We should all be Bayesian Statisticians

Feb 26 / Geoff Robinson

Ever wondered how leading investment analysts make their decisions? A significant part of their success is attributed to a technique grounded in a philosophical theory from the 18th century: Bayesian statistics. It has revolutionized the financial world, enabling investors to make more informed, precise, and adaptable investment decisions.

Listen to our blog

Understanding Bayesian Statistics
Named after Reverend Thomas Bayes, Bayesian statistics is an approach to statistics that incorporates prior knowledge into its calculations. As Nate Silver, a renowned statistician, aptly puts it, "Bayes' theorem is named after Thomas Bayes, who showed how to make probabilistic inferences about events from empirical data and also a mathematical lexicogrammar" (Silver, 2012).

In a traditional statistical approach, we perform an experiment, collect data, and draw conclusions based on that data. On the other hand, Bayesian statistics starts with an initial 'prior' belief, which is then updated with new data to form a 'posterior' belief. This continual update and flexibility represent the crux of Bayesian analysis.
The principle behind Bayesian statistics is Bayes' theorem, a mathematical formula describing how to update probabilities based on new evidence. In formal terms, Bayes' theorem is expressed as:

P(H|E) = [P(E|H) * P(H)] / P(E)

Here, P(H|E) is the probability of hypothesis H given the evidence E. P(E|H) is the probability of evidence E given that hypothesis H is true. P(H) and P(E) are the probabilities of hypothesis H and evidence E independently.

Bayesian Statistics in Investment Analysis
The primary reason Bayesian analysis is relevant in investment analysis is its unique approach to uncertainty and risk. Investment analysts must navigate a vast sea of economic data, company financials, and market trends while considering the inherent uncertainty and ambiguity that defines the financial world.
Legendary investor Howard Marks once said, "In the world of investing, nothing is certain. Consequently, everything the investor does involves uncertainty... the future is merely a range of possibilities" (Marks, 2011).

Bayesian statistics allows us to integrate these uncertainties into our investment models. It acknowledges that our understanding of financial markets isn't static; it evolves as we gain new information.

1. Prior and Posterior Beliefs: Investors start with prior beliefs about asset returns, risks, correlations, etc., and update these beliefs as new market data arrives. Andrew Gelman, a statistics and political science professor, emphasizes, "The idea behind Bayesian statistics is that learning is a process of updating our beliefs about the world" (Gelman, 2015).

2. Flexible Modeling: Bayesian models can handle complex and irregular data patterns and incorporate any prior information, making them more flexible and adaptable than traditional statistical models.

3. Probability Distributions: Bayesian statistics provides a full probability distribution of outcomes rather than a single estimate or range. This distribution can be used to understand the risk associated with different investment strategies.

4. Superior Predictive Power: Research suggests that Bayesian methods can provide superior predictive power in certain circumstances (Dijk & van der Wel, 2013). They can be instrumental in forecasting returns and assessing investment risk, both crucial for successful investing.


In a nutshell, Bayesian statistics is a modern, dynamic approach that marries experience with current data. It helps investors to assess risk better, make predictions, and adjust their beliefs based on the ever-changing financial environment. As we navigate the complexities of the investment world, we should remember another profound quote by Howard Marks: "The future is unpredictable... no approach will allow you to predict the next outcome. The best any method can do is assess probabilities" (Marks, 2011).

In the uncertain investment world, Bayesian statistics provides a structured framework for understanding and incorporating these probabilities into decision-making processes. As investors, the ability to update our beliefs and models in light of new information is not just advantageous; it's essential.

While Bayesian methods may not be a silver bullet for all investing challenges, their constant learning and adaptation principles align perfectly with the unpredictable nature of financial markets. Incorporating these methodologies into investment strategies can lead to more informed decision-making, a deeper understanding of risk and return dynamics, and the potential for enhanced investment performance.

Silver, N. (2012). The Signal and the Noise: Why So Many Predictions Fail—but Some Don't. Penguin.
Marks, H. (2011). The Most Important Thing: Uncommon Sense for The Thoughtful Investor. Columbia Business School Publishing.
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian Data Analysis. CRC press.
Dijk, D., & van der Wel, M. (2013). Forecasting volatility with the realized range in the presence of noise and non-trading. The Economic Journal, 123(567), 61-81.