The first contribution proposes dependent nonparametric models such as the dependent Dirichlet process and the dependent Pitman-Yor process to capture the inherent time-dependency in the problem at hand. These processes are used as priors for object state distributions to learn dependent information between previous and current time steps. Markov chain Monte Carlo sampling methods exploit the learned information to sample from posterior distributions and update the estimated object parameters.
The second contribution proposes a novel, robust, and fast nonparametric approach based on a diffusion process over infinite random trees to infer information on object cardinality and trajectory. This method follows the hierarchy induced by objects entering and leaving a scene and the time-dependency between unknown object parameters. Markov chain Monte Carlo sampling methods integrate the prior distributions over the infinite random trees with time-dependent diffusion processes to update object states.
The third contribution develops the use of hierarchical models to form a prior for statistically dependent measurements in a single object tracking setup. Dependency among the sensor measurements provides extra information which is incorporated to achieve the optimal tracking performance. The hierarchical Dirichlet process as a prior provides the required flexibility to do inference. Bayesian tracker is integrated with the hierarchical Dirichlet process prior to accurately estimate the object trajectory.
The fourth contribution proposes an approach to model both the multiple dependent objects and multiple dependent measurements. This approach integrates the dependent Dirichlet process modeling over the dependent object with the hierarchical Dirichlet process modeling of the measurements to fully capture the dependency among both object and measurements. Bayesian nonparametric models can successfully associate each measurement to the corresponding object and exploit dependency among them to more accurately infer the trajectory of objects. Markov chain Monte Carlo methods amalgamate the dependent Dirichlet process with the hierarchical Dirichlet process to infer the object identity and object cardinality.
Simulations are exploited to demonstrate the improvement in multiple object tracking performance when compared to approaches that are developed based on random finite set theory.
This paper presents a Bayesian framework for evaluative classification. Current education policy debates center on arguments about whether and how to use student test score data in school and personnel evaluation. Proponents of such use argue that refusing to use data violates both the public’s need to hold schools accountable when they use taxpayer dollars and students’ right to educational opportunities. Opponents of formulaic use of test-score data argue that most standardized test data is susceptible to fatal technical flaws, is a partial picture of student achievement, and leads to behavior that corrupts the measures.
A Bayesian perspective on summative ordinal classification is a possible framework for combining quantitative outcome data for students with the qualitative types of evaluation that critics of high-stakes testing advocate. This paper describes the key characteristics of a Bayesian perspective on classification, describes a method to translate a naïve Bayesian classifier into a point-based system for evaluation, and draws conclusions from the comparison on the construction of algorithmic (including point-based) systems that could capture the political and practical benefits of a Bayesian approach. The most important practical conclusion is that point-based systems with fixed components and weights cannot capture the dynamic and political benefits of a reciprocal relationship between professional judgment and quantitative student outcome data.