# Måns Karlsson: Statistical Methods for Taxon Classification and Bird Migration Phenology

**Time: **
Tue 2022-06-07 09.00

**Location: **
Kräftriket, house 5, room 15

**Doctoral student: **
Måns Karlsson

**Opponent: **
Benjamin Bolker (McMaster University)

**Supervisor: **
Ola Hössjer

### Abstract

The connection between ecology and statistics is deep. Methodological advancement in statistics open up new possibilities to understand the distribution of life on earth, and research questions in ecology cause new statistical methods to be developed. The four papers of this thesis examplify this exchange in providing a statistical approach to taxon classification, and developing novel measures of distributional properties driven by the application area of phenology.

Paper I contains a comprehensive Bayesian approach to phenotypical taxon classification with covariates. We formulate a multivariate regression model for a collection of phenotypical traits, which are assumed to be partial observations of latent variables with a Gaussian distribution. Through blocked Gibbs sampling we estimate the parameters of these distributions for a real data set, and derive decision regions of new observations in terms of set-valued classifiers, called Karlsson-Hössjer (K-H) classifiers, analogous to partial reject options. We introduce model selection through cross-validation and compare the K-H classifier’s performance with other existing methods on real data.

Paper II introduces a general Bayesian framework for K-H classification. This is achieved by using a reward function with a set-valued argument, and in this context we derive the optimal Bayes classifier, for a homogeneous block of hypotheses as well as for scenarios where the hypotheses are divided into blocks, and where misclassification or ambiguity within blocks is less or more serious than between. These reward functions include tuning parameters which we choose using cross-validation, and we apply the method to a real data set with block structure.

In Paper III a large class of L-functionals is studied for the response variable in regression models. These L-functionals are given order numbers through an orthogonal series expansion of the quantile function of the response variable. We apply the framework to quantile regression models with and without transformations of the outcome variable, and present a unified asymptotic theory for estimates of L-functionals. The derived estimators are applied to a quantile regression modelfor phenological analysis, and in this context a novel version of the coefficient of determination is introduced.

In Paper IV two statistical approaches for phenological analysis are compared, for singular as well as for multiple species models. For singular species, we show that the estimates from linear models fitted to empirical quantiles of the response distribution give less detailed results on the effects of covariates compared to non-parametric quantile regression. For multiple species models, we highlight an identifiability issue in quantile regression with random effects, and deduce similarity of performance of a mixed effects linear model for empirical quantiles and a quantile regression model with species as one of the covariates.