Alternative Information: Bayesian Statistics, Expert Elicitation and Information Theory in the Social Sciences

In this dissertation it is discussed how one can capture and utilize alternative sources of (prior) information compared to traditional method in the social sciences such as survey research. Specific attention is paid to expert knowledge. In Chapter 2 we propose an elicitation methodology for a single parameter that does not rely on specifying quantiles of a distribution. The proposed method is evaluated using a user feasibility study, a partial validation study and an empirical example of the full elicitation method. In Chapter 3 it is investigated how experts’ knowledge, as alternative source of information, can be contrasted with traditional data collection methods. At the same time, we explore how experts can be assessed and ranked borrowing techniques from information theory. We use the information theoretical concept of relative entropy or Kullback-Leibler divergence which assesses a loss of information when approximating one distribution by another. For those familiar with the concept of model selection, Akaike’s Information Criterion is an approximation of this (Burnham & Anderson, 2002, Chapter 2). In Chapter 4 an alternative way of enhancing the amount of information in a model is proposed. We introduce Bayesian hierarchical modelling to the field of infants’ speech discrimination analysis. This technique is not new on it’s own but was not applied to this field. Implementing this type of modelling enables individual analyses within a group structure. By taking the hierarchical structure of the data into account we can make the most of the, on individual level, small noisy data sets. In Chapter 5 we reflect on issues that come along with the estimation of increasingly complicated models. We show how even with weakly informative priors, adding the information that is available to us, sometimes we do not get a solution with our analysis plan. We guide the reader on what to do when this occurs and where to look for clues and possible causes. We provide some guidance and a textbook example that for once shows things not working out the way you would like. We believe this is important as there are few examples of this. In Chapter 6 we combine the previous chapters. We take more complex models and get experts to specify beliefs with respect to these models. We extend the method developed in Chapter 2 to elicit experts’ beliefs with respect to a hierarchical model, which is used in Chapters 4 and 5. In specific, we concern ourselves with a Latent Growth Curve model and utilize the information theoretical measures from Chapter 3 to compare the (groups) of experts to one another and to data collected in a traditional way. We do this in the context of Posttraumatic Stress Symptoms development in children with burn injuries. In Chapter 7 I reflect on the work and explanations provided within the chapters of this dissertation, including this introduction.