** by Elizabeth
Saers Bigün**

** Research
Report 1997:2**

Department of Statistics, Stockholm University, S-106 91 Stockholm, Sweden

**Abstract**

The sensitivity analysis in this paper concerns Bayesian prediction of rare events which are built on expert assessments and few existing data. The paper treats sensitivity of the prediction models, which utilise multivariate normal distributions, for different types of dependence assumptions. The three main types of dependencies which are of interest here are; the dependencies between time periods, between groups of experts and within a group of experts. Issues which this paper treats are mainly: (i) how different dependence assumptions affect the the predictions, (ii) if the prediction models are inluenced more by a certain type of of dependence assumption tha other types and (iii) how different values of correlation coefficients affect predictions. The sensitivity analysis uses data from a survey which was performed among 21 Swedish experts in aviation safety. The main goal of the survey was, by means of expert assessments, predict future major civil aircraft accidents in Europe. Furthermore, the sensitivity of the prediction models is studied by means of the simplest assumptions about the correlation coefficients, i.e., the different correlation coefficients in the covariance matrices of interest are assumed to be equal. The main numerical results of the sensitivity analysis can be summarised as: (i) to introduce positive and equal correlation coefficients to the prediction models increase the precision of the predictions, (ii) the expected values of the predictions in general decrease when correlation coefficients increase, while the prediction variances depend both on the covariance structure and the values of the correlation coefficients, (iii) the variances of predictions increase when the covariance structures do not take the correlations between the time periods into acount, (iv) the correlation between the time periods is more essential for prediction estimations than the correlations concerning the assessments within and between groups of experts.

**Key words:** Aggregating
opinions, Bayesian methods, Bayesian prediction, calibration, correlation
coefficient, expert assessments, probability assessments, reconciliation,
sensitivity analysis, subjective probabilities.

*Last update: 1997-12-16 / KH*