I work through a simple Python implementation of geometric Brownian motion and check it against the theoretical model.

1

Inference for hidden Markov models (HMMs) is numerically unstable. A standard approach to resolving this instability is to use scaling factors. I discuss this idea in detail.

2

I needed a Python implementation of the multivariate skew normal. I wrote one based on SciPy's multivariate distributions module.

3

For a project, I needed to compute the log PDF of a vector for multiple pairs of mean and variance parameters. I discuss a fast Python implementation.

4

I provide a numerical demonstration that the mutual information of two random variables, the observations and latent variables in a Gaussian mixture model, is symmetric.

5

Normalizing vectors of log probabilities is a common task in statistical modeling, but it can result in under- or overflow when exponentiating large values. I discuss the log-sum-exp trick for resolving this issue.

6

I needed a fast and numerically stable Python implementation of the multivariate t-distribution. I wrote one based on SciPy's multivariate distributions module.

7

Naively computing the probability density function for the multivariate normal can be slow and numerically unstable. I work through SciPy's implementation.

8

I discuss Rasmussen and Williams's Algorithm 2.1 for an efficient implementation of Gaussian process regression.

9

Computing the log likelihood is a common task in probabilistic machine learning, but it can easily under- or overflow. I discuss one such issue and its resolution.

10