Statistical Modelling

In a time series analysis it is sometimes necessary to assume that the effect of a regressor does not have only immediate impact on the mean response, but that its effects somehow propagate to future times. We adopt, in this work, transfer functions to model such impacts, represented by structural blocks present in dynamic generalized linear models. All the inference is carried under the Bayesian paradigm. Two sources of difficulties emerge for the analytical derivation of posterior distributions: non-Gaussian nature of the response, associated to non-conjugate priors and also non-linearity of the predictor on auto regressive parameters present in transfer functions. The purpose of this work is to produce full Bayesian inference on dynamic generalized linear models with transfer functions, using Markov chain Monte Carlo methods to build samples of the posterior joint distribution of the parameters involved in such models. Several transfer structures are specified, associated to Poisson, Binomial, Gamma and inverse Gaussian responses. Simulated data are analyzed under the resulting models in order to assess their performance. Finally, two applications to real data concerning environmental sciences are made under different model formulations.

Compositional data are commonly present in many disciplines. Nevertheless, it is often improperly incorporated into statistical modelling and a misleading interpretation of the results is given. This paper explains how partial least squares for discrimination is an adequate technique for compositional data when a dimensional reduction of original variables is needed and difining the variables that more influence the discrimination between the observations is the goal.

In randomized response (RR) designs, misclassification is used to protect the privacy of respondents when sensitive questions are asked. A generalized linear model with a composite link function is presented to formulate log linear models that take the RR design into account. The approach is extended to model the situation where some respondents do not follow the instructions of the RR design. For example, if there are three binary RR variables with regard to practicing fraud, the 2 × 2 × 2 cross-classification of the true answers is latent due to the misclassification. Using composite link functions, log linear models can be specified for the latent table to investigate possible association between the variables. Fast iteratively re-weighted least squares algorithms are presented.

Risk assessments relating to food safety over more than one step along a production chain are frequently hampered by lack of detailed quantitative data. This study set out to develop a Bayesian hidden variable model to integrate available limited data of the combined occurrence of three bacterial pathogens, Listeria monocytogenes, Yersinia enterocolitica and Yersinia pseudotuberculosis, with causal assumptions along three steps of pork production chain. The pathogen occurrence data were animal specific both on conventional and organic pig farms and at the abattoir, but merely farm specific at meat cutting plants. The model was able to incorporate all data concerning different types of testing at different steps of the chain, and missing data values were dealt with in a straightforward manner. It provides a tool for quantitative risk assessments and for estimating the causal risk mitigation effects by combining external data with the specific follow-up data. Intervention effects are provided with Bayesian credible intervals indicating the uncertainty due to all information sources included in the model. Combined prevalence in Finnish pork was estimated to be 1–11% and it could be reduced to 0–2% if head was removed intact and rectum sealed off.

We consider prediction and uncertainty analysis for the ‘history matching’ problem in petroleum reservoir evaluation. Unknown reservoir properties are represented on a fine three dimensional lattice. A ‘reservoir simulator’ takes the reservoir properties as input and gives production properties as output. The history matching problem is to infer the reservoir properties from the observed production history. To run the reservoir simulator on the lattice size of interest is computer intensive, and this severely limits the number of runs possible.

We formulate the problem in a Bayesian setting and, following suggestions in the statistical literature, consider the reservoir simulator as an unknown function. To obtain a realistic prior distribution for this function, we propose to combine a coarse lattice (faster) version of the simulator with parameters correcting for bias introduced by the coarser lattice. We simulate from the resulting posterior by Markov chain Monte Carlo (MCMC). We construct an artificial reference reservoir, generate corresponding flow observations, and use our procedure to evaluate the reservoir properties in the resulting posterior distribution. Convergence and mixing are acceptable. The case study demonstrates how the observed production history provides information about both the reservoir properties and the bias correcting parameters included in the prior specification.