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The astrophysical origins of the majority of the IceCube neutrinos remain unknown. Effectively characterizing the spatial distribution of the neutrino samples and associating the events with astrophysical source catalogs can be challenging given the large atmospheric neutrino background and underlying non-Gaussian spatial features in the neutrino and source samples. In this paper, we investigate a framework for identifying and statistically evaluating the cross-correlations between IceCube data and an astrophysical source catalog based on the k-nearest-neighbor cumulative distribution functions (kNN-CDFs). We propose a maximum likelihood estimation procedure for inferring the true proportions of astrophysical neutrinos in the point-source data. We conduct a statistical power analysis of an associated likelihood ratio test with estimations of its sensitivity and discovery potential with synthetic neutrino data samples and a WISE–2MASS galaxy sample. We apply the method to IceCube’s public ten-year point-source data and find no statistically significant evidence for spatial cross-correlations with the selected galaxy sample. We discuss possible extensions to the current method and explore the method’s potential to identify the cross-correlation signals in data sets with different sample sizes.

The radial velocity (RV) method, also known as Doppler spectroscopy, is a powerful technique for exoplanet discovery and characterization. In recent years, progress has been made thanks to the improvements in the quality of spectra from new extreme-precision RV spectrometers. However, detecting the RV signals of Earth-like exoplanets remains challenging, as the spectroscopic signatures of low-mass planets can be obscured or confused with intrinsic stellar variability. Changes in the shapes of spectral lines across time can provide valuable information for disentangling stellar activity from true Doppler shifts caused by low-mass exoplanets. In this work, we present a fixed effects linear model to estimate RV signals that controls for changes in line shapes by aggregating information from hundreds of spectral lines. Our methodology is fast and flexible, allowing us to use cross validation to evaluate model performance on unseen data. We evaluate the model’s ability to remove stellar activity using solar observations from the NEID spectrograph, as the Sun’s true center-of-mass motion is precisely known. Including line shape-change covariates reduces the RV rms errors by approximately 76% (from 1.722 to 0.403 m s−1) relative to using only the line-by-line Doppler shifts. The magnitude of the residuals is significantly less than that from traditional cross-correlation function-based RV estimators and comparable to other state-of-the-art methods for mitigating stellar variability.

While linear mixed modeling methods are foundational concepts introduced in any statistical education, adequate general methods for interval estimation involving models with more than a few variance components are lacking, especially in the unbalanced setting. Generalized fiducial inference provides a possible framework that accommodates this absence of methodology. Under the fabric of generalized fiducial inference along with sequential Monte Carlo methods, we present an approach for interval estimation for both balanced and unbalanced Gaussian linear mixed models. We compare the proposed method to classical and Bayesian results in the literature in a simulation study of two-fold nested models and two-factor crossed designs with an interaction term. The proposed method is found to be competitive or better when evaluated based on frequentist criteria of empirical coverage and average length of confidence intervals for small sample sizes. A MATLAB implementation of the proposed algorithm is available from the authors.

The 2013 Boston marathon was disrupted by two bombs placed near the finish line. The bombs resulted in three deaths and several hundred injuries. Of lesser concern, in the immediate aftermath, was the fact that nearly 6,000 runners failed to finish the race. We were approached by the marathon's organizers, the Boston Athletic Association (BAA), and asked to recommend a procedure for projecting finish times for the runners who could not complete the race. With assistance from the BAA, we created a dataset consisting of all the runners in the 2013 race who reached the halfway point but failed to finish, as well as all runners from the 2010 and 2011 Boston marathons. The data consist of split times from each of the 5 km sections of the course, as well as the final 2.2 km (from 40 km to the finish). The statistical objective is to predict the missing split times for the runners who failed to finish in 2013. We set this problem in the context of the matrix completion problem, examples of which include imputing missing data in DNA microarray experiments, and the Netflix prize problem. We propose five prediction methods and create a validation dataset to measure their performance by mean squared error and other measures. The best method used local regression based on a K-nearest-neighbors algorithm (KNN method), though several other methods produced results of similar quality. We show how the results were used to create projected times for the 2013 runners and discuss potential for future application of the same methodology. We present the whole project as an example of reproducible research, in that we are able to make the full data and all the algorithms we have used publicly available, which may facilitate future research extending the methods or proposing completely different approaches.

Gordon Belot argues that Bayesian theory is epistemologically immodest. In response, we show that the topological conditions that underpin his criticisms of asymptotic Bayesian conditioning are self-defeating. They require extreme a priori credences regarding, for example, the limiting behavior of observed relative frequencies. We offer a different explication of Bayesian modesty using a goal of consensus: rival scientific opinions should be responsive to new facts as a way to resolve their disputes. Also we address Adam Elga’s rebuttal to Belot’s analysis, which focuses attention on the role that the assumption of countable additivity plays in Belot’s criticisms.

As the first successful technique used to detect exoplanets orbiting distant stars, the radial velocity method aims to detect a periodic Doppler shift in a stellar spectrum due to the star's motion along the line sight. We introduce a new, mathematically rigorous approach to detect such a signal that accounts for the smooth functional relationship of neighboring wavelengths in the spectrum, minimizes the role of wavelength interpolation, accounts for heteroskedastic noise and easily allows for accurate calculation of the estimated radial velocity standard error. Using Hermite–Gaussian functions, we show that the problem of detecting a Doppler shift in the spectrum can be reduced to linear regression in many settings. A simulation study demonstrates that the proposed method is able to accurately estimate an individual spectrum's radial velocity with precision below 0.3 m s−1, corresponding to a Doppler shift much smaller than the size of a spectral pixel. Furthermore, the new method outperforms the traditional cross-correlation function approach for estimating the radial velocity by reducing the root mean squared error up to 15 cm s−1. The proposed method is also demonstrated on a new set of observations from the EXtreme PREcision Spectrometer (EXPRES) for the host star 51 Pegasi, and successfully recovers estimates of the planetary companion's parameters that agree well with previous studies. The method is implemented in the R package rvmethod, and supplemental Python code is also available.

Measured spectral shifts due to intrinsic stellar variability (e.g., pulsations, granulation) and activity (e.g., spots, plages) are the largest source of error for extreme-precision radial-velocity (EPRV) exoplanet detection. Several methods are designed to disentangle stellar signals from true center-of-mass shifts due to planets. The Extreme-precision Spectrograph (EXPRES) Stellar Signals Project (ESSP) presents a self-consistent comparison of 22 different methods tested on the same extreme-precision spectroscopic data from EXPRES. Methods derived new activity indicators, constructed models for mapping an indicator to the needed radial-velocity (RV) correction, or separated out shape- and shift-driven RV components. Since no ground truth is known when using real data, relative method performance is assessed using the total and nightly scatter of returned RVs and agreement between the results of different methods. Nearly all submitted methods return a lower RV rms than classic linear decorrelation, but no method is yet consistently reducing the RV rms to sub-meter-per-second levels. There is a concerning lack of agreement between the RVs returned by different methods. These results suggest that continued progress in this field necessitates increased interpretability of methods, high-cadence data to capture stellar signals at all timescales, and continued tests like the ESSP using consistent data sets with more advanced metrics for method performance. Future comparisons should make use of various well-characterized data sets—such as solar data or data with known injected planetary and/or stellar signals—to better understand method performance and whether planetary signals are preserved.

The Sleeping Beauty problem has spawned a debate between “thirders” and “halfers” who draw conflicting conclusions about Sleeping Beauty's credence that a coin lands heads. Our analysis is based on a probability model for what Sleeping Beauty knows at each time during the experiment. We show that conflicting conclusions result from different modeling assumptions that each group makes. Our analysis uses a standard “Bayesian” account of rational belief with conditioning. No special handling is used for self-locating beliefs or centered propositions. We also explore what fair prices Sleeping Beauty computes for gambles that she might be offered during the experiment.

Topological data analysis (TDA) uses persistent homology to quantify loops and higher-dimensional holes in data, making it particularly relevant for examining the characteristics of images of cells in the field of cell biology. In the context of a cell injury, as time progresses, a wound in the form of a ring emerges in the cell image and then gradually vanishes. Performing statistical inference on this ring-like pattern in a single image is challenging due to the absence of repeated samples. In this paper, we develop a novel framework leveraging TDA to estimate underlying structures within individual images and quantify associated uncertainties through confidence regions. Our proposed method partitions the image into the background and the damaged cell regions. Then pixels within the affected cell region are used to establish confidence regions in the space of persistence diagrams (topological summary statistics). The method establishes estimates on the persistence diagrams which correct the bias of traditional TDA approaches. A simulation study is conducted to evaluate the coverage probabilities of the proposed confidence regions in comparison to an alternative approach is proposed in this paper. We also illustrate our methodology by a real-world example provided by cell repair.

The astrophysical origins of the majority of the IceCube neutrinos remain unknown. Effectively characterizing the spatial distribution of the neutrino samples and associating the events with astrophysical source catalogs can be challenging given the large atmospheric neutrino background and underlying non-Gaussian spatial features in the neutrino and source samples. In this paper, we investigate a framework for identifying and statistically evaluating the cross-correlations between IceCube data and an astrophysical source catalog based on the \\(k\\)-nearest-neighbor cumulative distribution functions (\\(k\\)NN-CDFs). We propose a maximum likelihood estimation procedure for inferring the true proportions of astrophysical neutrinos in the point-source data. We conduct a statistical power analysis of an associated likelihood ratio test with estimations of its sensitivity and discovery potential with synthetic neutrino data samples and a WISE-2MASS galaxy sample. We apply the method to IceCube's public ten-year point-source data and find no statistically significant evidence for spatial cross-correlations with the selected galaxy sample. We discuss possible extensions to the current method and explore the method's potential to identify the cross-correlation signals in data sets with different sample sizes.