How Bayes' Rule Can Make You A Better Thinker - 1 views
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To find out more about this topic, we spoke to mathematician Spencer Greenberg, co-founder of Rebellion Research and a contributing member of AskAMathematician where he answers questions on math and physics. He has also created a free Bayesian thinking module that's available online.
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Bayes’s Rule is a theorem in probability theory that answers the question, "When you encounter new information, how much should it change your confidence in a belief?" It’s essentially about making decisions under uncertainty, and how we should update or revise our theories as new evidence emerges. It can also be used to help us reach decisions in those circumstances when very few observations or pieces of evidence are available. And it can also be used to help us avoid common mistakes and fallacies in our thinking.
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The key to Bayesianism is in understanding the power of probabilistic reasoning. But unlike games of chance, in which there’s no ambiguity and everyone agrees on what’s going on (like the roll of die), Bayesians use probability to express their degree of belief about something.
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When it comes to the confidence we have in our beliefs — what can be expressed in terms of probability — we can’t just make up any number we want. There’s only one consistent way to handle those degrees in beliefs.
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In the strictest sense, of course, this requires a bit of mathematical knowledge. But Greenberg says there’s still an easy way to use this principle in daily life — and one that can be converted to plain English.
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Greenberg says it’s the question of evidence which he should apply, which goes like this:: Assuming that our hypothesis is true, how much more plausible, or likely, is the evidence compared to the hypothesis if it was not true?
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“It’s important to note that the idea here is not to answer the question in a precise way — like saying that it’s 3.2 times more likely — rather, it’s to get a rough sense. Is it a high number, a modest number, or a small number?”
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To make Bayes practical, we have to start with the belief of how likely something is. Then we need to ask the question of evidence, and whether or not we should increase the confidence in our beliefs by a lot, a little, and so on.
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“Much of the time people will automatically try to shoot down evidence, but you can get evidence for things that are not true. Just because you have evidence doesn’t mean you should change your mind. But it does mean that you should change your degree of belief.”
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Greenberg also describes Representativeness Heuristic in which people tend to look at how similar things are.
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Greenberg also says that we should shy away from phrases like, “I believe,” or “I don’t believe.” “That’s the wrong way to frame it,” he says. “We should think about things in terms of how probable they are. You almost never have anything close to perfect certainty.”
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“Let’s say you believe that your nutrition supplement works,” he told us, “Then you get a small amount of evidence against it working, and you completely write that evidence off because you say, ‘well, I still believe it works because it’s just a small amount of evidence.’ But then you get more evidence that it doesn’t work. If you were an ideal reasoner, you’d see that accumulation of evidence, and every time you get that evidence, you should believe less and less that the nutritional supplements are actually working.” Eventually, says Greenberg, you end up tipping things so that you no longer believe. But instead, we end up never changing our mind.
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“You should never say that you have absolute certainty, because it closes the door to being able to revise your certainty in light of new information,” Greenberg told io9. “And the same thing can be said for having zero percent certainty about something happening. If you’re at 100% certainty, then the correct way of updating is to stay at 100% forever, and no amount of evidence can tip you.”
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Lastly, he also says that probabilities can depend on the observer — what is a kind of probability relativity. We all have access to different information, so different people should assign different rates of probability to different things based on different sets of evidence.
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"Having a strong opinion about an issue can make it hard to take in new information about it, or to consider other options when they're presented. Thankfully, there's an old rule that can help us avoid this problem - and even help us make good decisions when we're uncertain. Here's how Bayesian Reasoning works, and why it can make you a better thinker."