In this thesis I develop Bayesian approach to model galaxy surface brightness and apply it to a bulge-disc decomposition analysis of galaxies in near-infrared band, from Two Micron All Sky Survey (2MASS). The thesis has three main parts. First part is a technical development of Bayesian galaxy image decomposition package Galphat based on Markov chain Monte Carlo algorithm. I implement a fast and accurate galaxy model image generation algorithm to reduce computation time and make Bayesian approach feasible for real science analysis using large ensemble of galaxies. I perform a benchmark test of Galphat and demonstrate significant improvement in parameter estimation with a correct statistical confidence. Second part is a performance test for full Bayesian application to galaxy bulgedisc decomposition analysis including not only the parameter estimation but also the model comparison to classify different galaxy population. The test demonstrates that Galphat has enough statistical power to make a reliable model inference using galaxy photometric survey data. Bayesian prior update is also tested for parameter estimation and Bayes factor model comparison and it shows that informative prior significantly improves the model inference in every aspects. Last part is a Bayesian bulge-disc decomposition analysis using 2MASS Ks-band selected samples. I characterise the luminosity distributions in spheroids, bulges and discs separately in the local Universe and study the galaxy morphology correlation, by full utilising the ensemble parameter posterior of the entire galaxy samples. It shows that to avoid a biased inference, the parameter covariance and model degeneracy has to be carefully characterised by the full probability distribution.

Growth plays a key role in regulating ecological and population dynamics. Life history characteristics such as age at maturity, fecundity and age and size at migration are tightly linked to growth rate. In addition, size can often determine survival and individual breeding success. To fully understand the process of growth it is important to understand the mechanisms that drive growth rates. In Atlantic salmon, growth is critical in determining life history pathways. Models to estimate growth could be useful in the broader context of predicting population dynamics. In this dissertation I investigate the growth process in juvenile Atlantic salmon (Salmo salar). I first used basic modeling approaches and data on individually tagged salmon to investigate the assumptions of different growth metrics. I demonstrate the size-dependency in certain growth metrics when assumptions are violated. Next, I assessed the efficacy of linear mixed effects models in modeling length-weight relationships from longitudinal data. I show that combining a random effects approach with third order polynomials can be an effective way to model length-weight relationships with mark-recapture data. I extend this hierarchical modeling approach to develop a Bayesian growth model. With limited assumptions, I derive a relatively simple discrete time model from von Bertalanffy growth that includes a nonparametric seasonal growth function. The linear dynamics of this model allow for efficient estimation of parameters in a Bayesian framework. Finally, I investigated the role of life history in driving compensatory growth patterns in immature Atlantic salmon. This analysis demonstrates the importance of considering life history as a mechanism in compensatory growth. Information provided in this dissertation will help provide ecologists with statistical tools to estimate growth rates, estimate length-weight relationships, and forecast growth from mark-recapture data. In addition, comparisons of seasonal growth within and among life history groups and within and among tributaries should make a valuable contribution to the important literature on growth in Atlantic salmon.

Classical models for multivariate or spatial extremes are mainly based upon the asymptotically justified max-stable or generalized Pareto processes. These models are suitable when asymptotic dependence is present. However, recent environmental data applications suggest that asymptotic independence is equally important. Therefore, development of flexible subasymptotic models is in pressing need. This dissertation consists of four major contributions to subasymptotic modeling of multivariate and spatial extremes. Firstly, the dissertation proposes a new spatial copula model for extremes based on the multivariate generalized hyperbolic distribution. The extremal dependence of this distribution is revisited and a corrected theoretical description is provided. Secondly, the dissertation thoroughly investigates the extremal dependence of stochastic processes driven by exponential-tailed Lévy noise. It shows that the discrete approximation models, which are linear transformations of a random vector with independent components, bridge asymptotic independence and asymptotic dependence in a novel way, whilst the exact stochastic processes exhibit only asymptotic independence. Thirdly, the dissertation explores two different notions of optimal prediction for extremes, and compares the classical linear kriging predictor and the conditional mean predictor for certain non-Gaussian models. Finally, the dissertation proposes a multivariate skew-elliptical link model for correlated highly-imbalanced (extreme) binary responses, and shows that the regression coefficients have a closed-form unified skew-elliptical posterior with an elliptical prior.

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