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Bayesian talk and DIC

April 28, 2009

I gave an introduction to Bayesian talk for one of my classes. I’ve attached a PDF of the talk (click Thomas Bayes below to download it). Please feel free to leave comments and let me know what you think and if it’s helpful. It’s suppose to give a conceptual overview. It’s not meant to be definitive. Finally, I have included some humor in the presentation (e.g. Frequentist and Bayesian images). They are meant to be taken as a joke and do not at all imply that these individuals are representative of the different statistical lineages. There is one easter egg in the presentation. Click the word “Bayesian” on the Harry Potter slide. Enjoy!

thomas_bayes1

I recently started working with the MCMCglmm package in R and came across an interesting information criterion called the DIC (Deviance Information Criterion) that is often used for model selection when running MCMC. I look forward to seeing how the BIC and DIC differ. Additionally as I’m moving more in the direction of employing Bayesian statistics in my research, I’ll probably start to favor the DIC over the BIC as the former does not require maximum likelihood estimates. But we’ll see.

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4 comments

  1. How was your presentation received? As a social science graduate student (psychology) I find few if any colleagues are interested in utilizing Bayesian analysis. I feel that because most journals require significance testing no one is motivated to use Bayesian analysis. Is your experience similar?


  2. Hi Julius,
    Thanks for the comment. I would say in general Bayesian seems to be well received within my department (but we have been affected by a biostatistics department that has been infiltrated by Bayesians). Most people within my department and my class recognize the utility in Bayesian and the shortcomings of frequentist approaches. However, as you pointed out, most journals require significance testing so most individuals that are open to Bayesian still do not use it. A lot of these students/professors rely on collaborations with individuals like myself and when I collaborate I heavily favor Bayesian approaches and push them away from significance testing. Within the quantitative methods program in my department (where I am a graduate student) more and more of us are open to Bayesian and using Bayesian methods in model selection and MCMC. My professor, in the course where I presented my talk, commented on the importance of educating our colleagues through publishing on these methods. I think that is what will ultimately bring about a paradigm shift within the social sciences. I hope to have a few manuscripts submitted by the end of this summer utilizing the BIC in model selection (without any p-values) and possibly a manuscript where I reanalyze my data through Bayesian hierarchical modeling and formally incorporate priors. I use this blog as a way of educating individuals in my field about ways they can use Bayesian in their own research and why I believe it is the way of the future.
    So if you are interested in Bayesian I encourage you to continue to publish your results using Bayesian approaches and just cite the heck out of your techniques. My understanding is that the higher tier journals may be more open and sympathetic to these approaches and you might consider these more “sophisticated” journals. But even if you submit to a journal where a reviewer complains about your lack of p-values, I would encourage you to not back down. Also, I wanted to add that while I believe that psychology and it’s related field (such as my own educational psychology department) are slow to warm to Bayesian, there are other social science fields (economic and political science) where Bayesian methods are frequently used.


  3. As a non-statistician-but-having-some-interest-in-the-topic person, I’m having a hard time to see what is Bayesian justification for favoring simpler hypothesis over complex ones, while everyone seems to state that one of the strengths of Bayesian approach is that it favors simpler hypothesis. The equation of Bayesianism is posterior = likelihood * prior. Likelihood itself doesn’t tell us why we should favor simpler ones as it’s just joint probability of the data given a hypothesis. So the reason for favoring simpler hypothesis should somehow come from prior. But how? Aren’t they, literally, just prior degrees of belief that we confer to the hypothesis? How can they give us good reasons for favoring simpler theories? — I think I’m missing something important. Could you help me out?


    • Hi Shawn,
      Thanks for the comment. I am not sure I fully agree with “one of the strengths of Bayesian approach is that it favors simpler hypothesis”. The reason is that in model selection in Bayesian you can choose your model using Bayes factor, BIC, AIC, DIC, and possibly other model selection criteria that I’m not aware of. The BIC tends to favor parsimonious models and possibly a simpler hypothesis whereas AIC tends to favor models that contain more parameters. Frequentist statistics can use AIC and BIC and experiences this same dilemma. Additionally most frequentist model selection criterion involves the use of maximum likelihood which is the mode of the posterior distribution. These criteria allow you to compare multiple models at the same time and allows you to compare non-nested models, something that is impossible using a likelihood test.

      A hypothesis should be as simple as theory dictates not a statistical paradigm. Science tends to favor parsimony, perhaps it is because complexity is too difficult to explain and generalize. What I believe Bayesian offers over frequentist approaches is the formalization of your prior beliefs in Bayes theorem. This take the form of distributions with the selected parameters influenced by your “theory”. This can greatly affect your posterior distribution with a small sample size as well as the model you select. Additionally the use of hyper parameters allows creation of more complex models than frequentist approaches. Philosophically and mathematically I believe that Bayesian is the correct approach but I refer you to read something by Carlin, Lindley, or Gelman.

      Please feel free to ask for further clarification. I hope this helps.
      Chris



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