Organizer: Fernando Quintana, PUC Chile, Chile
Equating methods through Bayesian nonparametric models
Test equating is a family of statistical models and methods used to adjust scores on different test forms so that scores can be used interchangeably. The statistical challenge in this framework is to estimate the equating transformation which maps the scores on the scale of one test form, X, into their equivalents on the scale of another, Y. Even though score scales are usually subsets of integer numbers (e.g., total number of correct answers), in the equating literature, all the approaches proposed for the estimation of this function are based on continuous approximations of the score distributions. As a consequence, equated scores do not belong on the original scale of the tests.
In contrast to current equating methods, we develop an equating method which tries to avoid continuous assumptions of the score distributions. Considering scores as ordinal random variables, we propose a continuous latent variable formulation to perform an equipercentile-like equating based on a flexible Bayesian nonparametric model (Kottas et. al., 2005). The proposed model is applied to simulated and real data collected under an equivalent group design. Different methods are discussed to evaluate the performance of our method . Compared with discrete versions of equated scores obtained from traditional equating methods, the results show that the proposed method have better performance.
- Carlos Tadeu Pagani Zanini, Department of Statistics and Data Sciences, University of Texas at Austin, Austin, Texas, USA.
A Bayesian Random Partition Model for Sequential Refinement and Coagulation
We analyze time-course protein activation data to track the changes in protein expression over time after exposure to drugs such as protein inhibitors. Protein expression is expected to change over time in response to the intervention in different ways due to biological pathways. We therefore allow for clusters of proteins with different treatment effects, and allow these clusters to change over time. As the effect of the drug wears off, protein expression may revert back to the level before treatment. In addition, different drugs, doses, and cell lines may have different effects in altering the protein expression. To model and understand this process we develop random partitions that define a refinement and coagulation of protein clusters over time. We demonstrate the approach using a time-course reverse phase protein array (RPPA) dataset consisting of protein expression measurements under different drugs, dose levels, and cell lines. The proposed model can be applied in general to time-course data where clustering of the experimental units is expected to change over time in a sequence of refinement and coagulation.
On Dependent Dirichlet Processes for General Polish Spaces
We study Dirichlet process-based models for sets of predictor-dependent probability distributions, where the domain and predictor space are general Polish spaces. We generalize the definition of dependent Dirichlet processes, originally constructed on Euclidean spaces, to more general Polish spaces. We provide sufficient conditions under which dependent Dirichlet processes have appealing properties regarding continuity (weak and strong), association structure, and support (under different topologies). We also provide sufficient conditions under which mixture models induced by dependent Dirichlet processes have appealing properties regarding strong continuity, association structure, support, and weak consistency under i.i.d. sampling. The results can be easily extended to more general dependent stick-breaking processes.