Researcher course in quantitative foundations
Bayesian Statistics for Finance
Bayesian statistics for people who estimate things from too little data, which in finance is everyone: priors and posteriors, shrinkage of means and covariances, Bayesian regression, MCMC in practice, and judging strategies with uncertainty left in.
Bayesian statistics is a way to estimate with too little data, and in finance there is never enough. Ten years of monthly returns is 120 numbers, which says little about an expected return. Bayesian methods combine the data with a prior, shrink unstable estimates toward something sensible, and report what is still uncertain.
Where is it used on a desk?
In shrinkage of covariance matrices for portfolio construction, in Black-Litterman views, in regime and state-space models, in judging which of many strategies is genuinely better, and in machine learning models that need calibrated uncertainty. The course works each of these on real data.
How is the course taught?
Audio lessons cover the reasoning, explainer films show priors becoming posteriors, and the workbooks hold derivations, PyMC notebooks and cheat sheets. Assignments and the research note receive written feedback from the faculty.
Who is this course for?
Researchers in quantitative investing, machine learning and risk. It counts toward the Certificate in Machine Learning for Trading and so toward the Fellowship in Computational Finance.
What you will be able to do
- Set priors, compute posteriors and explain how they combine judgement with data.
- Shrink expected returns and covariance matrices and show the gain out of sample.
- Fit Bayesian regression and hierarchical models with MCMC, and check that the sampler has converged.
- Report a strategy's performance as a distribution rather than a single number.
Syllabus, module by module
Bayes' rule at work
Priors, likelihoods and posteriors on simple financial questions.
Conjugate models
Normal and Beta models for means, volatilities and hit rates.
Shrinkage
James-Stein and Ledoit-Wolf, and why shrunk estimates beat sample estimates out of sample.
Bayesian regression
Priors on coefficients, regularisation as a prior, and predictive distributions.
MCMC in practice
Metropolis-Hastings, Hamiltonian Monte Carlo, PyMC and convergence diagnostics.
Hierarchical models
Pooling information across assets, funds and strategies.
How the certificate is earned
Graded assignments and a final research note applying a hierarchical model to a cross-section of strategies or assets. On a pass you receive the Course certificate in Bayesian Statistics for Finance, issued by the Institute with a verification code. Read how certification works.
Before you start
Probability, statistics and regression at the level of the Institute's foundation courses.
This course counts toward
- Certificate in Machine Learning for TradingOne semester of eight courses and a capstone on applying machine learning to markets without fooling yourself: labelling, features, purged validation, deep and language models, regimes and reinforcement learning.
- Fellowship in Computational FinanceThe top credential on the researcher path. Four semesters, 38 courses, and a dissertation supervised in writing and examined by two faculty members.
Questions applicants ask
Why use Bayesian statistics in finance?
Because financial data is short and noisy, and sample estimates of means and covariances are unstable. Bayesian methods add structure through priors and shrinkage, and they keep the uncertainty in the answer instead of hiding it.
How does this relate to the Black-Litterman model?
Black-Litterman is a Bayesian model: market equilibrium returns act as the prior and the investor’s views as the data. This course gives the general machinery behind it.