Approximate Bayesian inference in multivariate Gaussian process regression and applications to species distribution models

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Sammanfattning

Gaussian processes are certainly not a new tool in the field of science. However, alongside the quick increasing of computer power during the last decades, Gaussian processes have proved to be a successful and flexible statistical tool for data analysis. Its practical interpretation as a nonparametric procedure to represent prior beliefs about the underlying data generating mechanism has gained attention among a variety of research fields ranging from ecology, inverse problems and deep learning in artificial intelligence.

The core of this thesis deals with multivariate Gaussian process model as an alternative method to classical methods of regression analysis in Statistics. I develop hierarchical models, where the vector of predictor functions (in the sense of generalized linear models) is assumed to follow a multivariate Gaussian process. Statistical inference over the vector of predictor functions is approached by means of the Bayesian paradigm with analytical approximations.

I developed also new parametrisations for the statistical models in order to improve the performance of the computations related to the inferential task. The methods developed in this thesis are also tightly connected to practical applications. The main applications considered involve multiple species surveys and species distribution modelling in quantitative ecology. This is a field of research which provides a rich variety of applications where statistical methods can be put at test.
Originalspråkengelska
Tilldelande institution
  • Helsingfors universitet
Tilldelningsdatum20 mar 2019
UtgivningsortUniversity of Helsinki
Utgåva1st
Förlag
Tryckta ISBN78-951-51-4974-9
Elektroniska ISBN978-951-51-4975-6
StatusPublicerad - 20 mar 2019
MoE-publikationstypG5 Doktorsavhandling (artikel)

Vetenskapsgrenar

  • 111 Matematik
  • 112 Statistik
  • 113 Data- och informationsvetenskap
  • 1172 Miljövetenskap

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