用简洁的画面（内容尽量居中放大），通俗易懂的语言讲解Bayes’ formula application

视频信息

答案文本 复制

视频字幕 复制

Bayes' formula helps us update our belief about something happening after we see new evidence. Imagine a big box representing everyone. A small part of the box is for people with a certain condition. When you get a test result, you look at the part of the box that tested positive. Bayes' formula helps you figure out what proportion of the people in that positive test part actually have the condition. The Bayes formula has four key components. What we want to find is the posterior probability - the chance of having the condition given a positive test. To calculate this, we use three pieces of information: the prior probability, which is our initial belief about having the condition; the likelihood, which is the probability of testing positive if we have the condition; and the evidence, which is the overall probability of testing positive. Let's work through a concrete example. Imagine a rare condition affecting 1 in 1000 people, so only 0.1% of the population has it. We have a test that's 99% accurate - it correctly identifies the condition 99% of the time, and gives false positives only 1% of the time. Now, if you test positive, what's the actual chance you have the condition? This might seem like it should be close to 99%, but let's see what Bayes' formula tells us. Let's break down the numbers step by step. From our 1000 people, 1 person has the condition and 999 are healthy. When we test everyone, the 1 person with the condition will likely test positive - that's 99% of 1, which is about 1 person. But here's the key insight: of the 999 healthy people, 1% will get false positive results. That's about 10 people. So out of all 11 people who test positive, only 1 actually has the condition. This gives us a probability of 1 out of 11, or about 9% - much lower than the test's 99% accuracy might suggest! The key takeaway from Bayes' formula is profound: even with a highly accurate test, a positive result doesn't guarantee you have the condition. In our example, despite 99% test accuracy, a positive result only gives you a 9% chance of actually having the disease. This happens because rare conditions stay rare, and false positives from the large healthy population can overwhelm the true positives. Bayes' formula is widely used in medical diagnosis, spam detection, machine learning, and risk assessment - anywhere we need to update our beliefs based on new evidence.