Bayesian Inference

Bayesian Inference is a statistical method for drawing conclusions from data, but for an investor, it’s something much more intuitive: a formal way of updating your beliefs in the face of new evidence. Think of it as a logical framework for changing your mind. Instead of starting from scratch every time new information comes out, a Bayesian approach takes what you already believe (your “prior” belief) and rigorously updates it with new facts to form a more refined conclusion (your “posterior” belief). For example, you might believe a company is a good investment based on its past performance. That's your prior. Then, it releases a surprisingly poor quarterly report. Bayesian inference provides a structured way to combine your initial optimism with this new, negative data to arrive at a more realistic, updated view of the company's prospects. It’s a powerful mental model for navigating the constant flow of news and data that defines the world of value investing.

At the heart of Bayesian Inference is a formula known as Bayes' Theorem. While the math can look intimidating, the concept is simple and incredibly useful for investors. It's about weighing new information correctly. Imagine you're trying to figure out if a company will beat its earnings estimates this quarter. Your thinking process, framed in a Bayesian way, would involve three key ingredients:

• Your Prior Belief (The “Prior”): This is your starting point. What is your initial gut feeling or researched opinion on the probability of the company beating its earnings? Based on your analysis of its competitive advantages and management, you might start with a 60% confidence level. This is your “prior.”
• The Likelihood of New Evidence: Now, new information arrives. Let's say a major supplier to the company reports blockbuster sales. You have to ask: “If my belief that the company is strong is true, how likely is it that its supplier would have such great results?” Let's say it's highly likely. This new piece of data supports your initial thesis.
• Your Posterior Belief (The “Posterior”): This is your updated belief after combining your prior with the new evidence. Because the supplier's good news supports your original theory, you can update your confidence. You might now believe there is an 80% chance the company will beat earnings. Your posterior belief becomes the new prior for the next piece of information that comes along, creating a continuous loop of learning and belief-updating.

You don't need a calculator to be a Bayesian investor. The real power comes from adopting the mindset. It offers a structured defense against the psychological traps that often lead to poor investment decisions.

Investing is the art of making decisions with incomplete information. A Bayesian approach acknowledges this reality head-on. It encourages you to think in terms of probabilities rather than certainties. Instead of asking, “Is this a good investment?”, you ask, “What is the probability this is a good investment, and how does this new piece of information change that probability?” This flexible thinking prevents you from becoming rigidly attached to your initial investment thesis and allows you to adapt as the facts change.

Legendary investor Philip Fisher championed the scuttlebutt method—the practice of talking to customers, suppliers, and competitors to gain a deeper understanding of a company. This is Bayesian inference in action. Let's say your “prior” belief is that a tech company has a durable competitive advantage. You then do some scuttlebutt:

1. New Evidence 1: You speak to a major customer who complains that the company's service has been declining. This new evidence weakens your prior.
2. New Evidence 2: You read a trade journal article about a new, disruptive competitor. This evidence also weakens your prior.
3. New Evidence 3: You talk to a former employee who praises the company's R&D culture. This strengthens your belief.

A Bayesian thinker doesn't throw out their thesis at the first bad news. Instead, they weigh each piece of evidence, updating their overall confidence level with each new “scuttlebutt” discovery.

Thinking like a Bayesian can be a powerful antidote to some of the most destructive cognitive biases in investing.

Confirmation bias is the tendency to seek out and favor information that confirms what we already believe. A Bayesian framework forces you to do the opposite. It demands that you ask how new information, especially information that contradicts your view, should quantitatively change your beliefs. It stops you from just patting yourself on the back and forces you to confront disconfirming evidence.

Overconfidence leads investors to take excessive risks based on a flawed sense of certainty. By forcing you to assign probabilities to your beliefs, Bayesian thinking makes your level of conviction explicit. It helps you distinguish between a 90% certainty and a 55% hunch, leading to better-calibrated decisions and more rational position sizing.

Bayesian inference isn't about complex math; it's a mental model for learning. It teaches you that your opinions should be treated as temporary hypotheses, not permanent truths. In a world overflowing with information, it provides a clear, logical system for processing new facts, updating your views, and making smarter decisions. By starting with a hypothesis, gathering evidence, and updating your beliefs accordingly, you are already thinking like a Bayesian—and becoming a more disciplined, adaptable, and ultimately more successful investor.