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Category Archives: Gibbs Sampling
Sampling: Rejection, Reservoir, and Slice
An article by Suilou Huang for catatrophe modeler AIR-WorldWide of Boston about rejection sampling in CAT modeling got me thinking about pulling together some notes about sampling algorithms of various kinds. There are, of course, books written about this subject, … Continue reading
Posted in accept-reject methods, American Statistical Association, Bayesian computational methods, catastrophe modeling, data science, diffusion processes, empirical likelihood, Gibbs Sampling, insurance, Markov Chain Monte Carlo, mathematics, Mathematics and Climate Research Network, maths, Monte Carlo Statistical Methods, multivariate statistics, numerical algorithms, numerical analysis, numerical software, numerics, percolation theory, Python 3 programming language, R statistical programming language, Radford Neal, sampling, slice sampling, spatial statistics, statistics, stochastic algorithms, stochastic search
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“Grid shading by simulated annealing” [Martyn Plummer]
Source: Grid shading by simulated annealing (or what I did on my holidays), aka “fun with GCHQ job adverts”, by Martyn Plummer, developer of JAGS. Excerpt: I wanted to solve the puzzle but did not want to sit down with … Continue reading
Posted in approximate Bayesian computation, Bayesian, Bayesian inversion, Boltzmann, BUGS, Christian Robert, Gibbs Sampling, JAGS, likelihood-free, Markov Chain Monte Carlo, Martyn Plummer, mathematics, maths, MCMC, Monte Carlo Statistical Methods, optimization, probabilistic programming, SPSA, stochastic algorithms, stochastic search
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high dimension Metropolis-Hastings algorithms
If attempting to simulate from a multivariate standard normal distribution in a large dimension, when starting from the mode of the target, i.e., its mean γ, leaving the mode γis extremely unlikely, given the huge drop between the value of the density at the mode γ and at likely realisations Continue reading
Posted in Bayes, Bayesian, Bayesian inversion, boosting, chance, Christian Robert, computation, ensembles, Gibbs Sampling, James Spall, Jerome Friedman, Markov Chain Monte Carlo, mathematics, maths, MCMC, Monte Carlo Statistical Methods, multivariate statistics, numerical software, numerics, optimization, reasonableness, Robert Schapire, SPSA, state-space models, statistics, stochastic algorithms, stochastic search, stochastics, Yoav Freund
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“The Bayesian Second Law of Thermodynamics” (Sean Carroll, and collaborators)
http://www.preposterousuniverse.com/blog/2015/08/11/the-bayesian-second-law-of-thermodynamics/ See also.
Posted in approximate Bayesian computation, Bayesian, bifurcations, Boltzmann, capricious gods, dynamical systems, ensembles, games of chance, Gibbs Sampling, information theoretic statistics, Josiah Willard Gibbs, mathematics, maths, physics, probability, rationality, reasonableness, science, statistics, stochastic algorithms, stochastics, thermodynamics, Wordpress
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“A vignette on Metropolis” (Christian Robert)
Originally posted on Xi'an's Og:
Over the past week, I wrote a short introduction to the Metropolis-Hastings algorithm, mostly in the style of our Introduction to Monte Carlo with R book, that is, with very little theory and…
Christian Robert on the amazing Gibbs sampler
Professor Christian Robert remarks on the amazing Gibbs sampler. Implicitly he’s also underscoring the power of properly done Bayesian computational analysis. For here we have a problem with a posterior distribution having two strong modes, so a point estimate, like … Continue reading
example of Bayesian inversion
This is based upon my solution of Exercise 2.3, page 18, R. Christensen, W. Johnson, A. Branscum, T. E. Hanson, Bayesian Ideas and Data Analysis, Chapman & Hall, 2011. The purpose is to show how information latent in a set … Continue reading
Bayesian deconvolution of stick lengths
Consider trying to determine the length of a straight stick. Instead of the measurement errors being clustered about zero, suppose the errors are known to be always positive, that is, no measurement ever underestimates the length of the stick. Such … Continue reading
The dp-means algorithm of Kulis and Jordan in R and Python
dp-means algorithm. Think k-means but with the number of clusters calculated. By John Myles White, in R. (Github link off that page.) By Scott Hendrickson, in Python. (Github link off that page.)
Posted in Bayesian, Gibbs Sampling, JAGS, mathematics, maths, R, statistics, stochastic algorithms, stochastic search
Tagged dp-means
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Blind Bayesian recovery of components of residential solid waste tonnage from totals data
This is a sketch of how maths and statistics can do something called blind source separation, meaning to estimate the components of data given only their totals. Here, I use Bayesian techniques for the purpose, sometimes called Bayesian inversion, using … Continue reading
“The joy and martyrdom of trying to be a Bayesian”
Bayesians have all been there. Some of us don’t depend upon producing publications to assure our pay, so we less have the pressure of pleasing peer reviewers. Nonetheless, it’s all reacting to “What the hell are you doing? I don’t … Continue reading
How fast is JAGS?
How fast is JAGS?.
The zero-crossings trick for JAGS: Finding roots stochastically
BUGS has a “zeros trick” (Lund, Jackson, Best, Thomas, Spiegelhalter, 2013, pages 204-206; see also an online illustration) for specifying a new distribution which is not in the standard set. The idea is to couple an invented-for-the-moment Poisson density to … Continue reading
Posted in Bayesian, BUGS, education, forecasting, Gibbs Sampling, JAGS, mathematics, MCMC, probabilistic programming, R, statistics, stochastic search
Tagged error-in-variables problem, optimization, zeros trick
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HadCRUT4 version “HadCRUT.4.2.0.0” available as .RData R workspace or image
I’m happy to announce that I have made available the HadCRUT4 observational ensemble data as an .RData image for use with R. These were downloaded from the MetOffice Hadley Observations Web site. Detailed documentation is available on this page, with the … Continue reading
