As I keep mentioning ad nauseam, I think probability’s really important in understanding all sorts of things about science.\u00a0 Here’s a really basic question that’s easy to ask but maybe not so easy to answer: What do probabilities mean anyway?<\/p>\n
Not surprisingly, this is a question that philosophers have taken a lot of interest in.\u00a0 Here’s a nice article<\/a> reviewing a bunch of interpretations of probability. \u00a0 The article lists a bunch of different interpretations, but ultimately I think the most important distinction to draw is between objective <\/em>and subjective<\/em> interpretations: Are probabilities statements about the world, or are they statements about our knowledge and belief about the world?<\/p>\n The poster child for the objective interpretation is frequentism<\/em>, and the main buzzword associated with the subjective interpretation is Bayesianism<\/em>.\u00a0 If you’re a frequentist, you think that probabilities are descriptions of the frequency with which a certain outcome will occur in many repeated trials of an experiment.\u00a0 If you want to talk about thing that don’t have many repeated trials (e.g., a weatherman who wants to say something about the chance of rain tomorrow, or a bookie who wants to set odds for the next Super Bowl), then you have to be willing to imagine many hypothetical <\/em>repeated trials.<\/p>\n The frequentist point of view strikes me as so utterly bizarre that I can’t understand why anyone takes it seriously.\u00a0 Suppose that I say that the Red Sox have a 20% chance of winning the World Series this year. Can anyone really believe that I’m making a statement about a large (in principle infinite) number of imaginary worlds, in some of which the Red Sox win and in others of which they lose?\u00a0 And that if Daisuke Matsuzaka breaks his arm tomorrow, something happens to a bunch of those hypothetical worlds, changing the relative numbers of winning and losing worlds? These sound utterly crazy to me, but as far as I can tell, frequentists really believe that that’s what probabilities are all about.<\/p>\n It seems completely obvious to me that, when I say that the Red Sox have a 20% chance of winning the World Series, I’m describing my state of mind (my beliefs, knowledge, etc.), not something about a whole bunch of hypothetical worlds.\u00a0 That makes me a hardcore Bayesian.<\/p>\n So here’s what I’m wondering. Lots of smart people seem to believe in a frequentist idea of probability.\u00a0 Yet to me the whole idea seems not just wrong, but self-evidently absurd.\u00a0 This leads me to think maybe I’m missing something. (Then again, John Baez agrees with me on this,<\/a> which reassures me.)\u00a0 So here’s a question for anyone who might have read this far: Do you know of anything I can read that would help me understand why frequentism is an idea that even deserves a serious hearing?<\/p>\n","protected":false},"excerpt":{"rendered":" As I keep mentioning ad nauseam, I think probability’s really important in understanding all sorts of things about science.\u00a0 Here’s a really basic question that’s easy to ask but maybe not so easy to answer: What do probabilities mean anyway? Not surprisingly, this is a question that philosophers have taken a lot of interest in.\u00a0 … Continue reading What is probability?<\/span><\/a><\/p>\n","protected":false},"author":12,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-93","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/blog.richmond.edu\/physicsbunn\/wp-json\/wp\/v2\/posts\/93","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.richmond.edu\/physicsbunn\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.richmond.edu\/physicsbunn\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.richmond.edu\/physicsbunn\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.richmond.edu\/physicsbunn\/wp-json\/wp\/v2\/comments?post=93"}],"version-history":[{"count":0,"href":"https:\/\/blog.richmond.edu\/physicsbunn\/wp-json\/wp\/v2\/posts\/93\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.richmond.edu\/physicsbunn\/wp-json\/wp\/v2\/media?parent=93"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.richmond.edu\/physicsbunn\/wp-json\/wp\/v2\/categories?post=93"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.richmond.edu\/physicsbunn\/wp-json\/wp\/v2\/tags?post=93"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}