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Computation of the marginal likelihood from a simulated posterior distribution is central to Bayesian model selection but is computationally difficult. I argue that the marginal likelihood can be reliably computed from a posterior sample by…

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…

If we cannot obtain all terms of a series, or if we cannot sum up a series, we have to turn to the partial sum approximation which approximate a function by the first several terms of the series. However, the partial sum approximation often…

Loopy belief propagation performs approximate inference on graphical models with loops. One might hope to compensate for the approximation by adjusting model parameters. Learning algorithms for this purpose have been explored previously,…

Accurate modeling for the evolution of the Baryon Acoustic Oscillations (BAO) is essential for using it as a standard ruler to probe cosmology. We explore the non-linearity of the BAO in different environments using the density-split…

Here, we present the angular diameter distance measurement obtained from the measurement of the Baryonic Acoustic Oscillation (BAO) feature using the completed Dark Energy Survey (DES) data, summarizing the main results of [Phys. Rev. D…

Bayesian inference is often used in cosmology and astrophysics to derive constraints on model parameters from observations. This approach relies on the ability to compute the likelihood of the data given a choice of model parameters. In…

Cosmological parameter estimation in the post-reionisation era via neutral hydrogen radio emission ($\text{\hi}$), is among the key science goals of the forthcoming SKA Observatory (SKAO). This paper explores detection capability for baryon…

Bayesian adaptive designs enable flexible clinical trials by adapting features based on accumulating data. Among these, Bayesian Response-Adaptive Randomization (BRAR) skews patient allocation towards more promising treatments based on…

We present angular diameter measurements obtained by measuring the position of Baryon Acoustic Oscillations (BAO) in an optimised sample of galaxies from the first three years of Dark Energy Survey data (DES Y3). The sample consists of 7…

We consider the Bayesian detection statistic for a targeted search for continuous gravitational waves, known as the $\mathcal{B}$-statistic. This is a Bayes factor between signal and noise hypotheses, produced by marginalizing over the four…

Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…

The measurement of cosmological distances using baryon acoustic oscillations (BAO) is crucial for studying the universe's expansion. The Chinese Space Station Telescope (CSST) galaxy redshift survey, with its vast volume and sky coverage,…

Motivated by Tweedie's formula for the Compound Decision problem, we examine the theoretical foundations of empirical Bayes estimators that directly model the marginal density $m(y)$. Our main result shows that polynomial log-marginals of…

We perform a frequentist analysis using the standard profile likelihood method for clustering measurements from Data Release 1 of the Dark Energy Spectroscopic Instrument (DESI). While Bayesian inferences for Effective Field Theory models…

Corrections induced by primordial non-Gaussianity to the linear halo bias can be computed from a peak-background split or the widespread local bias model. However, numerical simulations clearly support the prediction of the former, in which…

The baryon acoustic oscillation (BAO) feature provides an important distance scale for the measurement of the expansion history of the Universe. Theoretical models of the BAO in the distribution of biased tracers of the large scale…

Microwave background temperature and polarization observations are a powerful way to constrain cosmological parameters if the likelihood function can be calculated accurately. The temperature and polarization fields are correlated, partial…

We study the robustness of the baryon acoustic oscillation (BAO) analysis to the underlying cosmological model. We focus on testing the standard BAO analysis that relies on the use of a template. These templates are constructed assuming a…

The Bayesian lasso is well-known as a Bayesian alternative for Lasso. Although the advantage of the Bayesian lasso is capable of full probabilistic uncertain quantification for parameters, the corresponding posterior distribution can be…