[MUSIC] It's spelled out here in nice essay by Matthews 1998. Is that different people could use Bayes's Theorem and get different results. And so faced with some experimental evidence for say ESP, true believers could use Bayes's Theorem to show that the new results confirmed it, while skeptics could use it to show that the ESP didn't exist. Okay. And both views are possible because Bayes's Theorem only shows how to alter one's prior level of belief, and different people could start out with different opinions. Okay, so that's the issue. So the frequence approach laid out by Fisher and others were able to achieve what was thought to be impossible, which is a way of judging the significance of experimental data independent of any prior beliefs. Okay. So he had found a way that anyone could use to show that a result was too impressive, was too statistically significant to be dismissed as a fluke. And all you had to do was convert your raw data into this thing called a P-value. All right. Now, you still have to have some sort of a threshold to measure the significance of this P-value, and that was written up as 0.05 by Fisher in an original paper. So what were the insights that led to this particular value of 0.05? Well, Fisher admitted that there weren't any. He simply decided 0.05 because it was mathematically convenient. Okay. And, many people have pointed out say from the 60s on, there's been periods of times where there's been a significant amount of work showing that this approach, with these particular thresholds, are able to produce a lot of incorrect conclusions. So James Berger of Purdue wrote his entire series of papers warning about the quote, astonishing tendency of Fisher's p-values to exaggerate significance. Findings that met the 1 in 20 standard can actually arise when the data provide very little or no evidence in favor of an effect. Okay. So, that's the problem. So, now perhaps we can say that the pendulum is in some sense swinging back towards the Bayesian approach. One more problem with the Bayesian approach that I'll bring up that I don't necessarily have a slide on, which we'll see in a little bit of detail in perhaps the next segment, is that these conditional probabilities and these prior probabilities end up forcing you to model a situation mathematically. And that situation may be very difficult to model mathematically. Okay. So what you end up with is these chains of complicated conditional probabilities that need to be integrated in order to apply Bayes' rule. And so this was computationally intractable and there was a huge number of tricks and simplifications and ideas used to make this more tractable. Okay. But thanks to the development of methods that allow you to sample these complicated distributions computationally, this approach is becoming increasingly popular. Okay. And there's a lot of thinkers in this space that believe that for the 21st century, a combination of frequentness and Bayesian approaches is going to be dominant. Okay. So for these reasons we're gonna make sure we talk about the Bayesian approach at a very introductory level and leading up to a machine learning algorithm called naive Bayes. [MUSIC]