Bayesian Reasoning: Shark Attacks, and Making Better Decisions
How a fancy statistics concept can help you make better decisions in your day to day life
Making decisions can be challenging for most people, and there’s a good reason for that. Our brains are not always well-equipped to handle probabilities effectively. However, thanks to the work of Thomas Bayes and the development of Bayesian reasoning, we can improve our decision-making abilities in the face of uncertainty.
Give me 10 minutes, we’re going to cover:
- What Bayesian reasoning is
- How our brains process probabilities
- The advantages of thinking probabilistically
What is Bayesian reasoning?
Thomas Bayes, an 18th-century English minister, laid the groundwork for probability theory in his work “An Essay toward Solving a Problem in the Doctrine of Chances.” Richard Price, Bayes’ friend, later expanded upon his ideas, developing the Bayesian approach as a method for making decisions under uncertainty.
Pierre-Simon Laplace, a mathematician, refined and generalized Bayes’ theorem, applying it to problems such as predicting a planet’s future position based on past positions. Today, Bayes’ theorem has applications in medicine, statistics, and machine learning, among other fields.
Understanding the intuition behind Bayes’ theorem is more important than memorizing formulas. It involves honing your ability to accurately judge real-world probabilities and refining those probabilities as new information becomes available.
Bayes’ approach can be illustrated using a simple example. Suppose an assistant places a ball on a table without revealing its position. After observing the location of a second ball dropped several times and its relative position to the first ball, one can estimate the position of the first ball based on the evidence provided by the second. The Bayesian method builds upon this idea by incorporating prior knowledge or evidence-informed probability.
How our brains process probabilities
Humans generally struggle with processing probabilities effectively. Studies show that we tend to overestimate small probabilities and underestimate large ones. This can be attributed to the way our brains are wired.
The amygdala is responsible for threat detection, while the hippocampus is responsible for memory. The latter is more likely to store memories of negative events than positive ones. These two brain regions work together to create a “negativity bias,” causing us to focus more on the small likelihood of an event occurring rather than the many times it has not happened.
For example, you might be more likely to remember a time when you got sick after eating shellfish than all the times you didn’t. Our brains are not evolved to deal with the modern world, and the instincts that kept our ancestors alive are not always helpful today.
The benefits of thinking probabilistically
Developing a probabilistic mindset will make you more effective in various aspects of your life, from personal relationships to finances to your career. By considering all possible outcomes of a situation, you will be able to make better decisions.
Shark Attacks and Bayes:
Imagine you’re contemplating whether to swim in the ocean, but news stories of shark attacks make you hesitant. Applying Bayesian reasoning, you would consider all available information, such as the millions of people who swim in the ocean daily without incident and the increased media attention that makes shark attacks appear more common than they are.
After weighing this information, you’ll realize that the probability of a shark attack is relatively low, which can help you decide whether to swim. While there are no guarantees, thinking probabilistically will help you make the best decision based on the information at hand.
Conclusion
Bayesian thinking is a powerful concept that, when applied in your life, can lead to significant benefits. You don’t need to be an expert in math; just be open to considering all the possible outcomes of a situation.
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