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1. A Stein-Papangelou Goodness-of-Fit Test for Point Processes.

   Yang, J; Rao, V; Neville, J. (January 2019, Artificial Intelligence and Statistics (AISTATS 2019))

   Point processes provide a powerful framework for modeling the distribution and interactions of events in time or space. Their flexibility has given rise to a variety of sophisticated models in statistics and machine learning, yet model diagnostic and criticism techniques re- main underdeveloped. In this work, we pro- pose a general Stein operator for point pro- cesses based on the Papangelou conditional intensity function. We then establish a kernel goodness-of-fit test by defining a Stein dis- crepancy measure for general point processes. Notably, our test also applies to non-Poisson point processes whose intensity functions con- tain intractable normalization constants due to the presence of complex interactions among points. We apply our proposed test to sev- eral point process models, and show that it outperforms a two-sample test based on the maximum mean discrepancy. 

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2. Overdispersed Photon-Limited Sparse Signal Recovery Using Nonconvex Regularization

   https://doi.org/10.1109/CAMSAP58249.2023.10403416  

   Lu, Yu; Marcia, Roummel F. (December 2023, 2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP))

   This paper investigates the application of the ℓp quasinorm, where 0 < p < 1, in contexts characterized by photon-limited signals such as medical imaging and night vision. In these environments, low-photon count images have typically been modeled using Poisson statistics. In related algorithms, the ℓ1 norm is commonly employed as a regularization method to promotes sparsity in the reconstruction. However, recent research suggests that using the ℓp quasi-norm may yield lower error results. In this paper, we investigate the use of negative binomial statistics, which are more general models than Poisson models, in conjunction with the ℓp quasi-norm for recovering sparse signals in low-photon count imaging settings. 

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3. Universal inference

   https://doi.org/10.1073/pnas.1922664117  

   Wasserman, Larry; Ramdas, Aaditya; Balakrishnan, Sivaraman (July 2020, Proceedings of the National Academy of Sciences)

   We propose a general method for constructing confidence sets and hypothesis tests that have finite-sample guarantees without regularity conditions. We refer to such procedures as “universal.” The method is very simple and is based on a modified version of the usual likelihood-ratio statistic that we call “the split likelihood-ratio test” (split LRT) statistic. The (limiting) null distribution of the classical likelihood-ratio statistic is often intractable when used to test composite null hypotheses in irregular statistical models. Our method is especially appealing for statistical inference in these complex setups. The method we suggest works for any parametric model and also for some nonparametric models, as long as computing a maximum-likelihood estimator (MLE) is feasible under the null. Canonical examples arise in mixture modeling and shape-constrained inference, for which constructing tests and confidence sets has been notoriously difficult. We also develop various extensions of our basic methods. We show that in settings when computing the MLE is hard, for the purpose of constructing valid tests and intervals, it is sufficient to upper bound the maximum likelihood. We investigate some conditions under which our methods yield valid inferences under model misspecification. Further, the split LRT can be used with profile likelihoods to deal with nuisance parameters, and it can also be run sequentially to yield anytime-valid P values and confidence sequences. Finally, when combined with the method of sieves, it can be used to perform model selection with nested model classes. 

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4. Negative Binomial Optimization for Low-Count Overdispersed Sparse Signal Reconstruction

   https://doi.org/10.23919/EUSIPCO58844.2023.10289862  

   Lu, Yu; Marcia, Roummel F. (September 2023, 2023 European Signal Processing Conference (EUSIPCO))

   Low-photon count imaging has been typically modeled by Poisson statistics. This discrete probability distribution model assumes that the mean and variance of a signal are equal. In the presence of greater variability in a dataset than what is expected, the negative binomial distribution is a suitable overdispersed alternative to the Poisson distribution. In this work, we present a framework for reconstructing sparse signals in these low-count overdispersed settings. Specifically, we describe a gradient-based sequential quadratic optimization approach that minimizes the negative log-likelihood corresponding to the negative binomial distribution coupled with a sparsity-promoting regularization term. Numerical experiments on 1D and 2D sparse/compressible signals are presented. 

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5. Building and steering binned template fits with cabinetry

   https://doi.org/10.1051/epjconf/202125103067  

   Cranmer, Kyle; Held, Alexander (January 2021, EPJ Web of Conferences)

   Biscarat, C.; Campana, S.; Hegner, B.; Roiser, S.; Rovelli, C.I.; Stewart, G.A. (Ed.)

   The cabinetry library provides a Python-based solution for building and steering binned template fits. It tightly integrates with the pythonic High Energy Physics ecosystem, and in particular with pyhf for statistical inference. cabinetry uses a declarative approach for building statistical models, with a JSON schema describing possible configuration choices. Model building instructions can additionally be provided via custom code, which is automatically executed when applicable at key steps of the workflow. The library implements interfaces for performing maximum likelihood fitting, upper parameter limit determination, and discovery significance calculation. cabinetry also provides a range of utilities to study and disseminate fit results. These include visualizations of the fit model and data, visualizations of template histograms and fit results, ranking of nuisance parameters by their impact, a goodness-of-fit calculation, and likelihood scans. The library takes a modular approach, allowing users to include some or all of its functionality in their workflow. 

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