Erlang mixture modeling for Poisson process intensities

We develop a prior probability model for temporal Poisson process intensities through structured mixtures of Erlang densities with common scale parameter, mixing on the integer shape parameters. The mixture weights are constructed through increments of a cumulative intensity function which is modeled nonparametrically with a gamma process prior. Such model specification provides a novel extension of Erlang mixtures for density estimation to the intensity estimation setting. The prior model structure supports general shapes for the point process intensity function, and it also enables effective handling of the Poisson process likelihood normalizing term resulting in efficient posterior simulation. The Erlang mixture modeling approach is further elaborated to develop an inference method for spatial Poisson processes. The methodology is examined relative to existing Bayesian nonparametric modeling approaches, including empirical comparison with Gaussian process prior based models, and is illustrated with synthetic and real data examples.

A Practical Cross-Sectional Framework to Contextual Reactivity in Personality: Response Times as Indicators of Reactivity to Contextual Cues

Contextual reactivity refers to the degree in which personality states are affected by contextual cues. Research into contextual reactivity has mainly focused on repeated measurement designs. In this paper, we propose a cross-sectional approach to study contextual reactivity. We argue that contextual reactivity can be operationalized as different response processes which are characterized by different mean response times and different measurement properties. We propose a within-person mixture modeling approach that adopts this idea and which enables studying contextual reactivity in cross-sectional data. We applied the model to data from the Revised Temperament and Character Inventory. Results indicate that we can distinguish between two response specific latent states. We interpret these states as a high contextual reactive state and a low contextual reactive state. From the results it appears that the low contextual reactive state is generally associated with smaller response times and larger discrimination parameters, as compared to the high contextual reactivity state. The utility of this approach in personality research is discussed.