Bayes Theorem Quotes

“Imagine you're sitting having dinner in a restaurant. At some point during the meal, your companion leans over and whispers that they've spotted Lady Gaga eating at the table opposite. Before having a look for yourself, you'll no doubt have some sense of how much you believe your friends theory. You'll take into account all of your prior knowledge: perhaps the quality of the establishment, the distance you are from Gaga's home in Malibu, your friend's eyesight. That sort of thing. If pushed, it's a belief that you could put a number on. A probability of sorts. As you turn to look at the woman, you'll automatically use each piece of evidence in front of you to update your belief in your friend's hypothesis Perhaps the platinum-blonde hair is consistent with what you would expect from Gaga, so your belief goes up. But the fact that she's sitting on her own with no bodyguards isn't, so your belief goes down. The point is, each new observations adds to your overall assessment. This is all Bayes' theorem does: offers a systematic way to update your belief in a hypothesis on the basis of the evidence. It accepts that you can't ever be completely certain about the theory you are considering, but allows you to make a best guess from the information available. So, once you realize the woman at the table opposite is wearing a dress made of meat -- a fashion choice that you're unlikely to chance up on in the non-Gaga population -- that might be enough to tip your belief over the threshold and lead you to conclude that it is indeed Lady Gaga in the restaurant. But Bayes' theorem isn't just an equation for the way humans already make decisions. It's much more important that that. To quote Sharon Bertsch McGrayne, author of The Theory That Would Not Die: 'Bayes runs counter to the deeply held conviction that modern science requires objectivity and precision. By providing a mechanism to measure your belief in something, Bayes allows you to draw sensible conclusions from sketchy observations, from messy, incomplete and approximate data -- even from ignorance.”
― Hannah Fry, Hello World: Being Human in the Age of Algorithms