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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

We present a spectro-temporal analysis of 137 fast radio bursts (FRBs) from the first CHIME/FRB baseband catalog, including 125 one-off bursts and 12 repeat bursts, down to microsecond resolution using the least-squares optimization fitting routine: fitburst. Our measured values are compared with those in the first CHIME/FRB intensity catalog, revealing that nearly one-third of our sample exhibits additional burst components at higher time resolutions. We measure sub-burst components within burst envelopes as narrow as $\sim$23 $\mu$s (FWHM), with 20% of the sample displaying sub-structures narrower than 100 $\mu$s, offering constraints on emission mechanisms. Scattering timescales in the sample range from 30 $\mu$s to 13 ms at 600 MHz. We observe no correlations between scattering time and dispersion measure, rotation measure, or linear polarization fraction, with the latter suggesting that depolarization due to multipath propagation is negligible in our sample. Bursts with narrower envelopes ($\leq$ 1 ms) in our sample exhibit higher flux densities, indicating the potential presence of sub-ms FRBs that are being missed by our real-time system below a brightness threshold. Most multicomponent bursts in our sample exhibit sub-burst separations of $\leq$ 1 ms, with no bursts showing separations $<$41 $\mu$s, even at a time resolution of 2.56 $\mu$s, but both scattering and low signal-to-noise ratio can hinder detection of additional components. Lastly, given the morphological diversity of our sample, we suggest that one-off and repeating FRBs can come from different classes but have overlapping property distributions., Comment: 25 pages 14 figures

We present an extensive contemporaneous X-ray and radio campaign performed on the repeating fast radio burst (FRB) source FRB 20220912A for eight weeks immediately following the source's detection by CHIME/FRB. This includes X-ray data from XMM-Newton, NICER, and Swift, and radio detections of FRB 20220912A from CHIME/Pulsar and Effelsberg. We detect no significant X-ray emission at the time of 30 radio bursts with upper limits on $0.5-10.0$ keV X-ray fluence of $(1.5-14.5)\times 10^{-10}$ erg cm$^{-2}$ (99.7% credible interval, unabsorbed) on a timescale of 100 ms. Translated into a fluence ratio $\eta_{\text{ x/r}} = F_{\text{X-ray}}/F_{\text{radio}}$, this corresponds to ${\eta}_{\text{ x/r}} < 7\times10^{6}$. For persistent emission from the location of FRB 20220912A, we derive a 99.7% $0.5-10.0$ keV isotropic flux limit of $8.8\times 10^{-15}$ erg cm$^{-2}$ s$^{-1}$ (unabsorbed) or an isotropic luminosity limit of 1.4$\times10^{41}$ erg s$^{-1}$ at a distance of 362.4 Mpc. We derive a hierarchical extension to the standard Bayesian treatment of low-count and background-contaminated X-ray data, which allows the robust combination of multiple observations. This methodology allows us to place the best (lowest) 99.7% credible interval upper limit on an FRB ${\eta}_{\text{ x/r}}$ to date, ${\eta}_{\text{ x/r}} < 2\times10^6$, assuming that all thirty detected radio bursts are associated with X-ray bursts with the same fluence ratio. If we instead adopt an X-ray spectrum similar to the X-ray burst observed contemporaneously with FRB-like emission from Galactic magnetar SGR 1935+2154 detected on 2020 April 28, we derive a 99.7% credible interval upper limit on ${\eta}_{\text{ x/r}}$ of $8\times10^5$, which is only 3 times the observed value of ${\eta}_{\text{ x/r}}$ for SGR 1935+2154., Comment: 23 pages, 3 figures. ApJ in press (accepted after resubmission July 19th, 2024)

The relation between magnetic field strength B and gas density n in the interstellar medium is of fundamental importance to many areas of astrophysics, from protostellar disks to galaxy evolution. We present and compare Bayesian analyses of the B - n relation for a comprehensive observational data set, as well as a large body of numerical MHD simulations. We extend the original Zeeman relation of Crutcher et al. (2010) with a large body of magnetic data that includes 700 observations with the Davis-Chandrasekhar-Fermi method. By using a new multiparameter Bayesian analysis we present a new, more general, time-averaged observational relation: B \propto n^{0.27 \pm 0.017} for n \leq n_0 and B \propto n^{0.54 \pm 0.18} for n \geq n_0, with n_0 = 924^(+145-144) cm^-3. We perform a separate analysis on 19 numerical magnetohydrodynamics simulations that cover a wide range of scales, resolutions, initial conditions, and completed with a variety of codes: arepo, flash, pencil, and ramses. The power law exponents derived from the simulations depend on several physical factors including: dynamo effects, time scales, turbulence, and the initial seed field strength. In particular, early-time simulations where the density, velocity and magnetic fields are unevolved do not match the observational scalings. The simulations that trace the observed density range best, the evolved dwarf galaxy and Milky Way like galaxy simulations, settle into a near consistent exponent of = 0.5 in the dense gas, with variability in the diffuse gas exponent., Comment: 23 figures, 28 pages, submitted to MNRAS, Comments welcome

The scaling relation between the size of a galaxy's globular cluster (GC) population ($N_{GC}$) and the galaxy's stellar mass ($M_*$) is usually described with a continuous, linear model, but in reality it is a count relationship that should be modeled as such. For massive galaxies, a negative binomial (NB) model has been shown to describe the data well, but it is unclear how the scaling relation behaves at low galaxy masses where a substantial portion of galaxies have $N_{GC}=0$. In this work, we test the utility of Poisson and NB models for describing the low-mass end of the $N_{GC}-M_*$ scaling relation. We introduce the use of zero-inflated versions of these models, which allow for larger zero populations (e.g. galaxies without GCs) than would otherwise be predicted. We evaluate our models with a variety of predictive model comparison methods, including predictive intervals, leave-one-out cross-validation criterion, and posterior predictive comparisons. We find that the NB model is consistent with our data, but the naive Poisson is not. Moreover, we find that zero inflation of the models is not necessary to describe the population of low-mass galaxies that lack GCs, suggesting that a single formation and evolutionary process acts over all galaxy masses. Under the NB model, there does not appear to be anything unique about the lack of GCs in many low-mass galaxies; they are simply the low-mass extension of the larger $N_{GC}-M_*$ scaling relation., Comment: 12 pages, 4 figures, accepted for publication in ApJ

Studying transient phenomena, such as individual pulses from pulsars, has garnered considerable attention in the era of astronomical big data. Of specific interest to this study are Rotating Radio Transients (RRATs), nulling, and intermittent pulsars. This study introduces a new algorithm named LuNfit, tailored to correct the selection biases originating from the telescope and detection pipelines. Ultimately LuNfit estimates the intrinsic luminosity distribution and nulling fraction of the single pulses emitted by pulsars. LuNfit relies on Bayesian nested sampling so that the parameter space can be fully explored. Bayesian nested sampling also provides the additional benefit of simplifying model comparisons through the Bayes ratio. The robustness of LuNfit is shown through simulations and applying LuNfit onto pulsars with known nulling fractions. LuNfit is then applied to three RRATs, J0012+5431, J1538+1523, and J2355+1523, extracting their intrinsic luminosity distribution and burst rates. We find that their nulling fraction is 0.4(2), 0.749(5) and 0.995(2) respectively. We further find that a log-normal distribution likely describes the single pulse luminosity distribution of J0012+5431 and J1538+1523, while the Bayes ratio for J2355+1523 slightly favors an exponential distribution. We show the conventional method of correcting selection effects by "scaling up" the missed fraction of radio transients can be unreliable when the mean luminosity of the source is faint relative to the telescope sensitivity. Finally, we discuss the limitations of the current implementation of LuNfit while also delving into potential enhancements that would enable LuNfit to be applied to sources with complex pulse morphologies., Comment: Accepted by ApJ

In Patil et. al 2024a, we developed a multitaper power spectrum estimation method, mtNUFFT, for analyzing time-series with quasi-regular spacing, and showed that it not only improves upon the statistical issues of the Lomb-Scargle periodogram, but also provides a factor of three speed up in some applications. In this paper, we combine mtNUFFT with the harmonic F-test to test the hypothesis that a strictly periodic signal or its harmonic (as opposed to e.g. a quasi-periodic signal) is present at a given frequency. This mtNUFFT/F-test combination shows that multitapering allows detection of periodic signals and precise estimation of their frequencies, thereby improving both power spectrum estimation and harmonic analysis. Using asteroseismic time-series data for the Kepler-91 red giant, we show that the F-test automatically picks up the harmonics of its transiting exoplanet as well as certain dipole ($l=1$) mixed modes. We use this example to highlight that we can distinguish between different types of stellar oscillations, e.g., transient (damped, stochastically-excited) and strictly periodic (undamped, heat-driven). We also illustrate the technique of dividing a time-series into chunks to further examine the transient versus periodic nature of stellar oscillations. The harmonic F-test combined with mtNUFFT is implemented in the public Python package tapify (https://github.com/aaryapatil/tapify), which opens opportunities to perform detailed investigations of periodic signals in time-domain astronomy., Comment: 15 pages, 6 figures, Submitted to AJ as a companion paper to arXiv:2209.15027

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

We present a hidden Markov model (HMM) for discovering stellar flares in light curve data of stars. HMMs provide a framework to model time series data that are not stationary; they allow for systems to be in different states at different times and consider the probabilities that describe the switching dynamics between states. In the context of stellar flares discovery, we exploit the HMM framework by allowing the light curve of a star to be in one of three states at any given time step: Quiet, Firing, or Decaying. This three state HMM formulation is designed to enable straightforward identification of stellar flares, their duration, and associated uncertainty. This is crucial for estimating the flare's energy, and is useful for studies of stellar flare energy distributions. We combine our HMM with a celerite model that accounts for quasi periodic stellar oscillations. Through an injection recovery experiment, we demonstrate and evaluate the ability of our method to detect and characterize flares in stellar time series. We also show that the proposed HMM flags fainter and lower energy flares more easily than traditional sigma clipping methods. Lastly, we visually demonstrate that simultaneously conducting detrending and flare detection can mitigate biased estimations arising in multistage modelling approaches. Thus, this method paves a new way to calculating stellar flare energy. We conclude with an example application to one star observed by TESS, showing how the HMM compares with sigma clipping when using real data., Comment: To be submitted to AAS, comments welcomed

Fast radio bursts (FRBs) last for milliseconds and arrive at Earth from cosmological distances. While their origin(s) and emission mechanism(s) are presently unknown, their signals bear similarities with the much less luminous radio emission generated by pulsars within our Galaxy and several lines of evidence point toward neutron star origins. For pulsars, the linear polarisation position angle (PA) often exhibits evolution over the pulse phase that is interpreted within a geometric framework known as the rotating vector model (RVM). Here, we report on a fast radio burst, FRB 20221022A, detected by the Canadian Hydrogen Intensity Mapping Experiment (CHIME) and localized to a nearby host galaxy ($\sim 65\; \rm{Mpc}$), MCG+14-02-011. This one-off FRB displays a $\sim 130$ degree rotation of its PA over its $\sim 2.5\; \rm{ms}$ burst duration, closely resembling the "S"-shaped PA evolution commonly seen from pulsars and some radio magnetars. The PA evolution disfavours emission models involving shocks far from the source and instead suggests magnetospheric origins for this source which places the emission region close to the FRB central engine, echoing similar conclusions drawn from tempo-polarimetric studies of some repeating sources. This FRB's PA evolution is remarkably well-described by the RVM and, although we cannot determine the inclination and magnetic obliquity due to the unknown period/duty cycle of the source, we can dismiss extremely short-period pulsars (e.g., recycled millisecond pulsars) as potential progenitors. RVM-fitting appears to favour a source occupying a unique position in the period/duty cycle phase space that implies tight opening angles for the beamed emission, significantly reducing burst energy requirements of the source.

Blue Horizontal Branch (BHB) stars, excellent distant tracers for probing the Milky Way's halo density profile, are distinguished in the $(g-r)_0$ vs $(i-z)_0$ color space from another class of stars, blue straggler stars (BSs). We develop a Bayesian mixture model to classify BHB stars using high-precision photometry data from the Dark Energy Survey Data Release 2 (DES DR2). We select $\sim2100$ highly-probable BHBs based on their $griz$ photometry and the associated uncertainties, and use these stars to map the stellar halo over the Galactocentric radial range $20 \lesssim R \lesssim 70$ kpc. After excluding known stellar overdensities, we find that the number density $n_\star$ of BHBs can be represented by a power law density profile $n_\star \propto R^{-\alpha}$ with an index of $\alpha=4.28_{-0.12}^{+0.13}$, consistent with existing literature values. In addition, we examine the impact of systematic errors and the spatial inhomogeneity on the fitted density profile. Our work demonstrates the effectiveness of high-precision $griz$ photometry in selecting BHB stars. The upcoming photometric survey from the Rubin Observatory, expected to reach depths 2-3 magnitudes greater than DES during its 10-year mission, will enable us to investigate the density profile of the Milky Way's halo out to the virial radius, unravelling the complex processes of formation and evolution in our Galaxy., Comment: 22 pages, 18 figures. Submitted AAS Journal. Comments Welcome Code used in this work can be found at: https://github.com/sazabi4/Yu2024_BHB/

We present the discovery of twelve thus far non-repeating fast radio burst (FRB) sources, detected by the Canadian Hydrogen Intensity Mapping Experiment (CHIME) telescope. These sources were selected from a database comprising of order $10^3$ CHIME/FRB full-array raw voltage data recordings, based on their exceptionally high brightness and complex morphology. Our study examines the time-frequency characteristics of these bursts, including drifting, microstructure, and periodicities. The events in this sample display a variety of unique drifting phenomenologies that deviate from the linear negative drifting phenomenon seen in many repeating FRBs, and motivate a possible new framework for classifying drifting archetypes. Additionally, we detect microstructure features of duration $\lesssim$ 50 $\mu s$ in seven events, with some as narrow as $\approx$ 7 $\mu s$. We find no evidence of significant periodicities. Furthermore, we report the polarization characteristics of seven events, including their polarization fractions and Faraday rotation measures (RMs). The observed $|\mathrm{RM}|$ values span a wide range of $17.24(2)$ - $328.06(2) \mathrm{~rad~m}^{-2}$, with linear polarization fractions between $0.340(1)$ - $0.946(3)$. The morphological properties of the bursts in our sample appear broadly consistent with predictions from both relativistic shock and magnetospheric models of FRB emission, as well as propagation through discrete ionized plasma structures. We address these models and discuss how they can be tested using our improved understanding of morphological archetypes., Comment: 29 pages, 14 figures, submitted to ApJ, comments appreciated

We present a hierarchical Bayesian inference approach to estimating the structural properties and the phase space center of a globular cluster (GC) given the spatial and kinematic information of its stars based on lowered isothermal cluster models. As a first step towards more realistic modelling of GCs, we built a differentiable, accurate emulator of the lowered isothermal distribution function using interpolation. The reliable gradient information provided by the emulator allows the use of Hamiltonian Monte Carlo methods to sample large Bayesian models with hundreds of parameters, thereby enabling inference on hierarchical models. We explore the use of hierarchical Bayesian modelling to address several issues encountered in observations of GC including an unknown GC center, incomplete data, and measurement errors. Our approach not only avoids the common technique of radial binning but also incorporates the aforementioned uncertainties in a robust and statistically consistent way. Through demonstrating the reliability of our hierarchical Bayesian model on simulations, our work lays out the foundation for more realistic and complex modelling of real GC data., Comment: 16 pages, 12 figures, and 2 tables

In 2021, a catalog of 536 fast radio bursts (FRBs) detected with the Canadian Hydrogen Intensity Mapping Experiment (CHIME) radio telescope was released by the CHIME/FRB Collaboration. This large collection of bursts, observed with a single instrument and uniform selection effects, has advanced our understanding of the FRB population. Here we update the results for 140 of these FRBs for which channelized raw voltage ('baseband') data are available. With the voltages measured by the telescope's antennas, it is possible to maximize the telescope sensitivity in any direction within the primary beam, an operation called 'beamforming'. This allows us to increase the signal-to-noise ratio (S/N) of the bursts and to localize them to sub-arcminute precision. The improved localization is also used to correct the beam response of the instrument and to measure fluxes and fluences with a ~10% uncertainty. Additionally, the time resolution is increased by three orders of magnitude relative to that in the first CHIME/FRB catalog, and, applying coherent dedispersion, burst morphologies can be studied in detail. Polarization information is also available for the full sample of 140 FRBs, providing an unprecedented dataset to study the polarization properties of the population. We release the baseband data beamformed to the most probable position of each FRB. These data are analyzed in detail in a series of accompanying papers.

We present results from angular cross-correlations between select samples of CHIME/FRB repeaters and galaxies in three photometric galaxy surveys, which have shown correlations with the first CHIME/FRB catalog containing repeating and nonrepeating sources: WISE$\times$SCOS, DESI-BGS, and DESI-LRG. We find a statistically significant correlation ($p$-value $<0.001$, after accounting for look-elsewhere factors) between a sample of repeaters with extragalactic dispersion measure DM $>395$ pc cm$^{-3}$ and WISE$\times$SCOS galaxies with redshift $z>0.275$. We demonstrate that the correlation arises surprisingly because of a statistical association between FRB 20200320A (extragalactic DM $\approx550$ pc cm$^{-3}$) and a galaxy group in the same dark matter halo at redshift $z\approx0.32$. We estimate that the host halo, along with an intervening halo at redshift $z\approx0.12$, accounts for at least $\sim$$30\%$ of the extragalactic DM. Our results strongly motivate incorporating galaxy group and cluster catalogs into direct host association pipelines for FRBs with $\lesssim$$1'$ localization precision, effectively utilizing the two-point information to constrain FRB properties such as their redshift and DM distributions. In addition, we find marginal evidence for a negative correlation at 99.4% CL between a sample of repeating FRBs with baseband data (median extragalactic DM $=354$ pc cm$^{-3}$) and DESI-LRG galaxies with redshift $0.3\le z<0.45$, suggesting that the repeaters might be more prone than apparent nonrepeaters to propagation effects in FRB-galaxy correlations due to intervening free electrons over angular scales $\sim$$0\mbox{$.\!\!^\circ$}5$., Comment: 14 pages, 4 figures, 3 tables, published in ApJ

The presence or absence of star clusters in galaxies, and the properties of star cluster populations compared to their host galaxy properties, are important observables for validating models of cluster formation, galaxy formation, and galaxy assembly. In this work, we apply a Bayesian approach to fit two models to data from surveys of young clusters in star forming galaxies. The first model is a logistic regression, which allows us to include galaxies which do not have any young clusters. The second model is a hurdle model, which includes galaxies with zero clusters and also incorporates information about the total mass in the cluster system. We investigate two predictors (star formation rate and total stellar mass in the galaxy) and look at clusters younger than 10 or 100 Myr. We find that in all cases, star formation rate is the better predictor for both the probability of hosting clusters and the total mass in the cluster system. We compare our results to similar models for old globular clusters, and conclude that star cluster formation was more abundant and more efficient at higher redshifts, likely because of the high gas content of galaxies at that time., Comment: 10 pages, 5 figures, accepted by MNRAS

We report ten fast radio bursts (FRBs) detected in the far side-lobe region (i.e., $\geq 5^\circ$ off-meridian) of the Canadian Hydrogen Intensity Mapping Experiment (CHIME) from 2018 August 28 to 2021 August 31. We localize the bursts by fitting their spectra with a model of the CHIME/FRB synthesized beam response. We find that the far side-lobe events have on average ~500 times greater fluxes than events detected in CHIME's main lobe. We show that the side-lobe sample is therefore statistically ~20 times closer than the main-lobe sample. We find promising host galaxy candidates (P$_{\rm cc}$ < 1%) for two of the FRBs, 20190112B and 20210310B, at distances of 38 and 16 Mpc, respectively. CHIME/FRB did not observe repetition of similar brightness from the uniform sample of 10 side-lobe FRBs in a total exposure time of 35580 hours. Under the assumption of Poisson-distributed bursts, we infer that the mean repetition interval above the detection threshold of the far side-lobe events is longer than 11880 hours, which is at least 2380 times larger than the interval from known CHIME/FRB detected repeating sources, with some caveats, notably that very narrow-band events could have been missed. Our results from these far side-lobe events suggest one of two scenarios: either (1) all FRBs repeat and the repetition intervals span a wide range, with high-rate repeaters being a rare subpopulation, or (2) non-repeating FRBs are a distinct population different from known repeaters., Comment: 27 pages, 20 figures. This version is the result of the merger of arxiv:2307.05262 and the previous version of this paper. Accepted for publication in ApJ

FRB 20180916B is a repeating Fast Radio Burst (FRB) with a 16.3-day periodicity in its activity. In this study, we present morphological properties of 60 FRB 20180916B bursts detected by CHIME/FRB between 2018 August and 2021 December. We recorded raw voltage data for 45 of these bursts, enabling microseconds time resolution in some cases. We studied variation of spectro-temporal properties with time and activity phase. We find that the variation in Dispersion Measure (DM) is $\lesssim$1 pc cm$^{-3}$ and that there is burst-to-burst variation in scattering time estimates ranging from $\sim$0.16 to over 2 ms, with no discernible trend with activity phase for either property. Furthermore, we find no DM and scattering variability corresponding to the recent change in rotation measure from the source, which has implications for the immediate environment of the source. We find that FRB 20180916B has thus far shown no epochs of heightened activity as have been seen in other active repeaters by CHIME/FRB, with its burst count consistent with originating from a Poissonian process. We also observe no change in the value of the activity period over the duration of our observations and set a 1$\sigma$ upper limit of $1.5\times10^{-4}$ day day$^{-1}$ on the absolute period derivative. Finally, we discuss constraints on progenitor models yielded by our results, noting that our upper limits on changes in scattering and dispersion measure as a function of phase do not support models invoking a massive binary companion star as the origin of the 16.3-day periodicity., Comment: 25 pages, 10 figures

Galaxy stellar mass is known to be monotonically related to the size of the galaxy's globular cluster (GC) population for Milky Way sized and larger galaxies. However, the relation becomes ambiguous for dwarf galaxies, where there is some evidence for a downturn in GC population size at low galaxy masses. Smaller dwarfs are increasingly likely to have no GCs, and these zeros cannot be easily incorporated into linear models. We introduce the Hierarchical ERrors-in-variables Bayesian lognormAL hurdle (HERBAL) model to represent the relationship between dwarf galaxies and their GC populations, and apply it to the sample of Local Group galaxies where the luminosity range coverage is maximal. This bimodal model accurately represents the two populations of dwarf galaxies: those that have GCs and those that do not. Our model thoroughly accounts for all uncertainties, including measurement uncertainty, uncertainty in luminosity to stellar mass conversions, and intrinsic scatter. The hierarchical nature of our Bayesian model also allows us to estimate galaxy masses and individual mass-to-light ratios from luminosity data within the model. We find that 50% of galaxies are expected to host globular cluster populations at a stellar mass of $\log_{10}(M_*)=6.996$, and that the expected mass of GC populations remains linear down to the smallest galaxies. Our hierarchical model recovers an accurate estimate of the Milky Way stellar mass. Under our assumed error model, we find a non-zero intrinsic scatter of $0.59_{-0.21}^{+0.30}$ (95% credible interval) that should be accounted for in future models., Comment: 21 pages, 9 figures. Accepted for publication in The Astrophysical Journal

In agronomics, predicting crop yield at a per field/county granularity is important for farmers to minimize uncertainty and plan seeding for the next crop cycle. While state-of-the-art prediction techniques employ graph convolutional nets (GCN) to predict future crop yields given relevant features and crop yields of previous years, a dense underlying graph kernel requires long training and execution time. In this paper, we propose a graph sparsification method based on the Fiedler number to remove edges from a complete graph kernel, in order to lower the complexity of GCN training/execution. Specifically, we first show that greedily removing an edge at a time that induces the minimal change in the second eigenvalue leads to a sparse graph with good GCN performance. We then propose a fast method to choose an edge for removal per iteration based on an eigenvalue perturbation theorem. Experiments show that our Fiedler-based method produces a sparse graph with good GCN performance compared to other graph sparsification schemes in crop yield prediction.

Plasmodium spp. are the protozoan parasites responsible for malaria. Plasmodium spp. synthesise a biocrystal, hemozoin, which can be observed under cross-polarised light. These birefringent crystals can be seen due to different refractive indices of the hemozoin crystal and red blood cells. Here, we present a polarised light modular microscopy (Pol-ModMicro) solution, complete with illumination sources and a robust imaging system to capture birefringence and identify the parasites. We achieve this by combining ModLight light sources with bespoke components designed for the OpenFlexure microscope to image blood smears. Further, a simple and robust algorithm capable of enhancing birefringence is presented. This solution provides image quality that is comparable to a substantially more expensive proprietary microscope., Comment: 3 figures, files repository accessible at https://zenodo.org/record/7837389

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

In the last two decades, Bayesian inference has become commonplace in astronomy. At the same time, the choice of algorithms, terminology, notation, and interpretation of Bayesian inference varies from one sub-field of astronomy to the next, which can lead to confusion to both those learning and those familiar with Bayesian statistics. Moreover, the choice varies between the astronomy and statistics literature, too. In this paper, our goal is two-fold: (1) provide a reference that consolidates and clarifies terminology and notation across disciplines, and (2) outline practical guidance for Bayesian inference in astronomy. Highlighting both the astronomy and statistics literature, we cover topics such as notation, specification of the likelihood and prior distributions, inference using the posterior distribution, and posterior predictive checking. It is not our intention to introduce the entire field of Bayesian data analysis -- rather, we present a series of useful practices for astronomers who already have an understanding of the Bayesian "nuts and bolts" and wish to increase their expertise and extend their knowledge. Moreover, as the field of astrostatistics and astroinformatics continues to grow, we hope this paper will serve as both a helpful reference and as a jumping off point for deeper dives into the statistics and astrostatistics literature., Comment: 10 pages, 4 figures

The CHIME/FRB project has detected hundreds of fast radio bursts (FRBs), providing an unparalleled population to probe statistically the foreground media that they illuminate. One such foreground medium is the ionized halo of the Milky Way (MW). We estimate the total Galactic electron column density from FRB dispersion measures (DMs) as a function of Galactic latitude using four different estimators, including ones that assume spherical symmetry of the ionized MW halo and ones that imply more latitudinal-variation in density. Our observation-based constraints of the total Galactic DM contribution for $|b|\geq 30^\circ$, depending on the Galactic latitude and selected model, span 87.8 - 141 pc cm^-3. This constraint implies upper limits on the MW halo DM contribution that range over 52-111 pc cm^-3. We discuss the viability of various gas density profiles for the MW halo that have been used to estimate the halo's contribution to DMs of extragalactic sources. Several models overestimate the DM contribution, especially when assuming higher halo gas masses (~ 3.5 x 10^12 solar masses). Some halo models predict a higher MW halo DM contribution than can be supported by our observations unless the effect of feedback is increased within them, highlighting the impact of feedback processes in galaxy formation., Comment: 19 pages, 4 figures. ApJ in press (accepted February 8th, 2023)

Asteroseismic time-series data have imprints of stellar oscillation modes, whose detection and characterization through time-series analysis allows us to probe stellar interior physics. Such analyses usually occur in the Fourier domain by computing the Lomb-Scargle (LS) periodogram, an estimator of the power spectrum underlying unevenly-sampled time-series data. However, the LS periodogram suffers from the statistical problems of (1) inconsistency (or noise) and (2) bias due to high spectral leakage. Here, we develop a multitaper power spectrum estimator using the Non-Uniform Fast Fourier Transform (mtNUFFT) to tackle the inconsistency and bias problems of the LS periodogram. Using a simulated light curve, we show that the mtNUFFT power spectrum estimate of solar-like oscillations has lower variance and bias than the LS estimate. We also apply our method to the Kepler-91 red giant, and combine it with PBjam peakbagging to obtain mode parameters and a derived age estimate of $3.97 \pm 0.52$ Gyr. PBjam allows the improvement of age precision relative to the $4.27 \pm 0.75$ Gyr APOKASC-2 (uncorrected) estimate, whereas partnering mtNUFFT with PBjam speeds up peakbagging thrice as much as LS. This increase in efficiency has promising implications for Galactic archaeology, in addition to stellar structure and evolution studies. Our new method generally applies to time-domain astronomy and is implemented in the public Python package tapify, available at https://github.com/aaryapatil/tapify., Comment: 27 pages (3 pages in the Appendix), 12 figures, 3 tables, Revision submitted to AJ. This paper focuses solely on multitaper power spectrum estimation, whereas a companion paper showcases harmonic analysis using the multitaper F-test (v1 of this paper has been split). Both these papers have applications in asteroseismology

Prediction of annual crop yields at a county granularity is important for national food production and price stability. In this paper, towards the goal of better crop yield prediction, leveraging recent graph signal processing (GSP) tools to exploit spatial correlation among neighboring counties, we denoise relevant features via graph spectral filtering that are inputs to a deep learning prediction model. Specifically, we first construct a combinatorial graph with edge weights that encode county-to-county similarities in soil and location features via metric learning. We then denoise features via a maximum a posteriori (MAP) formulation with a graph Laplacian regularizer (GLR). We focus on the challenge to estimate the crucial weight parameter $\mu$, trading off the fidelity term and GLR, that is a function of noise variance in an unsupervised manner. We first estimate noise variance directly from noise-corrupted graph signals using a graph clique detection (GCD) procedure that discovers locally constant regions. We then compute an optimal $\mu$ minimizing an approximate mean square error function via bias-variance analysis. Experimental results from collected USDA data show that using denoised features as input, performance of a crop yield prediction model can be improved noticeably.

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