Bayesian data analysis involves describing data by meaningful mathematical models, and allocating credibility to parameter values that are consistent with the data and with prior knowledge. The Bayesian approach is ideally suited for constructing hierarchical models, which are useful for data structures with multiple levels, such as data from individuals who are members of groups which in turn ...

The hierarchical hidden Markov model (HHMM) is a generalization of the hidden Markov model (HMM) that models sequences with structure at many length/time scales [FST98]. Unfortunately, the original inference algorithm is rather complicated, and takes time, where is the length of the sequence, making it impractical for many domains. In this paper, we show how HHMMs are a special kind of dynamic ...

Railway maintenance planners require a predictive model that can assess the railway track geometry degradation. The present paper uses a hierarchical Bayesian model as a tool to model the main two quality indicators related to railway track geometry degradation: the standard deviation of longitudinal level defects and the standard deviation of horizontal alignment defects. Hierarchical Bayesian...

An image is never noise free. Visual inspection of a part from its image is therefore affected by image errors. Understanding how image errors affect measurement precision is therefore critical for accurate inspection. In this paper, we lay out a statistical framework that allows to explicitly handle image errors and characterize their impact on measurement precision. A hierarchical model is al...

An image is never noise free. Visual inspection of a part from its image is therefore aaected by image errors. Understanding how image errors aaect measurement precision is therefore critical for accurate inspection. Existing visual inspection methods either setup a highly controlled environment to minimize image errors or simply ignore image errors. They therefore suuer from limited accuracy a...

Abstract In this article, we present a behind-the-scenes look at a Bayesian hierarchical analysis of pathways of exposure to arsenic, a toxic heavy metal. Our analysis combines individual-level personal exposure measurements (biomarker and environmental media) with water, soil, and air observations from the ambient environment. We include details of our model-building exercise that involved a c...

A recent trend in decision neuroscience is the use of model-based fMRI using mathematical models of cognitive processes. However, most previous model-based fMRI studies have ignored individual differences due to the challenge of obtaining reliable parameter estimates for individual participants. Meanwhile, previous cognitive science studies have demonstrated that hierarchical Bayesian analysis ...