 Wentworth, Mami T. 1 Xiang, Hong all top 5 Cited in 7 Serials 2 Bulletin of Mathematical Biology 1 Inverse Problems 1 Bernoulli 1 Nonlinear Analysis. Real World Applications 1 Inverse Problems in Science and Engineering 1 Statistics and Computing 1 PUMP Journal of Undergraduate Research all top 5 Cited in 10 Fields 6 Biology and other natural sciences (92-XX) 5 Numerical analysis (65-XX) 3 Ordinary differential equations (34-XX) 3 Statistics (62-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Probability theory and stochastic processes (60-XX) 1 Fluid mechanics (76-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year