Bayesian Thinking: You Are Gullible Without This Simple Method

Bayesian thinking is a model which allows you to adapt your thinking to new evidence. It was developed in the 17th century by mathematician and philosopher Thomas Bayes. The mental model has seen application in statistics, education, philosophy, economics, law, finance, and even gambling. It emphasizes continuously updating your beliefs in light of new data. This helps mitigate biases, improve predictions, and refine decision-making in uncertain environments. Think of it as three steps: (1) start with your prior assumption, (2) incorporate new evidence, and (3) change your assumption to fit the data accurately.

In truth, this seemingly complex idea—like with most statistics concepts—is rather straightforward. You and I have been implementing it with great success throughout our lives without even knowing it. It’s a form of statistical reasoning. Calculating and updating probabilities to make the best possible predictions. It doesn’t tell you anything new. It just relies on existing data and historical evidence to help you anticipate what will happen in the future. The main idea is to update your assumptions about the world when you encounter new information. No theory is perfect. Everything can be considered a work in progress, always subject to further refinement.

Here is a simple example. Say you went to test for cancer. The doctor tells you the test is 95 percent accurate. That is, out of 100 people with cancer, the test will be positive for 95 and 95 of 100 people who do not have cancer test negative. If you test positive, does it mean there is a 95 percent chance of you having cancer? No. But people jump to conclusions like these. This is why we use Bayesian thinking. It teaches us to include our context and probability before jumping to conclusions. With that last statistic, assuming 1 percent of the population has cancer, you arrive at 16.1 percent. The probability is still high, but you shouldn’t conclude that you have cancer.

Bayesian thinking guards you against stereotypical inferences. For instance, suppose you see a nerdy looking guy at university. Big glasses. Long hair. Dumb looking smile. Even the voice and bowtie match the nerdy stereotype. Your first guess of what their major is would probably be mathematics or computer science. But your first instinct made you forget you are in a university dominated by business majors. The idea: combining the prior knowledge you have with the evidence you observe gives you a more accurate and robust conclusion.

How you might use Bayesian thinking as a mental model:

• Personal decision-making: instead of holding rigid opinions, use Bayesian thinking to refine your assumptions as new data arrives. Example: should you trust a particular news source? Context: you think the news source is 75 percent credible. Evidence: the source misreported a major story. Updated assumption: you downgrade the reliability to 50 percent or lower, adjusting based on the error.

• Business and investing: Bayesian thinking is priceless in high-stakes decision-making under uncertainty, such as investing, marketing, and business strategy. Example: evaluating a startup investment. Context: 30 percent of startups succeed based on historical data. Evidence: the startup has a strong leadership team and is an agile improver. Updated assumption: the success likelihood increases, making your investment more attractive.

• Medicine and diagnostics: a doctor can use Bayesian thinking to update diagnoses based on test results. Example: interpreting a medical test. Context: 1 percent of patients have this rare disease. Evidence: the test is 90 percent accurate, and has 5 percent false positives. Updated assumption: a positive result does not mean 90 percent certainty of illness, and a Bayesian analysis is needed to adjust prior odds.

• Artificial intelligence and machine learning: many artificial intelligence systems use Bayesian inference to make predictions and adjust dynamically. Example: the spam filters in an email service. Context: some words, like “free” and “win” and “sale” have a 50 percent chance of indicating spam. Evidence: the email just received also contains links to unverified sites. Updated assumption: the filter recalculates and marks it as 80 percent likely to be spam, thus putting it in the spam folder.

• Everyday life: Bayesian thinking helps adjust perceptions in relationships and day-to-day judgments. Example: your trust in a close friend. Context: you believe your friend is entirely honest. Evidence: they break a major promise. Updated assumption: their trustworthiness erodes slightly, but is not entirely dismissed—for now.

You get the idea. Keep your assumptions flexible and receptive to new data. Assess probability rather than thinking black-and-white. Counteract cognitive traps by doing so. This helps you adapt in our unpredictable world.