In this paper we present a novel inference methodology to perform Bayesian inference for spatiotemporal Cox processes where the intensity function depends on a multivariate Gaussian process. Dynamic Gaussian processes are introduced to allow for evolution of the intensity function over discrete time. The novelty of the method lies on the fact that no discretisation error is involved despite the non-tractability of the likelihood function and infinite dimensionality of the problem. The method is based on a Markov chain Monte Carlo algorithm that samples from the joint posterior distribution of the parameters and latent variables of the model. A particular choice of the dominating measure to obtain the likelihood function is shown to be crucial to devise a valid MCMC. The models are defined in a general and flexible way but they are amenable to direct sampling from the relevant distributions, due to careful characterisation of its components. The models also allow for the inclusion of regression covariates and/or temporal components to explain the variability of the intensity function. These components may be subject to relevant interaction with space and/or time. Real and simulated examples illustrate the methodology, followed by concluding remarks.
In this article, an integrated bayesian model for differential item functioning (DIF) analysis is proposed. The model is integrated in the sense of modeling the responses along with the DIF analysis. This approach allows DIF detection and explanation in a simultaneous setup. Previous empirical studies and/or subjective beliefs about the item parameters, including differential functioning behavior, may be conveniently expressed in terms of prior distributions. Values of indicator variables are estimated in the model, indicating which items have DIF and which do not; as a result, the data analyst may not be required to specify an “anchor set” of items that do not exhibit DIF a priori to identify the model. It reduces the iterative procedures that are commonly used for proficiency purification and DIF detection and explanation. Examples demonstrate the efficiency of this method in simulated and real situations.
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