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Complex dynamic phenomena in which dynamics is related to events (modes) that cause structural changes over time, are well described by the switching linear dynamical system (SLDS). We extend the SLDS by allowing the measurement noise to be mode-specific, a flexible way to model non stationary data. Additionally, for models that are functions of explanatory variables, we adapt a variable selection method to identify which of them are significant in each mode. Our proposed model is a flexible Bayesian nonparametric model that allows to learn about the number of modes and their location, and within each mode, it identifies the significant variables and estimates the regression coefficients. The model performance is evaluated by simulation and two application examples from a dataset of meteorological time series of Barranquilla, Colombia are presented.

Model-based learning of organism dynamics is challenging, particularly when modeling count correlated data. In this paper, we adapt the multivariate Poisson distribution to model nematode dynamics. This distribution relaxes the mean-equal-variance property of the univariate Poisson distribution and allows recovery of the correlation among nematode genera. An observational dataset with 68 soil samples, 11 nematode genera, and 12 soil parameters is analyzed. The Spike and Slab Variable Selection procedure is adapted to obtain parsimonious models for the nematode occurrence. Nematode genus to genus interaction is assessed through the correlation matrix of the model. A simulation study validated the model's implementation. As a result, the model determined the most important covariates for each nematode and classified pairs of nematodes as: sympathetic, antagonistic or neutral, based on their estimated correlations. The model is useful for researchers and practitioners interested in studying population dynamics. In particular, the current results are important inputs when planning strategies for improving or managing soil health regarding nematodes.

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