Related papers: Bayesian posterior classification of planetary neb…
Posterior predictive p-values are a common approach to Bayesian model-checking. This article analyses their frequency behaviour, that is, their distribution when the parameters and the data are drawn from the prior and the model…
In this study, we present a multi-class graphical Bayesian predictive classifier that incorporates the uncertainty in the model selection into the standard Bayesian formalism. For each class, the dependence structure underlying the observed…
The published properties of M1-78 are discussed with the purpose to resolve the object's classification as either a planetary nebula or an ultracompact HII region. A classification as a planetary nebula is rejected primarily because of the…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
Planetary Nebulae represent a powerful window into the evolution of low-intermediate mass stars that have undergone extensive mass-loss. The nebula manifests itself in an extremely wide variety of shapes, but exactly how the mass lost is…
The parameterized post-Einsteinian formalism was developed to search for generic deviations from general relativity with gravitational waves. We here present constraints on this framework using Bayesian analysis of a set of binary pulsar…
Preplanetary nebulae (PPNe) are formed from mass-ejecting late-stage AGB stars. Much of the light from the star gets scattered or absorbed by dust particles, giving rise to the observed reflection nebula seen at visible and near-IR…
Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…
Planetary nebulae (PNe) are valuable spatial and kinematic tracers of nearby galaxies. In this mini-review, I focus on their role in tracing the halo and intra-cluster/intra-group light assembly in groups and clusters of galaxies within…
Planetary nebulae (PNe) are circumstellar gas ejected during an intense mass-losing phase in the the lives of asymptotic giant branch stars. PNe have a stunning variety of shapes, most of which are not spherically symmetric. The debate over…
The total number of true, likely and possible planetary nebulae (PN) now known in the Milky Way is about 3000, approximately twice the number known a decade ago. The new discoveries are a legacy of the recent availability of wide-field,…
The spatial distribution of galaxies is a highly complex phenomenon currently impossible to predict deterministically. However, by using a statistical $\textit{bias}$ relation, it becomes possible to robustly model the average abundance of…
In their seminal 1990 paper, Wasserman and Kadane establish an upper bound for the Bayes' posterior probability of a measurable set $A$, when the prior lies in a class of probability measures $\mathcal{P}$ and the likelihood is precise.…
We investigate the discrimination of two candidates of an unknown parameter in quantum systems with continuous weak measurement, inspired by the application of hypothesis testing in distinguish-ing two Hamiltonians [Kiilerich and M{\o}lmer,…
Bayesian clustering methods have the widely touted advantage of providing a probabilistic characterization of uncertainty in clustering through the posterior distribution. An amazing variety of priors and likelihoods have been proposed for…
Naive Bayes classifiers, a family of classifiers that are based on the popular Bayes' probability theorem, are known for creating simple yet well performing models, especially in the fields of document classification and disease prediction.…
Radio continuum observations trace thermal emission of ionized plasma in planetary nebulae and bring useful information on nebular geometries. A model of homogeneous sphere or shell cannot fit the nebular spectra and brightness…
The final orbital configuration of a planetary system is shaped by both its early star-disk environment and late-stage gravitational interactions. Assessing the relative importance of each of these factors is not straightforward due to the…
Binary regression models represent a popular model-based approach for binary classification. In the Bayesian framework, computational challenges in the form of the posterior distribution motivate still-ongoing fruitful research. Here, we…
In the simple vs composite hypothesis test with a proper prior, the Bayes Factor (BF) is shown to be the posterior mean of the Likelihood Ratio (LR). Therefore, the posterior standard deviation of the LR or rather its posterior cumulative…