Category Archives: Measure Theory

Thinking about path integrals …

Been busy this past week running “micro-simulation” models for my day job; “micro-simulation” = build a computer code to simulate a whole population of people, send a swarm of simulated infectious mosquitos after them, and then simulate the process of … Continue reading

Posted in Astrostatistics, Gaussian Processes, Infinite-Dimensional Inference, Measure Theory, Statistics | Leave a comment

Question about algebras? Help needed …

To make sure I don’t forget too much of what I’ve learnt in the past I periodically try solving some standard textbook exercises.  But today I ran into a bit of an odd one in Rosenthal’s “A First Look at … Continue reading

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Arxived and rejected on the same day …

So I arXived my brief research note on a generalization of the Savage-Dickey Density Ratio (SDDR) to general probability spaces (including those not admitting a Lebesgue reference measure) yesterday (so it’ll be out in today’s mailing later).  But this morning … Continue reading

Posted in Marginal Likelihood Estimation, Measure Theory, Rants, Statistics | 2 Comments

Recursive marginal likelihood estimators …

Just a quick note to advertise the once-revised draft of my recursive marginal likelihood estimators paper, now on astro/stat-ph: http://arxiv.org/pdf/1301.6450.pdf . The new version includes a greater emphasis on the applicability of these ideas (characterised by biased sampling) to the problem … Continue reading

Posted in Dirichlet Processes, Marginal Likelihood Estimation, Measure Theory, Statistics | Leave a comment

Importance sampling reweighting from an infinite mixture model to a finite mixture model …

I finally derived an expression for the Radon-Nikodym derivative of a k component finite Normal mixture model with respect to an equivalent infinite dimensional (Dirichlet process prior) mixture model; this was required for the revisions to my recursive marginal likelihood … Continue reading

Posted in Dirichlet Processes, Infinite-Dimensional Inference, Marginal Likelihood Estimation, Measure Theory, Statistics | 1 Comment

Notes on sufficiency …

Just finished reading up on the measure-theoretic formulation of sufficiency; so for other neophytes I’m uploading my annotated version of Halmos & Savage (1949):  img-928022611-0001 . Presumably if Jstor want to do me like they did Aaron Schwartz I guess I’ll … Continue reading

Posted in Measure Theory, Statistics | 1 Comment

Transformations of the Prior through the Likelihood

A figure prepared for the revision of our paper on recursive marginal likelihood estimators. The likelihood function (if measurable, of course) induces a measure on the (positive) reals, as do other measurable transformations using the likelihood function, such as the … Continue reading

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