Math for Machine Learning: Introduction to Bayesian Statistics

Bayesian statistics is a way of thinking about probability that helps us make decisions and predictions by combining what we already know (called a prior) with new data we see.

It is a large field with many popular applications (bayesian networks, diffusion models, variational autoencoders), with a couple key ideas.

The probability density function (PDF), describes how likely different values of a variable are. This function is central to how we make math calculations using different distributions.

In machine learning applications, we often want to find the posterior distribution, which tells us what we believe about something after seeing the data. Since this can be hard to calculate exactly, we use sampling methods to estimate it (for instance, variational autoencoders sample from the distribution to generate new images).

We also can look at the joint probability distribution, which shows how several variables behave together, and from that, we can find marginal distributions by focusing on just one variable at a time.

Finally, the expectation (or expected value) summarizes what we think will happen on average.

C: Deepia

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