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Cinitiator
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Does anyone here know any good Bayesian statistics, Bayesian hypothesis testing, Bayesian inference, etc. learning materials (preferably online)?
Number Nine said:We can't say without knowing your background.
chiro said:If you are learning Bayesian Inference I'd strongly suggest you become comfortable with standard non-Bayesian Inference first before doing both at the same time.
Some books cover both in the one book, but I still stand by my recommendation.
camillio said:I know it's not online, but anyway, I strongly recommend this book (any edition, of course):
Gelman, A., Carlin, J. B., Stern, H. S. Rubin, D. B., Bayesian Data Analysis, Second Edition (Chapman & Hall/CRC Texts in Statistical Science), 2nd edn. (Chapman and Hall/CRC, 2003).
Its main advantage compared to other famous books (e.g. Robert's The Bayesian Choice or Bernardo&Smith's Bayesian Theory) is its straightforward approach. While the others first develop the decision-theoretic framework and set Bayesian methods within it, Gelman hits directly the "statistical core" of Bayesianism and provides computational means already in the first pages. For a newcomer I find this approach more digestible and better for getting the idea what's Bayesian statistics about.
Regarding the online sources, I recommend to walk through Christian Robert's blog, where, among others, you can find references to his teaching material. Jim Albert's teaching blog is great too.
camillio said:Well, the Bayesian approach is already a well established counterpart of the traditional frequentist statistics. The reason why it took so much time (although it's far older then frequentism) consisted mainly in the enormous denial from the traditional Fisher's and Neyman-Pearson's schools. However, their arguments were more or less philosophical and based on comparison of hardly comparable ideas. At this point it is worth to notice that even Fisherians and Neyman-Pearsonians fought each other :-)) If you become interested in the tangled history of Bayesian theory, I suggest reading McGraynes book "The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy", its really worth those $10 on Amazon. I also plan to read Gelman's and Robert's paper dealing with the affair.
The use of Bayesian methods is now widespread, you can meet them in the computer science, biology, geology, genetics, economy etc. etc. Unlike the traditional methods, they allow to quantify the uncertainty related to statistical decision (e.g. parameter estimation). This, in turn, allows to base decisions even on a very small sample and, if necessary, express the initial informative belief. I (not being a militant advocate of any of the two camps) believe that both Bayesian and frequentist methods are worth knowing and application when they suit circumstances. Both have pros and cons :-)
Cinitiator said:Thanks for your book suggestion, I will order that one as well.
But aren't Bayesian methods far less widespread than the frequentist ones? Most studies I read seem to be using the frequentist approach and frequentist hypothesis testing. Why is there such a preference for the frequentist methods in the scientific community, despite the Bayesian ones providing a far more clear and certain image of the real world?
Cinitiator said:Thanks for your book suggestion, I will order that one as well.
But aren't Bayesian methods far less widespread than the frequentist ones? Most studies I read seem to be using the frequentist approach and frequentist hypothesis testing. Why is there such a preference for the frequentist methods in the scientific community, despite the Bayesian ones providing a far more clear and certain image of the real world?
camillio said:In addition to chiro's reply, I'd add that the basic reasons why frequentist methods dominate are (i) historical - they were generally accepted quite recently, (ii) they are much harder to learn and understand for non-mathematicians (non-statisticians), (iii) they do not provide a simple bunch of methods easy to use and (very frequently) misuse. One usually needs to think about what he's doing, not simply feed a software with some (maybe spurious) data and click on a button to get some result (whatever one understands to be a result). Also, as you mentioned, the user doesn't obtain a simple dichotomous answer of type "yes" or "no" as, e.g. in classical hypotheses testing (again, whatever it means).
Bayesian statistics is a method of statistical inference that uses probability theory to update beliefs about a hypothesis as more evidence or data is collected. It is based on Bayes' theorem and is often used in decision making and predictive modeling.
Traditional statistics relies on fixed parameters and assumes that the data is a random sample from a population. Bayesian statistics, on the other hand, allows for the incorporation of prior beliefs and updates those beliefs as more data is collected. It also treats the parameters as random variables, rather than fixed values.
Bayesian statistics has a wide range of applications, including but not limited to decision making, predictive modeling, risk assessment, and data analysis in various fields such as medicine, engineering, and finance. It is also commonly used in machine learning and artificial intelligence.
There are various resources available for learning about Bayesian statistics, including textbooks, online courses, and tutorials. Some popular books on the subject include "Bayesian Data Analysis" by Andrew Gelman et al. and "Doing Bayesian Data Analysis" by John K. Kruschke. Online courses and tutorials can be found on platforms such as Coursera, Udemy, and YouTube.
Prior knowledge is not necessary to understand Bayesian statistics, as it can be learned independently. However, having some knowledge of probability theory and basic statistics can make it easier to grasp the concepts. It is also important to have a willingness to think in terms of probabilities and continuously update beliefs based on new evidence.