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The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…

This work presents the spatial error model with heteroskedasticity, which allows the joint modeling of the parameters associated with both the mean and the variance, within a traditional approach to spatial econometrics. The estimation…

A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in…

Over the past 10 years Bayesian methods have rapidly grown more popular as several computationally intensive statistical algorithms have become feasible with increased computer power. In this paper, we begin with a general description of…

The problem of estimating cosmological parameters such as $\Omega$ from noisy or incomplete data is an example of an inverse problem and, as such, generally requires a probablistic approach. We adopt the Bayesian interpretation of…

Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…

Model selection aims to determine which theoretical models are most plausible given some data, without necessarily asking about the preferred values of the model parameters. A common model selection question is to ask when new data require…

A critical step in data analysis for many different types of experiments is the identification of features with theoretically defined shapes in N-dimensional datasets; examples of this process include finding peaks in multi-dimensional…

The method of weighted least squares is widely used in parameter estimation problems such as asteroid orbit determination. A key difficulty is the treatment of observational uncertainties, especially when combining heterogeneous datasets…

In many inference problems, the evaluation of complex and costly models is often required. In this context, Bayesian methods have become very popular in several fields over the last years, in order to obtain parameter inversion, model…

Gravitational-wave astronomy of compact binaries relies on theoretical models of the gravitational-wave signal that is emitted as binaries coalesce. These models do not only need to be accurate, they also have to be fast to evaluate in…

The intrinsic alignment of galaxies is a key factor in modeling weak-lensing observations and can serve as a valuable signal for both cosmological and astrophysical studies. Modelling this signal requires understanding how galaxy shapes…

Methods for inferring the velocity field from the peculiar velocity data are described and applied to old and newer data. Inhomogeneous Malmquist bias and ways to avoid it are discussed and utilized. We infer that these biases are probably…

An important problem in precision cosmology is the determination of the effects of averaging and backreaction on observational predictions, particularly in view of the wealth of new observational data and improved statistical techniques. In…

We present a Bayesian hierarchical inference formalism to study the relation between the properties of dark matter halos and those of their central galaxies using weak gravitational lensing. Unlike traditional methods, this technique does…

Inverse analysis, such as model calibration, often suffers from a lack of informative data in complex real-world scenarios. The standard remedy, designing new experimental setups, is often costly and time-consuming, while readily available…

Photometric light curves suffer from fundamental degeneracies that limit surface information recovery. We demonstrate that astrometry enables access to complementary information through photocentre variations induced by rotating surface…

This paper presents a systematic literature review focusing on the application of machine learning techniques for deriving observational constraints in cosmology. The goal is to evaluate and synthesize existing research to identify…

We discuss the use of the Bayesian evidence ratio, or Bayes factor, for model selection in astronomy. We treat the evidence ratio as a statistic and investigate its distribution over an ensemble of experiments, considering both simple…

In this review, we present some advanced algorithms and programs used in our scientific school with short description of types of astrophysical systems, which we study. However, we discuss mainly mathematical methods, which may be applied…