Several papers have appeared recently discussing the issue of how to tune the number of particles used in the particle filter within a particle MCMC algorithm such as particle marginal Metropolis Hastings (PMMH). Three such papers are: Doucet, Arnaud, Michael Pitt, and Robert Kohn. Efficient implementation of Markov chain Monte Carlo when using an unbiased […]
Several papers have appeared recently discussing the issue of how to tune the number of particles used in the particle filter within a particle MCMC algorithm such as particle marginal Metropolis Hastings (PMMH). Three such papers are: Doucet, Arnaud, Michael Pitt, and Robert Kohn. Efficient implementation of Markov chain Monte Carlo when using an unbiased […]
Been reading a lot of Gelman, Carlin, Stern, Dunson, Vehtari, Rubin “Bayesian Data Analysis” 3rd edition lately. Overall in the Bayesian framework some ideas (such as regularization, and imputation) are way easier to justify (though calculating some seemingly basic quantities becomes tedious). A big advantage (and weakness) of this formulation is statistics has a much […] Related posts: Checking claims in published statistics papers Data Science, Machine Learning, and Statistics:…
Many data science projects and presentations are needlessly derailed by not having set shared business relevant quantitative expectations early on (for some advice see Setting expectations in data science projects). One of the most common issues is the common layman expectation of “perfect prediction” from classification projects. It is important to set expectations correctly so […] Related posts: Setting expectations in data science projects More on ROC/AUC On Being a…
We’ve seen Monday, in the MAT8595 course how to use the Generalized Pareto Distribution to estimate some downside risk measures, given a sample (assumed to be i.i.d., I will not mention here properties on extremes for stochastic processes) with distribution . The cumulative distribution function of the Pareto distribution is here For some threshold , and , we can write From Pickands–Balkema–de Haan theorem, if is large enough, then Given our…
This week, in the MAT8595 course, we will start the section on inference for extreme values. To start with something simple, we will use maximum likelihood techniques on a Generalized Pareto Distribution (we’ve seen Monday Pickands-Balkema-de Hann theorem). Maximum Likelihood Estimation In the context of parametric models, the standard technique is to consider the maximum of the likelihood (or the log-likelihod).Let denote the parameter (with ). Given some – stnardard…
Introduction In the previous post I showed that it is possible to couple parallel tempered MCMC chains in order to improve mixing. Such methods can be used when the target of interest is a Bayesian posterior distribution that is difficult to sample. There are (at least) a couple of obvious ways that one can temper […]
Introduction In the previous post I showed that it is possible to couple parallel tempered MCMC chains in order to improve mixing. Such methods can be used when the target of interest is a Bayesian posterior distribution that is difficult to sample. There are (at least) a couple of obvious ways that one can temper […]
As it stands right now Cory Booker has a very good chance of winning the New Jersey Special U.S. Senate election on October 16 to replace Frank Lautenberg and fill the remainder of his term for the next 15 months. So with the election only about a month away I took advantage of some of […]
The Beta distribution (and more generally the Dirichlet) are probably my favorite distributions. However, sometimes only limited information is available when trying set up the distribution. For example maybe you only know the lowest likely value, the highest likely value and the median, as a measure of center. That information is sufficient to construct a […]
