Course Description

Bayesian Approach in Social Science
by Hannes Kröger, Socio-Economic Panel Study (SOEP), German Institute for Economic Research (DIW), Berlin, Germany; European University Institute, Florence, Italy

Day 1 — Introduction

Philosophical differences between Bayes and Freq. What is probability? Where does the strong distinction between Bayesian and Frequentist approaches come from?

Some unique features of Bayesian statistics: Prior and Posterior distribution. Prior and Posterior are the features of Bayesian estimation that will be most often used in analyses that are actually distinct from frequentist analyses. So what do they do? How can we work with them?

When is it irrelevant whether we use Bayes or Frequentist approaches? Philosophy aside: When is it irrelevant which approach we use? If we use non-informative priors and ignore that our coefficients have a distribution…

Day 2 — Application 1: Including prior knowledge I – Measurement error in surveys

Income reported in surveys is prone to have measurement error. We use a literature review on external validation studies to get an estimate of the degree of measurement error (prior information) and integrate this information in an analysis of the association of income and health.

Day 3 — Application 2: Including prior knowledge II – Small samples and identification problems

Sometimes we have limited data available, because the total number of observations in the population is very small. In these cases, certain models might no longer be identified. We can use Bayesian statistics to get estimates in such cases.

Day 4 — A brief look on Bayesian Estimation

In this day, we will take some time to understand the basics of how Bayesian models can be estimated. It will not be exhaustive and focus mostly on Markov Chain Monte Carlo (MCMC) approaches. It will to understand how statistics program arrive at a posterior distribution.

Day 5 — Application 3: Escaping the significance trap: Using degrees of support instead of tests and Bayesian updating of evidence

Tests of statistical significance are the most common way of testing hypotheses in quantitative social sciences. However, the way it is used has several problems. These will be recapped and Bayesian alternatives of presenting and interpreting uncertainty in estimates will be discussed. Further, we will see how we can use a Bayesian approach to combine an update results from different studies to reduce uncertainty.

Day 6 — Bayesian Evaluation of Informative Hypotheses (BEIH)

Many theories in social sciences make complex predictions about behavior of humans or association of variables in different contexts. In applied research we often test these hypotheses via a chain of null-hypotheses-significance-tests instead of directly testing the prediction against possible alternative hypotheses. BEIH is a framework in which results can be assessed in terms of complex hypotheses that make statements beyond: A is related to B. This allows for more differentiated tests of hypotheses and forces researchers to be more precise in theory development. The logic of this approach and an example of the implementation will be discussed.

Day 7 — Model checking and selection

Here, we will discuss how results of an estimation can be checked on their validity. We try to identify possible problems and look at formal and visual tests of model quality and predictive performance. This model checking prepares the discussion of Bayesian model averaging and multiple bias modelling.

Day 8 — Bayesian Model Averaging and Multiple Bias modelling

When presenting results for a certain scientific problem, it is still common to present only one model as the ideal solution. However, it is widely recognized that many small modelling decisions have been taken before that might influence the results. Bayesian Model Averaging provides a way to represent this model uncertainty in quantitative way. This resembles certain approaches of “sensitivity analyses” in frequentist approaches. Multiple bias modelling works similarly, but with a stronger focus on a-priori set classes of possible sources of bias.

Day 9 — My own Research as Bayesian

We will discuss some examples of research questions by the participants and try to convert their models into Bayesian models. We will discuss basic interpretation and advantages and disadvantages of changing into a Bayesian framework.

Day 10 — Repetitions, more own research

The last day will be used to either finish discussing research examples from the previous and/or to go deeper or repeat certain aspects which are not yet clear or which have come up throughout the course.

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Ronald F. Inglehart Laboratory for Comparative Social Research

Course Description