What should he read to pivot into research with a Bayesian focus?

Someone who wishes to remain anonymous writes:

I am currently finishing my PhD in statistics/biostatistics. I have recently accepted a postdoc to work on Bayesian clinical trials.

I have done all of my dissertation work in frequentist statistics. I learned about the basics of Bayesian methods in a number of my courses, but haven’t done formal research using many of these methods. I was wondering if you had any advice/resources for someone with a strong statistics background, but wants to prepare to pivot into research with a Bayesian focus. Particularly a good resource for somebody wishing to learn how to code their own samplers etc.

My reply:

I recommend our Bayesian Data Analysis book and also McElreath’s book Statistical Rethinking. You should not need to be coding your own samplers. You can do that in Stan. You can take a look at the Stan user’s guide and the Stan case studies, also our Bayesian workflow paper.

19 thoughts on “What should he read to pivot into research with a Bayesian focus?

  1. I think its a good idea to code your own sampler at least once for a prototype.

    Otherwise software like Stan seems like magic, when really the “magic” is just optimizations and generalizations. The basic idea is quite simple though.

  2. Start with, and stay with books written by working scientists. Statistical Rethinking is by far the best place to start. Follow that with Doing Bayesian Data Analysis, by Kruschke. DBDA will be especially helpful if you are designing and analyzing experiments.

        • I also liked reading the causal inference chapters in Regression and Other Stories, particularly because I, like other commenters here, learned Bayesian data analysis mainly from Statistical Rethinking and McElreath’s lectures on YouTube. McElreath has really seemed to buy into the DAG approach, so seeing a different perspective from AG was beneficial.

          I think the recommendations for Statistical Rethinking (and free lectures on YouTube) and BDA3 are great.

      • When I look at what I consider to be great stats books, across topics, they are all written by working scientists who focused on methods and statistics (e.g., Cohen, Howell, Allison). I generally find stats books written by statisticians to be inscrutable. And I don’t think I’m alone on this.

        • Sentinel:

          Again, I disagree with your implicit distinction between “statisticians” and “working scientists.” I’m both, and I’m not the only one.

    • Good point, Keith. Actually, in FDA’s Bayesian guidance for medical devices (https://www.fda.gov/regulatory-information/search-fda-guidance-documents/guidance-use-bayesian-statistics-medical-device-clinical-trials), there’s a nice reference list for non-technical introduction to Bayesian analysis, clinical-trial perspective for Bayesian analysis, Introduction to Bayesian analysis from a general perspective (including Gelman et al). For ease of access, here’s the except:

      “Non-technical introductory references to Bayesian statistics and their application to medicine include Malakoff (1999), Hively (1996), Kadane (1995), Brophy & Joseph (1995), Lilford & Braunholtz (1996), Lewis & Wears (1993), Bland & Altman (1998), and Goodman (1999a, 1999b). O’Malley & Normand (2003) discuss the FDA process and Bayesian methods for medical device trials. Berry (1997) has written an introduction on Bayesian medical device trials specifically for FDA.

      Brophy & Joseph (1995) provide a well-known synthesis of three clinical trials using Bayesian methods. A comprehensive summary on the use of Bayesian methods to design and analyze clinical trials or perform healthcare evaluations appears in Spiegelhalter, Abrams, & Myles (2004).

      Introductions to Bayesian statistics that do not emphasize medical applications include Berry (1996), DeGroot (1986), Stern (1998), Lee (1997), Lindley (1985), Gelman, et al. (2004), and Carlin and Louis (2008).

      References with technical details and statistical terminology are Spiegelhalter, et al. (2000), Spiegelhalter, et al. (1994), Berry & Stangl (1996), Breslow (1990), Stangl & Berry (1998), and Box and Tiao (1992).

      Technical overviews of Markov Chain Monte Carlo methods for Bayesian computation include Gamerman and Lopes (2006) and Chapter 1 of Gilks, Richardson and Spiegelhalter (1996).

      Practical applications of Bayesian analyses appear in a number of excellent books, including Spiegelhalter et al (2004), , Congdon (2003), Broemeling (2007), Congdon (2007), Congdon (2005), Albert (2007), and Gilks et al. (1996).

      Excellent books on optimal Bayesian decision making (a.k.a., Bayesian decision theory) include Berger (1986), Robert (2007), Raiffa and Schlaifer (2000), and MH DeGroot (1970).”

  3. It would also be worth looking at https://discourse.datamethods.org/ for biostatistics11 recommendations — which has several prominent Bayesian trial statistician members — but I’d say the initial recommendations will be similar to above, from past browsing.

    But also note that you can’t post questions anonymously on that site :0

  4. For me, the book that got me into Bayes was Student’s Guide to Bayesian Statistics by Ben Lambert, & I think it definitely belongs up there with Statistical Rethinking & Doing Bayesian Data Analysis. Actually, for someone more applied/with less statistical background, I’d probably recommend Student’s Guide over the other two, I feel like it’s more trim & presents only the *really* necessary theory, nothing more.

    On the other hand, if the person is finishing their PhD in statistics/biostatistics & have already a decent grasp on frequentist theory, then they might get a lot out of Chris Bishop’s Pattern Recognition & Machine Learning? Despite the title, the vast majority of the content is framed in Bayesian statistics.

  5. For someone with a background in classical statistics, a book that might be very motivating is Probability Theory: The Logic of Science by Jaynes. In addition to providing some good examples of deriving Bayesian concepts from first principles, it spends a ton of time talking about problems with classical statistics.

    It’s not really in the same vein as BDA3 or Statistical Rethinking—both amazing books—but those have already been mentioned and this one hasn’t. Between the three, I think you get everything you need.

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