Related papers: A Bayesian Framework for Exoplanet Direct Detectio…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
We consider the high energy physics unfolding problem where the goal is to estimate the spectrum of elementary particles given observations distorted by the limited resolution of a particle detector. This important statistical inverse…
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…
In reply to hep-ph/0701204 we demonstrate why the arguments made therein do not address the criticism exposed in hep-ph/0607246 on the fundamental shortcomings of the Bayesian approach when it comes to the extraction of parameters of Nature…
We perform extensive Monte Carlo simulations to systematically compare the frequentist and Bayesian treatments of the Lomb--Scargle periodogram. The goal is to investigate whether the Bayesian period search is advantageous over the…
We present a general probabilistic formalism for cross-identifying astronomical point sources in multiple observations. Our Bayesian approach, symmetric in all observations, is the foundation of a unified framework for object matching,…
Due to their great flexibility, nonparametric Bayes methods have proven to be a valuable tool for discovering complicated patterns in data. The term "nonparametric Bayes" suggests that these methods inherit model-free operating…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
A common problem in astrophysics is determining how bright a source could be and still not be detected. Despite the simplicity with which the problem can be stated, the solution involves complex statistical issues that require careful…
In statistical practice, whether a Bayesian or frequentist approach is used in inference depends not only on the availability of prior information but also on the attitude taken toward partial prior information, with frequentists tending to…
Bayesian Inference is a powerful approach to data analysis that is based almost entirely on probability theory. In this approach, probabilities model {\it uncertainty} rather than randomness or variability. This thesis is composed of a…
Detecting the faint emission of a secondary source in the proximity of the much brighter source has been the most severe obstacle for using direct imaging in searching for exoplanets. Using quantum state discrimination and quantum imaging…
In this paper, we study frequentist coverage errors of Bayesian credible sets for an approximately linear regression model with (moderately) high dimensional regressors, where the dimension of the regressors may increase with but is smaller…
Detecting and measuring a non-Gaussian signature of primordial origin in the density field is a major science goal of next-generation galaxy surveys. The signal will permit us to determine primordial physics processes and constrain models…
Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without…
This paper presents a brief, semi-technical comparison of the essential features of the frequentist and Bayesian approaches to statistical inference, with several illustrative examples implemented in Python. The differences between…
We present an analytic theory for the resolution attainable via eclipse mapping of exoplanets, based on the Fourier components of the brightness distribution on the planetary disk. We find that the impact parameter determines which features…
A method is presented for performing joint analyses of cosmological datasets, in which the weight assigned to each dataset is determined directly by it own statistical properties. The weights are considered in a Bayesian context as a set of…
The data analysis problem of coherently searching for unmodeled gravitational-wave bursts in the data generated by a global network of gravitational-wave observatories has been at the center of research for almost two decades. As data from…
We explore the detection condition of a wide-separation planet through the perturbation induced by the planetary caustic for various microlensing parameters, especially for the size of the source stars. By constructing the fractional…