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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

We present \textsc{Mathpop}, a novel method to infer the globular cluster (GC) counts in ultra-diffuse galaxies (UDGs) and low-surface brightness galaxies (LSBGs). Many known UDGs have a surprisingly high ratio of GC number to surface brightness. However, standard methods to infer GC counts in UDGs face various challenges, such as photometric measurement uncertainties, GC membership uncertainties, and assumptions about the GC luminosity functions (GCLFs). \textsc{Mathpop} tackles these challenges using the mark-dependent thinned point process, enabling joint inference of the spatial and magnitude distributions of GCs. In doing so, \textsc{Mathpop} allows us to infer and quantify the uncertainties in both GC counts and GCLFs with minimal assumptions. As a precursor to \textsc{Mathpop}, we also address the data uncertainties coming from the selection process of GC candidates: we obtain probabilistic GC candidates instead of the traditional binary classification based on the color--magnitude diagram. We apply \textsc{Mathpop} to 40 LSBGs in the Perseus cluster using GC catalogs from a \textit{Hubble Space Telescope} imaging program. We then compare our results to those from an independent study using the standard method. We further calibrate and validate our approach through extensive simulations. Our approach reveals two LSBGs having GCLF turnover points much brighter than the canonical value with Bayes' factor being $\sim4.5$ and $\sim2.5$, respectively. An additional crude maximum-likelihood estimation shows that their GCLF TO points are approximately $0.9$~mag and $1.1$~mag brighter than the canonical value, with $p$-value $\sim 10^{-8}$ and $\sim 10^{-5}$, respectively., Comment: 8 figures, 5 tables; submitted to ApJ, comments are welcomed

CDG-1 is a tight grouping of four likely globular clusters in the Perseus cluster, and a candidate dark galaxy with little or no diffuse light. Here we provide new constraints on the luminosity of any underlying stellar emission, using HST/UVIS F200LP imaging. No diffuse emission is detected, with a 2$\sigma$ upper limit of F200LP>28.1 mag/arcsec$^2$ on the 5'' scale of CDG-1. This surface brightness limit corresponds to a 2$\sigma$ lower limit of >0.5 for the fraction of the total luminosity that is in the form of globular clusters. The most likely alternative, although improbable, is that CDG-1 is a chance grouping of four globular clusters in the halo of the Perseus galaxy IC312., Comment: To appear in Research Notes of the American Astronomical Society

Approximate Bayesian inference based on Laplace approximation and quadrature methods have become increasingly popular for their efficiency at fitting latent Gaussian models (LGM), which encompass popular models such as Bayesian generalized linear models, survival models, and spatio-temporal models. However, many useful models fall under the LGM framework only if some conditioning parameters are fixed, as the design matrix would vary with these parameters otherwise. Such models are termed the conditional LGMs with examples in change-point detection, non-linear regression, etc. Existing methods for fitting conditional LGMs rely on grid search or Markov-chain Monte Carlo (MCMC); both require a large number of evaluations of the unnormalized posterior density of the conditioning parameters. As each evaluation of the density requires fitting a separate LGM, these methods become computationally prohibitive beyond simple scenarios. In this work, we introduce the Bayesian optimization sequential surrogate (BOSS) algorithm, which combines Bayesian optimization with approximate Bayesian inference methods to significantly reduce the computational resources required for fitting conditional LGMs. With orders of magnitude fewer evaluations compared to grid or MCMC methods, Bayesian optimization provides us with sequential design points that capture the majority of the posterior mass of the conditioning parameters, which subsequently yields an accurate surrogate posterior distribution that can be easily normalized. We illustrate the efficiency, accuracy, and practical utility of the proposed method through extensive simulation studies and real-world applications in epidemiology, environmental sciences, and astrophysics., Comment: The authors contributed equally to this work. The names are listed alphabetically

We propose a novel set of Poisson Cluster Process (PCP) models to detect Ultra-Diffuse Galaxies (UDGs), a class of extremely faint, enigmatic galaxies of substantial interest in modern astrophysics. We model the unobserved UDG locations as parent points in a PCP, and infer their positions based on the observed spatial point patterns of their old star cluster systems. Many UDGs have somewhere from a few to hundreds of these old star clusters, which we treat as offspring points in our models. We also present a new framework to construct a marked PCP model using the marks of star clusters. The marked PCP model may enhance the detection of UDGs and offers broad applicability to problems in other disciplines. To assess the overall model performance, we design an innovative assessment tool for spatial prediction problems where only point-referenced ground truth is available, overcoming the limitation of standard ROC analyses where spatial Boolean reference maps are required. We construct a bespoke blocked Gibbs adaptive spatial birth-death-move MCMC algorithm to infer the locations of UDGs using real data from a \textit{Hubble Space Telescope} imaging survey. Based on our performance assessment tool, our novel models significantly outperform existing approaches using the Log-Gaussian Cox Process. We also obtained preliminary evidence that the marked PCP model improves UDG detection performance compared to the model without marks. Furthermore, we find evidence of a potential new ``dark galaxy'' that was not detected by previous methods., Comment: 47 pages, 8 figures, 3 tables; submitted to AoAS, comments are welcome

We introduce a new method for detecting ultra-diffuse galaxies by searching for over-densities in intergalactic globular cluster populations. Our approach is based on an application of the log-Gaussian Cox process, which is a commonly used model in the spatial statistics literature but rarely used in astronomy. This method is applied to the globular cluster data obtained from the PIPER survey, a \textit{Hubble Space Telescope} imaging program targeting the Perseus cluster. We successfully detect all confirmed ultra-diffuse galaxies with known globular cluster populations in the survey. We also identify a potential galaxy that has no detected diffuse stellar content. Preliminary analysis shows that it is unlikely to be merely an accidental clump of globular clusters or other objects. If confirmed, this system would be the first of its kind. Simulations are used to assess how the physical parameters of the globular cluster systems within ultra-diffuse galaxies affect their detectability using our method. We quantify the correlation of the detection probability with the total number of globular clusters in the galaxy and the anti-correlation with increasing half-number radius of the globular cluster system. The S\'{e}rsic index of the globular cluster distribution has little impact on detectability., Comment: 35 pages, 17 figures, accepted to ApJ

We demonstrate the power of Gibbs point process models from the spatial statistics literature when applied to studies of resolved galaxies. We conduct a rigorous analysis of the spatial distributions of objects in the star formation complexes of M33, including giant molecular clouds (GMCs) and young stellar cluster candidates (YSCCs). We choose a hierarchical model structure from GMCs to YSCCs based on the natural formation hierarchy between them. This approach circumvents the limitations of the empirical two-point correlation function analysis by naturally accounting for the inhomogeneity present in the distribution of YSCCs. We also investigate the effects of GMCs' properties on their spatial distributions. We confirm that the distribution of GMCs and YSCCs are highly correlated. We found that the spatial distributions of YSCCs reaches a peak of clustering pattern at ~250 pc scale compared to a Poisson process. This clustering mainly occurs in regions where the galactocentric distance >~4.5 kpc. Furthermore, the galactocentric distance of GMCs and their mass have strong positive effects on the correlation strength between GMCs and YSCCs. We outline some possible implications of these findings for our understanding of the cluster formation process., Comment: MNRAS in press; 22 pages