## Julia for Probabilistic Metaprogramming

Since around 2010, I've been involved with using and developing probabilistic programming languages. So when I learn about new language, one of my first questions is whether it's a good fit for this kind of development. In this post, I'll talk a bit about working in this area with Julia, to motivate my Soss project. Domain-Specific Languages At a high level, a probabilistic programming languages is a kind of domain-specific language, or DSL. [Read More]

## A Prelude to Pyro

Lately I've been exploring Pyro, a recent development in probabilistic programming from Uber AI Labs. It's an exciting development that has a huge potential for large-scale applications. In any technical writing, it's common (at least for me) to realize I need to add some introductory material before moving on. In writing about Pyro, this happened quite a bit, to the point that it warranted this post as a kind of warm-up. [Read More]

## Bayesian Optimal Pricing, Part 2

This is Part 2 in a series on Bayesian optimal pricing. Part 1 is here. Introduction In Part 1 we used PyMC3 to build a Bayesian model for sales. By the end we had this result: A common advantage of Bayesian analysis is the understanding it gives us of the distribution of a given result. For example, we very easily analyze a sample from the posterior distribution of profit for a given price. [Read More]

## Bayesian Optimal Pricing, Part 1

Pricing is a common problem faced by businesses, and one that can be addressed effectively by Bayesian statistical methods. We'll step through a simple example and build the background necessary to extend get involved with this approach. Let's start with some hypothetical data. A small company has tried a few different price points (say, one week each) and recorded the demand at each price. We'll abstract away some economic issues in order to focus on the statistical approach. [Read More]

## The Bias-Variance Decomposition

Say there's some experiment that generates noisy data. You and I each go through the process independently, and model the results. Would the resulting models be exactly the same? Well no, of course not. That's the whole problem with noise. Instead, we'll usually end up with something like this (for a quadratic fit): The idea is that we'd like to find an approximation to $$f(x)$$, but we can never observe this function directly. [Read More]

## Bayesian Changepoint Detection with PyMC3

A client comes to you with this problem: The coal company I work for is trying to make mining safer. We made some change around 1900 that seemed to improve things, but the records are all archived. Tracking down such old records can be expensive, and it would help a lot if we could narrow the search. Can you tell us what year we should focus on? Also, it would really help to know this is a real effect, and not just due to random variability - we don't want to waste resources digging up the records if there's not really anything there. [Read More]