Browsing by Subject "Laplace approximation"

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  • Vanhatalo, Jarno; Hartmann, Marcelo; Veneranta, Lari (2020)
    Species distribution models (SDM) are a key tool in ecology, conservation and management of natural resources. Two key components of the state-of-the-art SDMs are the description for species distribution response along environmental covariates and the spatial random effect that captures deviations from the distribution patterns explained by environmental covariates. Joint species distribution models (JSDMs) additionally include interspecific correlations which have been shown to improve their descriptive and predictive performance compared to single species models. However, current JSDMs are restricted to hierarchical generalized linear modeling framework. Their limitation is that parametric models have trouble in explaining changes in abundance due, for example, highly non-linear physical tolerance limits which is particularly important when predicting species distribution in new areas or under scenarios of environmental change. On the other hand, semi-parametric response functions have been shown to improve the predictive performance of SDMs in these tasks in single species models. Here, we propose JSDMs where the responses to environmental covariates are modeled with additive multivariate Gaussian processes coded as linear models of coregionalization. These allow inference for wide range of functional forms and interspecific correlations between the responses. We propose also an efficient approach for inference with Laplace approximation and parameterization of the interspecific covariance matrices on the euclidean space. We demonstrate the benefits of our model with two small scale examples and one real world case study. We use cross-validation to compare the proposed model to analogous semi-parametric single species models and parametric single and joint species models in interpolation and extrapolation tasks. The proposed model outperforms the alternative models in all cases. We also show that the proposed model can be seen as an extension of the current state-of-the-art JSDMs to semi-parametric models.
  • Vanhatalo, Jarno; Foster, Scott D.; Hosack, Geoffrey R. (2021)
    The categorization of multidimensional data into clusters is a common task in statistics. Many applications of clustering, including the majority of tasks in ecology, use data that is inherently spatial and is often also temporal. However, spatiotemporal dependence is typically ignored when clustering multivariate data. We present a finite mixture model for spatial and spatiotemporal clustering that incorporates spatial and spatiotemporal autocorrelation by including appropriate Gaussian processes (GP) into a model for the mixing proportions. We also allow for flexible and semiparametric dependence on environmental covariates, once again using GPs. We propose to use Bayesian inference through three tiers of approximate methods: a Laplace approximation that allows efficient analysis of large datasets, and both partial and full Markov chain Monte Carlo (MCMC) approaches that improve accuracy at the cost of increased computational time. Comparison of the methods shows that the Laplace approximation is a useful alternative to the MCMC methods. A decadal analysis of 253 species of teleost fish from 854 samples collected along the biodiverse northwestern continental shelf of Australia between 1986 and 1997 shows the added clarity provided by accounting for spatial autocorrelation. For these data, the temporal dependence is comparatively small, which is an important finding given the changing human pressures over this time.