Tagged “conditional probability”

Aug 26, 2014

Joint, conditional and marginal probabilities

In this post I will discuss a topic that seems very dry at first but turns out to have many cool applications. While I will not discuss Bayesian inference in this post, understanding the relationship between joint, conditional and marginal probabilities is essential for the application of Bayesian thinking. As a result, I'll will often refer back to this discussion in future posts.

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Sep 11, 2014

Medical tests, a first example of Bayesian calculations

In this post I will discuss a first example of a Bayesian calculation using a well-known example of testing for breast cancer.

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Oct 24, 2014

Inferring probabilities, a second example of Bayesian calculations

In this post I will focus on an example of inferring probabilities given a short data series. I will start by tackling the theory of how to do the desired inference in a Bayesian way and will end by implementing the theory in Python so that we can play around with the ideas. In an attempt to keep the post more accessible, I will only consider a small set of candidate probabilities. This restriction allows me to minimize the mathematical difficulty of the inference and still obtain really cool results, including nice plots of the prior, likelihood and posterior.

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Dec 11, 2014

Inferring probabilities with a Beta prior, a third example of Bayesian calculations

In this post I will expand on a previous example of inferring probabilities from a data series. In particular, instead of considering a discrete set of candidate probabilities, I'll consider all (continuous) values between \( 0 \) and \( 1 \). This means our prior (and posterior) will now be a probability density function (pdf) instead of a probabilty mass function (pmf). More specifically, I'll use the Beta Distribution for this example.

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May 4, 2015

Probabilistic programming with Python and Lea

In this post I will cover installation of a probabilistic programming package for Python called Lea and provide some simple examples of using the package to do calculations with joint, conditional and marginal distributions. These examples follow the by-hand calculations done in a previous post.

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May 27, 2015

Revisiting the medical tests example with Python and Lea

In this post I will use Python, and the probabilistic programming package Lea, to re-analyze an example of Bayes' Theorem covered in an earlier post. The focus will be on translating the by-hand calculations into Python code.

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