Informative Priors for Effect Sizes in Bayesian Regressions

Informative Priors for Effect Sizes in Bayesian Regressions

Principal speaker

Associate Professor Sama Low-Choy

Many data analytic procedures, for instance from classical (Frequentist) statistics or machine learning, are built around analysis of a single dataset. However, in some situations you may wish to incorporate other information. The Bayesian statistical framework is set up to explicitly incorporate information from previous studies, allowing you to accumulate knowledge. If your work is pioneering, you may have very little data; your best source of information could simply be the opinions of experts in the field. Alternatively, you may have collected a small amount of high quality data and wish to see how this builds on a previous large body of work. In either case, information about plausible effect sizes can be obtained a priori (i.e. before the data is analysed), and then used to construct what is called a prior model. Bayesian statistical modelling provides a natural framework to update your prior understandings of the problem (expressed in the prior model) with new empirical data to obtain what is called a posterior model. In this way Bayesian statistics focuses what we have learnt from the data, rather than focussing on "significance", whose limitations have recently been making headlines, at least in the academic arena.

In this workshop, we revisit regression from a modelling perspective in a way that ensures you understand what the effect sizes mean, so that you are better positioned to identify and utilise relevant prior information and/or experts. We examine several ways of constructing prior models and show how these affect posterior models. The process of eliciting relevant knowledge from experts or prior studies, and then quantifying it (with uncertainty) in a way that fits into the regression model, requires a balance of skills.

Format: This workshop will be delivered in a more traditional fashion via Collaborate Ultra, as a series of mini-lectorials (a hybrid lecture/tutorial), with unsupervised breakout sessions for groups to discuss concepts at regular points.

Relationship to other RED workshops: This workshop complements other workshops delivered via RED. A workshop on Eliciting effect sizes from experts addresses how to design a semi-structured interview to elicit relevant information from experts (with uncertainty), express that into a prior model, and check its validity, before supplying it as input into a regression. Workshops on Interviewing Skills and Formulating Open-ended Questions for Interviews provide relevant background on conduct and questions of a semi-structured interview. Several workshops on model-based regression and Bayesian regression provide introductions to regression.

Recommended Readings: You may get more out of the session with a little prior reading to identify your "sticking points". For an introduction to the concepts of Bayesian inference, with priors, try: Van de Schoot, Rens, et al. "A gentle introduction to Bayesian analysis: Applications to developmental research." Child development, 85.3 (2014): 842-860.
This book chapter considers a wide range of priors, and gives several different examples: Low Choy, Samantha. "Priors: Silent or active partners of Bayesian inference?" Chapter 3 in Alston et al (eds) Case studies in Bayesian statistical modelling and analysis. John Wiley & Sons Ltd, 2013.


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