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Estimating the distribution of rat population in Helsinki with non-stationary Gaussian model interpreting coastline as a physical barrier

Show simple item record 2022-06-15T08:49:01Z 2022-06-15T08:49:01Z 2022-06-15
dc.title Estimating the distribution of rat population in Helsinki with non-stationary Gaussian model interpreting coastline as a physical barrier en
ethesis.faculty Matemaattis-luonnontieteellinen tiedekunta fi
ethesis.faculty Faculty of Science en
ethesis.faculty Matematisk-naturvetenskapliga fakulteten sv
ethesis.faculty.URI Helsingin yliopisto fi University of Helsinki en Helsingfors universitet sv
dct.creator Nikkanen, Leo
dct.issued 2022 xx
dct.abstract Often in spatial statistics the modelled domain contains physical barriers that can have impact on how the modelled phenomena behaves. This barrier can be, for example, land in case of modelling a fish population, or road for different animal populations. Common model that is used in spatial statistics is a stationary Gaussian model, because of its computational requirements, relatively easy interpretation of results. The physical barrier does not have an effect on this type of models unless the barrier is transformed into variable, but this can cause issues in the polygon selection. In this thesis I discuss how the non-stationary Gaussian model can be deployed in cases where spatial domain contains physical barriers. This non-stationary model reduces spatial correlation continuously towards zero in areas that are considered as a physical barrier. When the correlation is selected to reduce smoothly to zero, the model is more likely to results similar output with slightly different polygons. The advantage of the barrier model is that it is as fast to train as the stationary model because both models can be trained using finite equation method (FEM). With FEM we can solve stochastic partial differential equations (SPDE). This method interprets continuous random field as a discrete mesh, and the computational requirements increases as the number of nodes in mesh increases. In order to create stationary and non-stationary models, I have described the required methods such as Bayesian statistics, stochastic process, and covariance function in the second chapter. I use these methods to define spatial random effect model, and one commonly used spatial model is the Gaussian latent variable model. At the end of second chapter, I describe how the barrier model is created, and what types of requirements this model has. The barrier model is based on a Matern model that is a Gaussian random field, and it can be represented by using Matern covariance function. The second chapter ends with description of how to create a mesh mentioned above, and how the FEM is used to solve SPDE. The performance of stationary and non-stationary Gaussian models are first tested by training both models with simulated data. This simulated data is a random sample from polygon of Helsinki where the coastline is interpreted as a physical barrier. The results show that the barrier model estimates the true parameters better than the stationary model. The last chapter contains data analysis of the rat populations in Helsinki. The data contains number of rat observations in each zip code, and a set of covariates. Both models, stationary and non-stationary, are trained with and without covariates, and the best model out of these four models was the stationary model with covariates. en
ethesis.isPublicationLicenseAccepted false
ethesis.language englanti fi
ethesis.language English en
ethesis.language engelska sv
ethesis.thesistype pro gradu -tutkielmat fi
ethesis.thesistype master's thesis en
ethesis.thesistype pro gradu-avhandlingar sv
dct.identifier.ethesis E-thesisID:9d08e9bd-bfc2-4dce-8445-d97b8e415387
dct.identifier.urn URN:NBN:fi:hulib-202206152700
ethesis.facultystudyline Tilastotiede fi
ethesis.facultystudyline Statistics en
ethesis.facultystudyline Statistik sv
ethesis.mastersdegreeprogram Matematiikan ja tilastotieteen maisteriohjelma fi
ethesis.mastersdegreeprogram Master 's Programme in Mathematics and Statistics en
ethesis.mastersdegreeprogram Magisterprogrammet i matematik och statistik sv

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