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Category Archives: MCMC
Repaired R code for Markov spatial simulation of hurricane tracks from historical trajectories
I’m currently studying random walk and diffusion processes and their connections with random fields. I’m interested in this because at the core of dynamic linear models, Kalman filters, and state-space methods there is a random walk in a parameter space. … Continue reading
Posted in American Meteorological Association, American Statistical Association, AMETSOC, Arthur Charpentier, atmosphere, diffusion, diffusion processes, dynamic linear models, dynamical systems, environment, geophysics, hurricanes, Kalman filter, Kerry Emanuel, Lévy flights, Lorenz, Markov chain random fields, mathematics, mathematics education, maths, MCMC, mesh models, meteorological models, meteorology, model-free forecasting, Monte Carlo Statistical Methods, numerical analysis, numerical software, oceanography, open data, open source scientific software, physics, random walk processes, random walks, science, spatial statistics, state-space models, statistical dependence, statistics, stochastic algorithms, stochastics, time series
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Newt Gingrich and Van Jones. Right on.
It’s the thing. And it addresses how media and people forget about the actual statistics, and focus on the White Hot Bright Light. A study by Gelman, Fagan, and Kiss A study by Freyer A counterpoint to the Freyer study … Continue reading
Posted in American Statistical Association, Bayes, Bayesian, citizen science, criminal justice, Daniel Kahneman, ethics, evidence, fear uncertainty and doubt, humanism, Lives Matter, logistic regression, Markov Chain Monte Carlo, MCMC, organizational failures, population biology, rationality, reasonableness, risk, statistics, Susan Jacoby, the right to know
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On Smart Data
One of the things I find surprising, if not astonishing, is that in the rush to embrace Big Data, a lot of learning and statistical technique has been left apparently discarded along the way. I’m hardly the first to point … Continue reading
Posted in Akaike Information Criterion, Bayes, Bayesian, Bayesian inversion, big data, bigmemory package for R, changepoint detection, data science, data streams, dlm package, dynamic generalized linear models, dynamic linear models, dynamical systems, Generalize Additive Models, generalized linear models, information theoretic statistics, Kalman filter, linear algebra, logistic regression, machine learning, Markov Chain Monte Carlo, mathematics, mathematics education, maths, maximum likelihood, MCMC, Monte Carlo Statistical Methods, multivariate statistics, numerical analysis, numerical software, numerics, quantitative biology, quantitative ecology, rationality, reasonableness, sampling, smart data, state-space models, statistical dependence, statistics, the right to know, time series
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p-values and hypothesis tests: the Bayesian(s) rule
The American Statistical Association of which I am a longtime member issued an important statement today which will hopefully move statistical practice in engineering and especially in the sciences away from the misleading practice of using p-values and hypothesis tests. … Continue reading
Posted in approximate Bayesian computation, arXiv, Bayes, Bayesian, Bayesian inversion, bollocks, Christian Robert, climate, complex systems, data science, Frequentist, information theoretic statistics, likelihood-free, Markov Chain Monte Carlo, MCMC, Monte Carlo Statistical Methods, population biology, rationality, reasonableness, science, scientific publishing, statistical dependence, statistics, stochastics, Student t distribution
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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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R and “big data”
On 2nd November 2015, Wes McKinney, the developer of the highly useful Python pandas module (and other things, including books), wrote an amusing blog post, “The problem with the data science language wars“. I by no means disagree with him. … Continue reading
Sea Surface Anomalies
(Hat tip to Susan Stone.) The graphic below shows sea surface temperature anomalies relative to the 1971-2000 baseline First data are courtesy of the Climate Reanalyzer, a joint project of the Climate Change Institute at the University of Maine, and … Continue reading
Posted in Anthropocene, carbon dioxide, climate, climate change, climate disruption, climate education, differential equations, diffusion processes, dynamical systems, ecology, ENSO, environment, forecasting, geophysics, global warming, Hyper Anthropocene, IPCC, mathematics, MCMC, NASA, NCAR, NOAA, oceanography, open data, physics, Principles of Planetary Climate, rationality, reasonableness, risk, science, science education, sea level rise, statistics, sustainability, the right to know, time series, transparency
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“… the most patronizing start to an answer I have ever received …”
Professor Christian Robert tries to help out a student of MCMC on Cross Validated and earns the comment that his help had “the most patronizing start to an answer I have ever received“. I learned a new term: primitivus petitor.
“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…
“Unbiased Bayes for Big Data: Path of partial posteriors” (Christian Robert)
Unbiased Bayes for Big Data: Path of partial posteriors.
Markov Chain Monte Carlo methods and logistic regression
This post could also be subtitled “Residual deviance isn’t the whole story.” My favorite book on logistic regression is by Dr Joseph Hilbe, Logistic Regression Models, CRC Press, 2009, Chapman & Hill. It is a solidly frequentist text, but its … Continue reading
Posted in Bayes, Bayesian, logistic regression, MCMC, notes, R, statistics, stochastic algorithms, stochastic search
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Bayesian change-point analysis for global temperatures, 1850-2010
Professor Peter Congdon reports on two Bayesian models for global temperature shifts in his textbook, Applied Bayesian Modelling, as “Example 6.12: Global temperatures, 1850-2010”, on pages 252-253. A direct link is available online. The first is apparently original with Congdon, … Continue reading
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
On nested equivalence classes of climate models, ordered by computational complexity
I’m digging into the internals of ABC, for professional and scientific reasons. I’ve linked a great tutorial elsewhere, and argued that this framework, advanced by Wood, and Wilkinson (Robert), and Wilkinson (Darren), and Hartig and colleagues, and Robert and colleagues, … Continue reading
Posted in approximate Bayesian computation, Bayes, Bayesian, biology, ecology, environment, forecasting, geophysics, IPCC, mathematics, maths, MCMC, meteorology, NCAR, NOAA, oceanography, optimization, population biology, Principles of Planetary Climate, probabilistic programming, R, science, stochastic algorithms, stochastic search
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Liddell and Kruschke, on conditional logistic Bayesian estimation
(“Ostracism and fines in a public goods game with accidental contributions: The importance of punishment type”) An overview. The article
Posted in Bayes, Bayesian, biology, citizenship, civilization, compassion, ecology, economics, ethics, humanism, investing, MCMC, politics, rationality, reasonableness, risk, sociology, statistics
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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
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?.
Sea Level Rise, after Church and White (2006)
Modeling done with a Bayesian Rauch-Tung-Striebel algorithm, estimating priors of variance for observations and state by using a stationary bootstrap for the series using Politis and Romano algorithm.
Posted in Bayesian, carbon dioxide, civilization, climate, climate education, conservation, consumption, ecology, economics, education, efficiency, energy, energy reduction, engineering, environment, forecasting, geoengineering, geophysics, humanism, MCMC, meteorology, oceanography, optimization, physics, politics, rationality, reasonableness, science, statistics
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Bayes vs the virial theorem
Bayes vs the virial theorem.
Posted in Bayesian, mathematics, maths, MCMC, reasonableness, science, statistics
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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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“Data-driven science is a failure of imagination” (Petr Keil)
Happened across this today … I could not agree more: “Data-driven science is a failure of imagination” by Petr Keil. I look forward to reading his posts on Bayesian statistics.
Posted in Bayesian, engineering, history, mathematics, maths, MCMC, probabilistic programming, rationality, science
Tagged data mining, data science
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