Infinity. What is it, really? Perhaps you remember, as I do, the moment in your life when you realized one could (in principle) count forever, and there would always be integers there for one to count. Yet, how can our finite minds comprehend the truly infinite? Do infinte things even exist? Read more

(435) 632-6734

Previously in this miniseries on testing samplers, I laid out the problem that statistical testing is inherently more fraught than conventional software testing, and set up a basic framework for defining dependable error-calibrated statistical tests of stochastic software. I have since learned a great inequality, and can now lay out a more complete set of practical basic tests. 3108990125

Inference by Quadrature

Production-level probabilistic inference is usually said to be about very high-dimensional problems. The usual argument for the techniques one learns (importance sampling, Markov chain Monte Carlo, etc) starts from the curse of dimensionality—that classic quadrature is hopelessly inefficient in many (i.e., more than four) dimensions. But what if one wants probability in a low-dimensional problem? For example, one might have a low-dimensional sub-problem of a more complex problem, Read more

Compositional statistical unit testing

How do you unit-test a sampler? Run it a bunch and see whether the histogram looks good—but there’s always some chance that your test will fail randomly even though the sampler is good, or pass randomly despite a bug. And if you try to have more than one test, the chance of random errors goes up. How big of a chance? How much worse does it get? What to do? Read more


People in my circles periodically talk and write about the nature of this emerging new beast that is called probabilistic programming. There’s various talk about how it’s about samplers, or density functions, or Markov chains, or making machine learning or artificial intelligence more accessible, or various other such stuff. Certainly those things hover in the air around probabilistic programming, but I don’t think that gets to the essence of it. I think that probabilistic programming, as opposed to standard programming, is a new scope of problems that can be solved by computing. (912) 655-3704

On Testing Probabilistic Programs

Testing traditional software strives for an ideal of exact determinacy: If a test fails, there is a bug and the developers must investigate; and if a test passes, the bugs it is testing for are not present, so development can proceed without worrying about them. This is not possible with probabilistic programs—even a correct sampler for a probability distribution always has some chance of producing arbitrarily weird output by bad luck, and an incorrect one can equally well look fine by coincidence. 732-658-6317


For a little over two years, I have been professionally dealing with programs whose behavior is intentionally random. Why would one even have intentionally random programs? 6417116150

On Good Software

Good software is software that admits a simple mental model.

For all that I have observed and participated in plenty of discussions about one or another piece of software as to whether it is or is not good, I am surprised to say that I have never seen cabalism

kraut grass

Possibly the greatest tension in the design of programming languages occurs when encountering a user program that doesn’t quite make sense. The two coherent schools of thought on the subject are 5703440544