advanced-algorithmic-trading

Chapter 2
Introduction to Bayesian Statistics
The first part of Advanced Algorithmic Trading is concerned with a detailed look at Bayesian
Statistics. As I mentioned in the introduction, Bayesian methods underpin many of the techniques
in Time Series Analysis and Machine Learning, so it is essential that we gain an understanding
of the "philosophy" of the Bayesian approach and how to apply it to real world
quantitative finance problems.
This chapter has been written to help you understand the basic ideas of Bayesian Statistics,
and in particular, Bayes’ Theorem (also known as Bayes’ Rule). We will see how the Bayesian
approach compares to the more traditional Classical, or Frequentist, approach to statistics
and the potential applications in both quantitative trading and risk management.
In the chapter we will:
• Define Bayesian statistics and Bayesian inference
• Compare Classical/Frequentist statistics and Bayesian statistics
• Derive the famous Bayes’ Rule, an essential tool for Bayesian inference
• Interpret and apply Bayes’ Rule for carrying out Bayesian inference
• Carry out a concrete probability coin-flip example of Bayesian inference
2.1 What is Bayesian Statistics?
Bayesian statistics is a particular approach to applying probability to statistical problems.
It provides us with mathematical tools to update our beliefs about random events in light
of seeing new data or evidence about those events.
In particular Bayesian inference interprets probability as a measure of believability or confidence
that an individual may possess about the occurance of a particular event.
We may have a prior belief about an event, but our beliefs are likely to change when new evidence
is brought to light. Bayesian statistics gives us a solid mathematical means of incorporating
our prior beliefs, and evidence, to produce new posterior beliefs.
Bayesian statistics provides us with mathematical tools to rationally update our subjective
beliefs in light of new data or evidence.
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