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zakruti.com » Knowledge, science, education » Crash Course
Probability Part 2: Updating Your Beliefs with Bayes: Crash Course Statistics #14

Probability Part 2: Updating Your Beliefs with Bayes: Crash Course Statistics #14

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Rating: 4.0; Vote: 1
Today we're going to introduce bayesian statistics and discuss how this new approach to statistics has revolutionized the field from artificial intelligence and clinical trials to how your computer filters spam! We'll also discuss the Law of Large Numbers and how we can use simulations to help us better understand the rules of our data, even if we don't know the equations that define those rules. Want to try out the law of large numbers simulation yourself? More details here
Date: 2022-04-04

Comments and reviews: 8


Great to see that at least one thinking mind has come to a conclusion that spreading the knowledge about the Bayesian statistics is worth to try. Many thanks for that!
I had finished my master thesis in psychology at University of Warsaw and I am really shocked how little knowledge of statistics psychologists/ psychiatrists have (yes, non-psychologists, this topic is consisted of 70% of statistics, methodology, testing, experiments, designs etc. and only in 30% of ideas of such individuals as Freud, Horney, Maslow or Pavlov. 5 years of studying this field have given me two sad conclusions about methodology of verifying new thesis of psychology:
1. Even psychology PhDs/ professors (globally, not only in Poland) have just a tiny tiny (if any) knowledge of basics of statistics (no one, except statistic tutors, cares about normal distribution, skewness of the frequencies, size of the sample and type of the sample when it comes to analyzing the data. As I was helping other students to deal with statistics, I was facing a really shocking attitudes towards stats from PhDs/ professors like -hey, I don't have a clue on what to do with gathered material, so let's do anything - correlation (r Pearsons test) or causation (t Student's test, whatever-. That freaked me out a bit as I started to think that really so little psychology PhDs/ professors really know what they are talking about in their papers.
Moreover, as I was looking for some literature for my masters, about 50-70% of ALREADY PRINTED papers was a garbage data IMO. Like -hey, I just did a research on 50 Iranian/Polish/American (any nation is applicable) students from 1st year - 35 female and 15 male. I pushed it through the SPSS machine (pushed some buttons and some numbers occur, yay) and the conclusion is that generally speaking FEMALE are more open to xxx than man (place whatever you want instead of -xxx- (and yet - please don't make me write every mistake made in this description because it will take me another 15 minutes to summarize it: ).
2. (Which is the result of point 1) If such honored people around the world rarely cares about the key assumptions to be fulfilled, how come a. other students would be able to learn stuff? b. how come these students will be able to verify the meaning of their data? c. therefore, how future thesis would be verified if we both get rid of any theoretical assumptions and forget about statistical knowledge? d. what comes next?
Another topic is also the machine of printing scientific papers and the silence of the experiments that did not fit to the already assumed thesis (or those which just crushed the thesis, but it is a whole new area of discussion. :)

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Just a brief note: If you run the simulation, in the last line of the code -hist(simulated_samples, xlim = c(0, 100, breaks=seq(0, 100, 1)- add a space before -breaks- and after the comma which preceeds -breaks-. Otherwise, the code will give you an error.
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This makes me think about the false dichotomy fallacy a lot, since we tend to reduce probabilities into the simplest terms, like 50%, instead of more complex and harder to visualize mathematics.
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Yes! Bayesian statistics!
I was fearing that this series (like - sadly - so much of modern science) would be all about frequentist statistics. I'm so glad to be proven wrong!

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-As long as the distribution doesn't have infinite variance-. And even then it still works. As long as the distribution doesn't have infinite expectation is the real condition.
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Wow, this visualization is very helpful. More teachers and resources need to use this method because it helps understand so much more than just a formula.
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I dont' understand how the simulation arrived at 49. 2%, when the true positive chance was at 90% - shouldn't it then also have been at 90%?
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you have got here the best explanation i have seen so far in my life for P(A-B. that -venn diagram arithmetic- totally makes sense.
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