Fyrirlesari: Haakon Bakka, Ph.D. student, Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway
Titill: Barriers for spatial correlation - how to stop fish from swimming over land (in your models)
Hvar: Oddi, stofa 202
Hvenær: Miðvikudaginn 19. október 2016 kl. 12:00-13:00.
Haakon Bakka er doktorsnemi við stærðfræðideild við Norwegian University of Science and Technology í Trondheim, Noregi. Í fyrirlestri sínum mun Haakon fjalla um tölfræðilíkön fyrir magn fiska í rúm þegar mælt er við fjöru eða í kringum eyjur þar sem tekið er tillit til þeirra takmarka sem sjávarlínan settur.
Abstract: A major advantage of spatial modeling, through hierarchical models with a spatial random effect, is our ability to separate out the different assumptions and investigate their appropriateness. In this talk we challenge the assumption of spatial stationarity in cases where there are physical barriers in the study area. In these situations it is important to force the spatial dependencies around the barriers, to make our modelling assumptions more realistic.
We develop a non-stationary Gaussian field that treats land as a barrier to spatial correlation. The core idea is to construct a Mat\' ern Gaussian field with range zero on land. This is achieved by defining the field as a continuous solution to a differential equation with spatially varying coefficients, based on the SPDE approach by Lindgren et. al. [2011]. We achieve a computational cost similar to the stationary model.
We demonstrate the benefits of the new model with a real application of species distribution modeling (SDM), analysing the reproduction habitats of a commercially important fish species in the Finnish archipelago. SDMs are used to predict the abundance pattern of species and to identify the environmental variables that best describe these patterns, e.g. to aid environmental managers in spatial planning.
There are many important applications where there is a lack of data, and we must put a lot of faith in our modeling assumptions. Then, the appropriateness of the a priori model is very important, but predictive checks may not be able to detect the difference in model fitness. We show that the application herein is an example of this.
We also provide code examples that you may use.