Ever feel like you stubbornly stick to your opinions, even when faced with new information? That’s human nature. But what if there was a mental tool to help you be more flexible and accurate in your thinking? Enter Bayesian updating, a powerful mental model that helps you refine your beliefs as new evidence surfaces. Let’s dive in!

1. What is Bayesian updating? #

Bayesian updating is a method of revising a probability estimate as new evidence becomes available, adjusting beliefs incrementally rather than in absolute terms. Think of it as gradually tweaking a dial on your belief system instead of flipping a switch.

This model comes from the world of statistics and probability theory, named after the 18th-century British statistician and philosopher Thomas Bayes. Bayes developed a theorem that mathematically describes how to update the probability of a hypothesis based on new evidence. While the theorem itself can get quite technical, the underlying principle is incredibly useful for navigating uncertainty in all aspects of life.

Essentially, it’s about constantly recalibrating your understanding of the world based on what you learn.

2. How It Works #

The core of Bayesian updating revolves around a few key components:

• Prior Probability (Prior): This is your initial belief or assessment of a situation before any new evidence is considered. Think of it as your starting point. For example, before a coin flip, your prior probability of it landing on heads might be 50%.

• Likelihood: This measures how likely the new evidence is, given the hypothesis. In our coin flip example, if you flipped the coin 10 times and it landed on heads 8 times, the likelihood of observing that outcome given that the coin is fair (50/50) would be relatively low.

• Posterior Probability (Posterior): This is your updated belief after taking the new evidence into account. It’s the result of combining your prior belief with the likelihood of the evidence. In the coin flip example, the posterior probability of the coin being biased towards heads would increase after seeing 8 heads in 10 flips.

Think of it like this: You have a “belief bucket” that’s already partially filled (your prior). You then add water to the bucket based on new evidence (the likelihood). The resulting fill level of the bucket represents your updated belief (the posterior).

(Diagram - imagine a bucket partially filled representing the prior. A tap pours water (likelihood) into the bucket, and the new level is the posterior.)

The formula underpinning it all is Bayes’ Theorem, but understanding the concept is more important than memorizing the equation.

3. Examples of the Model in Action #

Let’s see Bayesian updating in action:

• Medicine: A doctor suspects a patient might have a rare disease (low prior probability). They order a test that is highly accurate. If the test comes back positive, the doctor doesn’t automatically conclude the patient has the disease. They must consider the base rate (the prior probability) of the disease in the population. Even with a highly accurate test, a positive result might still be a false positive due to the rarity of the disease. This is a classic application of updating beliefs with new evidence.

• Investing: An investor believes a particular stock will perform well (prior belief). They then see a quarterly earnings report indicating lower-than-expected profits (new evidence). Bayesian updating would suggest they re-evaluate their initial assessment. While they might still believe in the long-term potential of the company, the negative report should lower their confidence and potentially lead to a revised investment strategy.

• Personal Relationships: You initially think a new colleague is quiet and reserved (prior belief). Over time, you observe them cracking jokes and engaging in lively conversations during team lunches (new evidence). Bayesian updating would lead you to adjust your initial assessment of them. You might now believe they are more outgoing than you initially thought.

4. Common Misunderstandings or Pitfalls #

One common pitfall is ignoring the prior probability. People often overemphasize new evidence without properly considering their initial belief. This can lead to drastically overreacting to isolated pieces of information. This is similar to base rate neglect which is explained by Daniel Kahneman.

Another mistake is confirmation bias: seeking out evidence that confirms your existing beliefs and ignoring evidence that contradicts them. This prevents true Bayesian updating because you’re not objectively assessing the likelihood of the new evidence.

Finally, some struggle with being precise with probabilities. It’s okay if you can’t quantify everything perfectly. The point is to consider the direction of the update, not necessarily the exact numerical change.

5. How to Apply It in Daily Life #

Applying Bayesian updating is a mindset shift. Here are some actionable tips:

• State Your Initial Beliefs: Before evaluating new information, explicitly state your prior belief. This forces you to acknowledge your starting point.
• Seek Diverse Information: Actively search for information that challenges your beliefs, not just confirms them.
• Ask “How Likely is This Evidence, Given My Beliefs?”: When faced with new evidence, pause and consider how likely it is, assuming your current beliefs are true.
• Be Open to Change: Recognize that it’s okay to change your mind when faced with compelling evidence. Don’t get stuck in your initial position.
• Practice Humility: Acknowledge that you are fallible and that your initial beliefs might be wrong.

6. Related Mental Models #

Bayesian updating works well with other mental models, including:

• First Principles Thinking: Deconstructing a problem to its fundamental truths helps establish a solid prior probability.
• Confirmation Bias: Being aware of this bias helps you avoid selectively interpreting evidence to support your pre-existing beliefs, allowing for more objective updating.
• Second-Order Thinking: Considering the consequences of your beliefs helps refine your prior probabilities by anticipating potential outcomes.
• Occam’s Razor: The simplest explanation is usually the best - which helps establish the most probable prior hypothesis.

By embracing Bayesian updating, you can become a more adaptable, rational, and insightful thinker. It’s not about being right all the time; it’s about being willing to learn and adapt your beliefs as new information becomes available. Go ahead, update your world view!