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An important task in the study of fast radio bursts (FRBs) remains the automatic classification of repeating and non-repeating sources based on their morphological properties. We propose a statistical model that considers a modified logistic regression to classify FRB sources. The classical logistic regression model is modified to accommodate the small proportion of repeaters in the data, a feature that is likely due to the sampling procedure and duration and is not a characteristic of the population of FRB sources. The weighted logistic regression hinges on the choice of a tuning parameter that represents the true proportion $\tau$ of repeating FRB sources in the entire population. The proposed method has a sound statistical foundation, direct interpretability, and operates with only 5 parameters, enabling quicker retraining with added data. Using the CHIME/FRB Collaboration sample of repeating and non-repeating FRBs and numerical experiments, we achieve a classification accuracy for repeaters of nearly 75\% or higher when $\tau$ is set in the range of $50$ to $60$\%. This implies a tentative high proportion of repeaters, which is surprising, but is also in agreement with recent estimates of $\tau$ that are obtained using other methods., Comment: 16 pages, 7 figures. Submitted to ApJ

This paper introduces an approach to analyze nonhomogeneous Poisson processes (NHPP) observed with noise, focusing on previously unstudied second-order characteristics of the noisy process. Utilizing a hierarchical Bayesian model with noisy data, we estimate hyperparameters governing a physically motivated NHPP intensity. Simulation studies demonstrate the reliability of this methodology in accurately estimating hyperparameters. Leveraging the posterior distribution, we then infer the probability of detecting a certain number of events within a given radius, the $k$-contact distance. We demonstrate our methodology with an application to observations of fast radio bursts (FRBs) detected by the Canadian Hydrogen Intensity Mapping Experiment's FRB Project (CHIME/FRB). This approach allows us to identify repeating FRB sources by bounding or directly simulating the probability of observing $k$ physically independent sources within some radius in the detection domain, or the $\textit{probability of coincidence}$ ($P_{\text{C}}$). The new methodology improves the repeater detection $P_{\text{C}}$ in 86% of cases when applied to the largest sample of previously classified observations, with a median improvement factor (existing metric over $P_{\text{C}}$ from our methodology) of $\sim$ 3000., Comment: 24 pages, 8 figures, submitted to the Annals of Applied Statistics. Feedback/comments welcome

The light we receive from distant astrophysical objects carries information about their origins and the physical mechanisms that power them. The study of these signals, however, is complicated by the fact that observations are often a mixture of the light emitted by multiple localized sources situated in a spatially-varying background. A general algorithm to achieve robust and accurate source identification in this case remains an open question in astrophysics. This paper focuses on high-energy light (such as X-rays and gamma-rays), for which observatories can detect individual photons (quanta of light), measuring their incoming direction, arrival time, and energy. Our proposed Bayesian methodology uses both the spatial and energy information to identify point sources, that is, separate them from the spatially-varying background, to estimate their number, and to compute the posterior probabilities that each photon originated from each identified source. This is accomplished via a Dirichlet process mixture while the background is simultaneously reconstructed via a flexible Bayesian nonparametric model based on B-splines. Our proposed method is validated with a suite of simulation studies and illustrated with an application to a complex region of the sky observed by the \emph{Fermi} Gamma-ray Space Telescope.

The radial velocity method is one of the most successful techniques for detecting exoplanets. It works by detecting the velocity of a host star induced by the gravitational effect of an orbiting planet, specifically the velocity along our line of sight, which is called the radial velocity of the star. Low-mass planets typically cause their host star to move with radial velocities of 1 m/s or less. By analyzing a time series of stellar spectra from a host star, modern astronomical instruments can in theory detect such planets. However, in practice, intrinsic stellar variability (e.g., star spots, convective motion, pulsations) affects the spectra and often mimics a radial velocity signal. This signal contamination makes it difficult to reliably detect low-mass planets. A principled approach to recovering planet radial velocity signals in the presence of stellar activity was proposed by Rajpaul et al. (2015). It uses a multivariate Gaussian process model to jointly capture time series of the apparent radial velocity and multiple indicators of stellar activity. We build on this work in two ways: (i) we propose using dimension reduction techniques to construct new high-information stellar activity indicators; and (ii) we extend the Rajpaul et al. (2015) model to a larger class of models and use a power-based model comparison procedure to select the best model. Despite significant interest in exoplanets, previous efforts have not performed large-scale stellar activity model selection or attempted to evaluate models based on planet detection power. In the case of main sequence G2V stars, we find that our method substantially improves planet detection power compared to previous state-of-the-art approaches., Comment: 37 pages, 7 figures