Occam's Razor: Simplifying Complexities with Probability

Occam's Razor, a timeless concept of simplicity, directs us to choose the hypothesis with the fewest assumptions. How does this connect to statistics and probability?

In probability theory, simpler explanations are frequently associated with higher likelihoods. Assume you throw a coin and it lands heads 80 times out of 100. One possible explanation is that the coin is biased toward heads. Another possibility is that invisible forces have a selective influence on the outcome. Occam's Razor suggests the former since it requires fewer assumptions and is more statistically plausible.

This concept is mirrored by Bayesian inference, which is a cornerstone of modern statistics. When analyzing hypotheses, Bayesian approaches frequently prefer those with higher prior probabilities, basically applying Occam's Razor mathematically. Complex hypotheses with intricate assumptions have lower prior probabilities, therefore simple explanations are statistically preferred unless evidence clearly shows otherwise.

However, there is one caveat: simplicity does not always imply truth. An overly simplistic hypothesis may omit important details. It's about striking a balance between seeking simplicity and being open to complexity when necessary.

When you're faced with a perplexing scenario, use Occam's Razor. Ask the question: "What's the simplest explanation here?" You might simply find clarity in plain sight.