A Bayesian Approach for Clustering Constant-wise Change-point Data

Change-point models deal with ordered data sequences. Their primary goal is to infer the locations where an aspect of the data sequence changes. In this paper, we propose and implement a nonparametric Bayesian model for clustering observations based on their constant-wise change-point profiles via Gibbs sampler. Our model incorporates a Dirichlet Process on the constant-wise change-point structures to cluster observations while performing change-point estimation simultaneously. Additionally, our approach controls the number of clusters in the model, not requiring the specification of the number of clusters a priori. Our method's performance is evaluated on simulated data under various scenarios and on a publicly available single-cell copy-number dataset.Comment: 30 pages, 12 figure

Bayesian Adaptive Selection of Variables for Function-on-Scalar Regression Models

Considering the field of functional data analysis, we developed a new Bayesian method for variable selection in function-on-scalar regression (FOSR). Our approach uses latent variables, allowing an adaptive selection since it can determine the number of variables and which ones should be selected for a function-on-scalar regression model. Simulation studies show the proposed method's main properties, such as its accuracy in estimating the coefficients and high capacity to select variables correctly. Furthermore, we conducted comparative studies with the main competing methods, such as the BGLSS method as well as the group LASSO, the group MCP and the group SCAD. We also used a COVID-19 dataset and some socioeconomic data from Brazil for real data application. In short, the proposed Bayesian variable selection model is extremely competitive, showing significant predictive and selective quality

Variational Bayesian analysis of survival data using a log-logistic accelerated failure time model

The log-logistic regression model is one of the most commonly used accelerated failure time (AFT) models in survival analysis, for which statistical inference methods are mainly established under the frequentist framework. Recently, Bayesian inference for log-logistic AFT models using Markov chain Monte Carlo (MCMC) techniques has also been widely developed. In this work, we develop an alternative approach to MCMC methods and infer the parameters of the log-logistic AFT model via a mean-field variational Bayes (VB) algorithm. A piecewise approximation technique is embedded in deriving the VB algorithm to achieve conjugacy. The proposed VB algorithm is evaluated and compared with typical frequentist inferences and MCMC inference using simulated data under various scenarios. A publicly available dataset is employed for illustration. We demonstrate that the proposed VB algorithm can achieve good estimation accuracy and has a lower computational cost compared with MCMC methods

J-PLUS : a catalogue of globular cluster candidates around the M 81/M 82/NGC 3077 triplet of galaxies

Globular clusters (GCs) are proxies of the formation assemblies of their host galaxies. However, few studies exist targeting GC systems of spiral galaxies up to several effective radii. Through 12-band Javalambre Photometric Local Universe Survey (J-PLUS) imaging, we study the point sources around the M 81/M 82/NGC 3077 triplet in search of new GC candidates. We develop a tailored classification scheme to search for GC candidates based on their similarity to known GCs via a principal component analysis projection. Our method accounts for missing data and photometric errors. We report 642 new GC candidates in a region of 3.5 deg2 around the triplet, ranked according to their Gaia astrometric proper motions when available. We find tantalizing evidence for an overdensity of GC candidate sources forming a bridge connecting M 81 and M 82. Finally, the spatial distribution of the GC candidates (g − i) colours is consistent with halo/intra-cluster GCs, i.e. it gets bluer as they get further from the closest galaxy in the field. We further employ a regression-tree-based model to estimate the metallicity distribution of the GC candidates based on their J-PLUS bands. The metallicity distribution of the sample candidates is broad and displays a bump towards the metal-rich end. Our list increases the population of GC candidates around the triplet by threefold, stresses the usefulness of multiband surveys in finding these objects, and provides a testbed for further studies analysing their spatial distribution around nearby (spirals) galaxies