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In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the…
There are several assumptions made in a standard $\chi^2$ analysis of data, including the frequent assumption that the likelihood function is well approximated by a multivariate Gaussian distribution. This article briefly reviews the…
Quantifying spatial and/or temporal associations in multivariate geolocated data of different types is achievable via spatial random effects in a Bayesian hierarchical model, but severe computational bottlenecks arise when spatial…
Computer models are commonly used to represent a wide range of real systems, but they often involve some unknown parameters. Estimating the parameters by collecting physical data becomes essential in many scientific fields, ranging from…
Clustering is a crucial task in various domains of knowledge, including medicine, epidemiology, genomics, environmental science, economics, and visual sciences, among others. Methodologies for inferring the number of clusters have often…
Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…
Network models provide a powerful framework for analysing single-cell count data, facilitating the characterisation of cellular identities, disease mechanisms, and developmental trajectories. However, uncertainty modeling in unsupervised…
We look at the distribution of the Bayesian evidence for mock realizations of supernova and baryon acoustic oscillation data. The ratios of Bayesian evidences of different models are often used to perform model selection. The significance…
Assessing variability according to distinct factors in data is a fundamental technique of statistics. The method commonly regarded to as analysis of variance (ANOVA) is, however, typically confined to the case where all levels of a factor…
Bi-clustering is a useful approach in analyzing biological data when observations come from heterogeneous groups and have a large number of features. We outline a general Bayesian approach in tackling bi-clustering problems in moderate to…
This paper describes a Bayesian method for learning causal networks using samples that were selected in a non-random manner from a population of interest. Examples of data obtained by non-random sampling include convenience samples and…
Fitting a simplifying model with several parameters to real data of complex objects is a highly nontrivial task, but enables the possibility to get insights into the objects physics. Here, we present a method to infer the parameters of the…
We describe and analyze a broad class of mixture models for real-valued multivariate data in which the probability density of observations within each component of the model is represented as an arbitrary combination of basis functions.…
Bayesian data analysis techniques, together with suitable statistical models, can be used to obtain much more information from noisy data than the traditional frequentist methods. For instance, when searching for periodic signals in noisy…
Cosmological experiments often employ Bayesian workflows to derive constraints on cosmological and astrophysical parameters from their data. It has been shown that these constraints can be combined across different probes such as Planck and…
Hierarchical probabilistic models, such as mixture models, are used for cluster analysis. These models have two types of variables: observable and latent. In cluster analysis, the latent variable is estimated, and it is expected that…
In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…
We present a unified framework to derive fundamental stellar parameters by combining all available observational and theoretical information for a star. The algorithm relies on the method of Bayesian inference, which for the first time…
This paper introduces and reviews some of the principles and methods used in Bayesian reliability. It specifically discusses methods used in the analysis of success/no-success data and then reminds the reader of a simple Monte Carlo…
The analysis of gravitational wave data involves many model selection problems. The most important example is the detection problem of selecting between the data being consistent with instrument noise alone, or instrument noise and a…