Howdy, Stranger!

It looks like you're new here. If you want to get involved, click one of these buttons!

Supported by

Bayes Factor versus P (M1|data) / P (M2|data) ?

edited March 2016 in JASP & BayesFactor

Please help me interpret. I am new to JASP and Bayesian stats, so please point out my mistakes and enlighten me :)

Richard Moery writes on the Bayesfactor blog: "The Bayes factor is the relative predictive success between two hypotheses: it is the ratio of the probabilities of the observed data under each of the hypotheses. If the probability of the observed data is higher under one hypothesis than another, then that hypothesis is preferred."

My question: " If the probability of the observed data is higher under one hypothesis than another, then that hypothesis is preferred" ???

Why ? The Bayes Factor is the evidence in the data. But if my prior distribution was very informed, I may still prefer that distribution, even after the data. It is only after repeated new data that my prior will be "swamped", right?

In other words, what is more useful:

a) the Bayes Factor (the relative probability of the data under two competing models); or
b) the relative probability of the models, given the data? (which is the Bayes Factor * the relative probability of the models, prior to the data)

In yet other words, what good are Bayes Factors?

I know I a making mistakes here, so please correct my thinking. Thanks!

Comments

  • EJEJ
    edited 7:38AM

    Hi Pieter,

    I can't speak for Richard but I'll do it anyway :-) What I think Richard meant by "preferred" is "receives the most support from the observed data" or perhaps he meant "preferred if the prior odds are equal".

    Of course the overall belief in a model depends also on its prior plausibility, as you point out. What the BF gives you is the change in belief, aka the predictive updating factor. This is often useful because although researchers may differ a lot with respect to their prior enthusiasm about a hypothesis, they may agree on the extent to which the data change that enthusiasm. Everybody can take the BF and use it to adjust their own prior opinion.

    Cheers,
    E.J.

  • edited March 2016

    Wow, thanks for the fast response! I am learning (basic) Bayesian statistics, by reading a bunch of papers (as collected on http://alexanderetz.com/understanding-bayes/ , but also others, including some by you). And by playing with JASP.

    My goal is to teach students Bayesian statistics first and frequentist only after that (if at all). They study marketing, so it will be mostly market research. In this field, p-values are still king and misinterpretations galore. Everybody interprets confidence intervals as "I can be 95% sure that the true mean is between x and y". And of course low p-values "prove" that hypotheses are true.

    Bayesian statistics would (in theory) fit marketing like a glove. Credible intervals go well with how students (and staff!) interpret intervals. Using prior knowlegde is only logical. It goes well with market research is done usually: find usable secondary data, and then (if needed) collect new data yourself. In the classical approach, it is hard to really integrate old and new data, so what you see (if you see it at all) is: "hey! If find X, whereas existing market data says Y. This is remarkable......" sometimes followed by some ad-hoc explanation.

    I hope my students will welcome JASP. They do not like SPSS. JASP seems much more "user friendly". FYI, we are talking about students who mostly are not very interested in research and who are new to statistical packages. Using R or Python would be out of the question. :)

    My plan is to start with Bayesian statistics, using JASP. I would prefer to not do frequentist analysis at all, but on the other hand, it still is the dominant method so students should understand some key concepts. Problem is that frequentist statistics is conceptually difficult and prone to misinterpretations. Plus, "it answers the wrong question" because in my field no-one is interested in how likely "data of this sort or more extreme" are under some hypothesis; everybody wants to know: "what do these data tell us?" Sorry for the rambling :)

  • EJEJ
    edited 7:38AM

    Well I strongly agree, of course :-)
    We are working on a manual, videos, and a course book; I hope these may be useful to you when they come out (might take a while still).
    E.J.

  • edited 7:38AM

    I'd be VERY interested in a course book

  • Sorry to necrobump, but still relevant. I am teaching some introductory statistics classes. In total we are talking 40 students, subject is basic market research. Some (totally subjective) impressions:

    1. The students definitely prefer JASP over SPSS. "Just easier to use", "makes more sense". They liked the "tagline" that JASP is the 'low fat alternative' for SPSS....

    Simple things like clicking hypotheses (in frequentist analyses) (H1>H0; H1 != H0, H1<H0) are already helpful. The menus are logical. They like that analyses are done "immediately" and that there is no separate output file. Less confusion on their side. The output given (tables, plots) are simple but useful.

    1. Frequentist statistics is hard to teach. It requires twice an "upside down" way of thinking:
    • first, they must learn the "straw man thinking" of "to accept H1, you must reject H0. Only H0 is tested".
    • secondly, they must learn that probabilities are not P(hypotheses|data), which is what they actually want, but rather P(data|hypotheses). Hence the seemingly ineradicable misunderstandings about (frequentist) confidence intervals ("the likelihood that the population mean falls between these two boundaries") and significance ("the likelyhood of the hypotheses"). Not helped of course by the fact that misinformation about (specifically) confidence intervals is (pun intended) wide spread in textbooks and online......

    Sorry for the rambling, thanks for the software, the ideas and the support.

  • Thanks Pieter. Richard wrote a nice paper on confidence intervals (now that you mention them :-)):
    https://learnbayes.org/papers/confidenceIntervalsFallacy/

    Cheers,
    E.J.

  • Thank you E.J. I know that paper. :-)

Sign In or Register to comment.

agen judi bola , sportbook, casino, togel, number game, singapore, tangkas, basket, slot, poker, dominoqq, agen bola. Semua permainan bisa dimainkan hanya dengan 1 ID. minimal deposit 50.000 ,- bonus cashback hingga 10% , diskon togel hingga 66% bisa bermain di android dan IOS kapanpun dan dimana pun. poker , bandarq , aduq, domino qq , dominobet. Semua permainan bisa dimainkan hanya dengan 1 ID. minimal deposit 10.000 ,- bonus turnover 0.5% dan bonus referral 20%. Bonus - bonus yang dihadirkan bisa terbilang cukup tinggi dan memuaskan, anda hanya perlu memasang pada situs yang memberikan bursa pasaran terbaik yaitu http://45.77.173.118/ Bola168. Situs penyedia segala jenis permainan poker online kini semakin banyak ditemukan di Internet, salah satunya TahunQQ merupakan situs Agen Judi Domino66 Dan BandarQ Terpercaya yang mampu memberikan banyak provit bagi bettornya. Permainan Yang Di Sediakan Dewi365 Juga sangat banyak Dan menarik dan Peluang untuk memenangkan Taruhan Judi online ini juga sangat mudah . Mainkan Segera Taruhan Sportbook anda bersama Agen Judi Bola Bersama Dewi365 Kemenangan Anda Berapa pun akan Terbayarkan. Tersedia 9 macam permainan seru yang bisa kamu mainkan hanya di dalam 1 ID saja. Permainan seru yang tersedia seperti Poker, Domino QQ Dan juga BandarQ Online. Semuanya tersedia lengkap hanya di ABGQQ. Situs ABGQQ sangat mudah dimenangkan, kamu juga akan mendapatkan mega bonus dan setiap pemain berhak mendapatkan cashback mingguan. ABGQQ juga telah diakui sebagai Bandar Domino Online yang menjamin sistem FAIR PLAY disetiap permainan yang bisa dimainkan dengan deposit minimal hanya Rp.25.000. DEWI365 adalah Bandar Judi Bola Terpercaya & resmi dan terpercaya di indonesia. Situs judi bola ini menyediakan fasilitas bagi anda untuk dapat bermain memainkan permainan judi bola. Didalam situs ini memiliki berbagai permainan taruhan bola terlengkap seperti Sbobet, yang membuat DEWI365 menjadi situs judi bola terbaik dan terpercaya di Indonesia. Tentunya sebagai situs yang bertugas sebagai Bandar Poker Online pastinya akan berusaha untuk menjaga semua informasi dan keamanan yang terdapat di POKERQQ13. Kotakqq adalah situs Judi Poker Online Terpercayayang menyediakan 9 jenis permainan sakong online, dominoqq, domino99, bandarq, bandar ceme, aduq, poker online, bandar poker, balak66, perang baccarat, dan capsa susun. Dengan minimal deposit withdraw 15.000 Anda sudah bisa memainkan semua permaina pkv games di situs kami. Jackpot besar,Win rate tinggi, Fair play, PKV Games