Browsing by Subject "Model comparison"

Disgust features prominently in many facets of human life, from dining etiquette to spider phobia to genocide. For some applications, such as public health campaigns, it might be desirable to know how to increase disgust, whereas for things like legal and political decision-making it might be desirable to know how to suppress disgust. However, interventions in neither direction can take place until the basic structure of disgust is better understood. Disgust is notoriously difficult to model, largely due to the fact that it is a highly individually variable, multifactorial construct, with a great breadth of eliciting stimuli and contexts. As such, many of the theories which attempt to comprehensively describe disgust come into conflict with each other, impeding progress towards more efficient and effective ways of predicting disgust-related outcomes. The aim of this dissertation is to explore the possible contribution of data-driven methods to resolving theoretical questions, evaluating extant theories, and the generation of novel conceptual structures from bottom-up insights. Data were collected to sample subjective experience as well as psychophysiological reactivity. Through the use of techniques such as factor analysis and support vector machine classification, several insights about the approaching the study of disgust emerged. In one study, results indicated that the level of abstraction across subdivisions of disgust is not necessarily constant, in spite of a priori theoretical expectations: in other words, some domains of disgust are more general than others, and recognizing as much will improve the predictive validity of a model. Another study highlighted the importance of recognizing one particular category of disgust elicitors (mutilation) as a separate entity from the superordinate domains into which extant theories placed it. Finally, another study investigated the influence of concurrent emotions on variability in disgust physiology, and demonstrated the difference in the representations of the structure of disgust between the level of subjective experience and the level of autonomic activity. In total, the studies conducted as part of this dissertation suggest that for constructs as complex as disgust, data-driven approaches investigations can be a boon to scientists looking to evaluate the quality of the theoretical tools at their disposal.

Problems involving computer model emulation arise when scientists simulate expensive experiments with computationally expensive computer models. To more quickly probe the experimental design space, statisticians build emulators that act as fast surrogates to the computationally expensive computer models. The emulators are typically Gaussian processes, in order to induce spatial correlation in the input space. Often the main scientific interest lies in inference on one or more input parameters of the computer model which do not vary in nature. Inference on these input parameters is referred to as ``calibration,'' and these inputs are referred to as ``calibration parameters.'' We first detail our emulation and calibration model for an application in high-energy particle physics; this model brings together some existing ideas in the literature on handling multivariate output, and lays out a foundation for the remainder of the thesis.

In the next two chapters, we introduce novel ideas in the field of computer model emulation and calibration. The first addresses the problem of model comparison in this context, and how to simultaneously compare competing computer models while performing calibration. Using a mixture model to facilitate the comparison, we demonstrate that by conditioning on the mixture parameter we can recover the calibration parameter posterior from an independent calibration model. This mixture is then extended in the case of correlated data, a crucial innovation for this comparison framework to be useful in the particle collision setting. Lastly, we explore two possible non-exchangeable mixture models, where model preference changes over the input space.

The second novel idea addresses density estimation when only coarse bin counts are available. We develop an estimation method which avoids costly numerical integration and maintains plausible correlation for nearby bins. Additionally, we extend the method to density regression so that full a full density can be predicted from an input parameter, having only been trained on coarse histograms. This enables inference on the input parameter, and we develop an importance sampling method that compares favorably to the foundational calibration method detailed earlier.