Probability elicitation : predictive approach

Akbarov, A

Abstract

Probability elicitation is an important area of research with a wide scope for investigation and experimentation. The existing literature on the subject is vast and
spread over many disciplines. This indicates the importance of the subject and the ubiquitous nature of the concept of probability.
In this thesis, we focus on a probability elicitation method known as predictive elicitation. Predictive elicitation is a method for estimating hyperparameters of prior distributions by inverting corresponding prior predictive distributions. The uncertainty associated with prior predictive distributions is the uncertainty associated with socalled observable quantities. This uncertainty is generally accepted to be fundamentally more robust for elicitation than the uncertainty about unobservable parameters associated with prior distributions.
Although predictive elicitation is the most natural way for eliciting probabilities for Bayesian models, it has two major difficulties for practical implementation. The first
of these difficulties is related to inverting integral equations. Here, we deal with this difficulty by restricting the space of possible classes of prior distributions into three families, namely the beta, gamma and normal families as suggested by Percy (2002-
2004). The second difficulty is the problem of constraints on eliciting quantiles of the prior predictive distribution. In this thesis, we propose a method for identifying such constraints for single parameter models. We also propose a computational algorithm that makes predictive elicitation accessible for two-parameter models. We demonstrate that using the proposed elicitation method for two-parameter models it is possible to identify associated constraints.
In summary, we extend the current literature related to predictive elicitation by adding to it the following main points:
We propose a method for identifying constraints on the elicitation of quantiles for single parameter models.
We propose the use of a new hybrid elicitation procedure for two-parameter models. We also investigate a method for identifying constraints on the elicitation process posed by the hybrid elicitation strategy.
We provide numerical algorithms, programmed using MathCAD software, that enable full implementation of predictive elicitation for single parameter models.
We also provide similar programs for selected two-parameter models that enable implementation of the proposed hybrid elicitation method. These algorithms can be used as bases for developing generic software for implementing predictive
elicitation.
Further research is needed to address the issue of the practical applicability of predictive elicitation to multi-parameter and multivariate models. The advancements
made in this thesis provide foundations and an approach for dealing with the problem of constraints that can be extended to solve similar problems for multi-parameter and
multivariate models.

Citation

Akbarov, A. Probability elicitation : predictive approach. (Thesis). University of Salford

• Thesis Type: Thesis
• Deposit Date: Oct 3, 2012
• Award Date: Jan 1, 2009