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1. Generalized fiducial inference on the mean of zero-inflated Poisson and Poisson hurdle models

   https://doi.org/10.1186/s40488-021-00117-0  

   Zou, Yixuan; Hannig, Jan; Young, Derek S. (December 2021, Journal of Statistical Distributions and Applications)

   null (Ed.)

   Abstract Zero-inflated and hurdle models are widely applied to count data possessing excess zeros, where they can simultaneously model the process from how the zeros were generated and potentially help mitigate the effects of overdispersion relative to the assumed count distribution. Which model to use depends on how the zeros are generated: zero-inflated models add an additional probability mass on zero, while hurdle models are two-part models comprised of a degenerate distribution for the zeros and a zero-truncated distribution. Developing confidence intervals for such models is challenging since no closed-form function is available to calculate the mean. In this study, generalized fiducial inference is used to construct confidence intervals for the means of zero-inflated Poisson and Poisson hurdle models. The proposed methods are assessed by an intensive simulation study. An illustrative example demonstrates the inference methods. 

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2. Search for low mass dark matter in DarkSide-50: the bayesian network approach

   https://doi.org/10.1140/epjc/s10052-023-11410-4  

   Agnes, P.; Albuquerque, I. F. M.; Alexander, T.; Alton, A. K.; Ave, M.; Back, H. O.; Batignani, G.; Biery, K.; Bocci, V.; Bonivento, W. M.; et al (April 2023, The European Physical Journal C)

   Abstract We present a novel approach for the search of dark matter in the DarkSide-50 experiment, relying on Bayesian Networks. This method incorporates the detector response model into the likelihood function, explicitly maintaining the connection with the quantity of interest. No assumptions about the linearity of the problem or the shape of the probability distribution functions are required, and there is no need to morph signal and background spectra as a function of nuisance parameters. By expressing the problem in terms of Bayesian Networks, we have developed an inference algorithm based on a Markov Chain Monte Carlo to calculate the posterior probability. A clever description of the detector response model in terms of parametric matrices allows us to study the impact of systematic variations of any parameter on the final results. Our approach not only provides the desired information on the parameter of interest, but also potential constraints on the response model. Our results are consistent with recent published analyses and further refine the parameters of the detector response model. 

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3. Zero‐inflated count distributions for capture–mark–reencounter data

   https://doi.org/10.1002/ece3.9274  

   Riecke, Thomas V; Gibson, Daniel; Sedinger, James S; Schaub, Michael (September 2022, Ecology and Evolution)

   Abstract The estimation of demographic parameters is a key component of evolutionary demography and conservation biology. Capture–mark–recapture methods have served as a fundamental tool for estimating demographic parameters. The accurate estimation of demographic parameters in capture–mark–recapture studies depends on accurate modeling of the observation process. Classic capture–mark–recapture models typically model the observation process as a Bernoulli or categorical trial with detection probability conditional on a marked individual's availability for detection (e.g., alive, or alive and present in a study area). Alternatives to this approach are underused, but may have great utility in capture–recapture studies. In this paper, we explore a simple concept:in the same way that counts contain more information about abundance than simple detection/non‐detection data, the number of encounters of individuals during observation occasions contains more information about the observation process than detection/non‐detection data for individuals during the same occasion. Rather than using Bernoulli or categorical distributions to estimate detection probability, we demonstrate the application of zero‐inflated Poisson and gamma‐Poisson distributions. The use of count distributions allows for inference on availability for encounter, as well as a wide variety of parameterizations for heterogeneity in the observation process. We demonstrate that this approach can accurately recover demographic and observation parameters in the presence of individual heterogeneity in detection probability and discuss some potential future extensions of this method. 

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4. A Robust Approach for Estimating Field Reliability Using Aggregate Failure Time Data

   https://doi.org/10.1109/RAMS.2019.8769305  

   Karimi, Samira; Liao, Haitao; Pohl, Ed (January 2019, Proceedings of 2019 Reliability and Maintainability Symposium (RAMS))

   Failure time data of fielded systems are usually obtained from the actual users of the systems. Due to various operational preferences and/or technical obstacles, a large proportion of field data are collected as aggregate data instead of the exact failure times of individual units. The challenge of using such data is that the obtained information is more concise but less precise in comparison to using individual failure times. The most significant needs in modeling aggregate failure time data are the selection of an appropriate probability distribution and the development of a statistical inference procedure capable of handling data aggregation. Although some probability distributions, such as the Gamma and Inverse Gaussian distributions, have well-known closed-form expressions for the probability density function for aggregate data, the use of such distributions limits the applications in field reliability estimation. For reliability practitioners, it would be invaluable to use a robust approach to handle aggregate failure time data without being limited to a small number of probability distributions. This paper studies the application of phase-type (PH) distribution as a candidate for modeling aggregate failure time data. An expectation-maximization algorithm is developed to obtain the maximum likelihood estimates of model parameters, and the confidence interval for the reliability estimate is also obtained. The simulation and numerical studies show that the robust approach is quite powerful because of the high capability of PH distribution in mimicking a variety of probability distributions. In the area of reliability engineering, there is limited work on modeling aggregate data for field reliability estimation. The analytical and statistical inference methods described in this work provide a robust tool for analyzing aggregate failure time data for the first time. 

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5. Inferring the astrophysical population of gravitational wave sources in the presence of noise transients

   https://doi.org/10.1093/mnras/stad1823  

   Heinzel, Jack; Talbot, Colm; Ashton, Gregory; Vitale, Salvatore (June 2023, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT The global network of interferometric gravitational wave (GW) observatories (LIGO, Virgo, KAGRA) has detected and characterized nearly 100 mergers of binary compact objects. However, many more real GWs are lurking sub-threshold, which need to be sifted from terrestrial-origin noise triggers (known as glitches). Because glitches are not due to astrophysical phenomena, inference on the glitch under the assumption it has an astrophysical source (e.g. binary black hole coalescence) results in source parameters that are inconsistent with what is known about the astrophysical population. In this work, we show how one can extract unbiased population constraints from a catalogue of both real GW events and glitch contaminants by performing Bayesian inference on their source populations simultaneously. In this paper, we assume glitches come from a specific class with a well-characterized effective population (blip glitches). We also calculate posteriors on the probability of each event in the catalogue belonging to the astrophysical or glitch class, and obtain posteriors on the number of astrophysical events in the catalogue, finding it to be consistent with the actual number of events included. 

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