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AbstractInductive learning is impossible without overhypotheses, or constraints on the hypotheses considered by the learner. Some of these overhypotheses must be innate, but we suggest that hierarchical Bayesian models can help to explain how the rest are acquired. To illustrate this claim, we develop models that acquire two kinds of overhypotheses – overhypotheses about feature variability (e.g. the shape bias in word learning) and overhypotheses about the grouping of categories into ontological kinds like objects and substances.

We present a new Bayesian hierarchical model (BHM) named Steve for performing Type Ia supernova (SN Ia) cosmology fits. This advances previous works by including an improved treatment of Malmquist bias, accounting for additional sources of systematic uncertainty, and increasing numerical efficiency. Given light-curve fit parameters, redshifts, and host-galaxy masses, we fit Steve simultaneously for parameters describing cosmology, SN Ia populations, and systematic uncertainties. Selection effects are characterized using Monte Carlo simulations. We demonstrate its implementation by fitting realizations of SN Ia data sets where the SN Ia model closely follows that used in Steve. Next, we validate on more realistic SNANA simulations of SN Ia samples from the Dark Energy Survey and low-redshift surveys (DES Collaboration et al. 2018). These simulated data sets contain more than 60,000 SNe Ia, which we use to evaluate biases in the recovery of cosmological parameters, specifically the equation of state of dark energy, w. This is the most rigorous test of a BHM method applied to SN Ia cosmology fitting and reveals small w biases that depend on the simulated SN Ia properties, in particular the intrinsic SN Ia scatter model. This w bias is less than 0.03 on average, less than half the statistical uncertainty on w. These simulation test results are a concern for BHM cosmology fitting applications on large upcoming surveys; therefore, future development will focus on minimizing the sensitivity of Steve to the SN Ia intrinsic scatter model. ; The DES data management system is supported by the National Science Foundation under grant Nos. AST-1138766 and AST-1536171. The DES participants from Spanish institutions are partially supported by MINECO under grants AYA2015-71825, ESP2015-66861, FPA2015-68048, SEV2016-0588, SEV-2016-0597, and MDM-2015-0509, some of which include ERDF funds from the European Union. IFAE is partially funded by the CERCA program of the Generalitat de Catalunya. Research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Program (FP7/2007- 2013), including ERC grant agreements 240672, 291329, and 306478. We acknowledge support from the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO) through project No. CE110001020 and the Brazilian Instituto Nacional de Ciência e Tecnologia (INCT) e-Universe (CNPq grant 465376/2014-2). This manuscript has been authored by the Fermi Research Alliance, LLC, under contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes

This article explores the statistical methodologies used in demonstration and effectiveness studies when the treatments are applied across multiple settings. The importance of evaluating and how to evaluate these types of studies are discussed. As an alternative to standard methodology, the authors of this article offer an empirical binomial hierarchical Bayesian model as a way to effectively evaluate multisite studies. An application of using the Bayesian model in a real-world multisite study is given.

Assessing within‐batch and between‐batch variability is of major interest for risk assessors and risk managers in the context of microbiological contamination of food. For example, the ratio between the within‐batch variability and the between‐batch variability has a large impact on the results of a sampling plan. Here, we designed hierarchical Bayesian models to represent such variability. Compatible priors were built mathematically to obtain sound model comparisons. A numeric criterion is proposed to assess the contamination structure comparing the ability of the models to replicate grouped data at the batch level using a posterior predictive loss approach. Models were applied to two case studies: contamination by Listeria monocytogenes of pork breast used to produce diced bacon and contamination by the same microorganism on cold smoked salmon at the end of the process. In the first case study, a contamination structure clearly exists and is located at the batch level, that is, between batches variability is relatively strong, whereas in the second a structure also exists but is less marked.

The present paper's focus is the modeling of interindividual and intraindividual variability in longitudinal data. We propose a hierarchical Bayesian model with correlated residuals, employing an autoregressive parameter AR(1) for focusing on intraindividual variability. The hierarchical model possesses four individual random effects: intercept, slope, variability, and autocorrelation. The performance of the proposed Bayesian estimation is investigated in simulated longitudinal data with three different sample sizes (N = 100, 200, 500) and three different numbers of measurement points (T = 10, 20, 40). The initial simulation values are selected according to the results of the first 20 measurement occasions from a longitudinal study on working memory capacity in 9th graders. Within this simulation study, we investigate the root mean square error (RMSE), bias, relative percentage bias, and the 90% coverage probability of parameter estimates. Results indicate that more accurate estimates are associated with a larger sample size. One exception to this tendency is the autocorrelation parameter, which shows more sensitivity to an increasing number of time points.

Photometric galaxy surveys constitute a powerful cosmological probe but rely on the accurate characterization of their redshift distributions using only broad-band imaging, and can be very sensitive to incomplete or biased priors used for redshift calibration. A hierarchical Bayesian model has recently been developed to estimate those from the robust combination of prior information, photometry of single galaxies, and the information contained in the galaxy clustering against a well-characterized tracer population. In this work, we extend the method so that it can be applied to real data, developing some necessary new extensions to it, especially in the treatment of galaxy clustering information, and we test it on realistic simulations. After marginalizing over the mapping between the clustering estimator and the actual density distribution of the sample galaxies, and using prior information from a small patch of the survey, we find the incorporation of clustering information with photo-z's tightens the redshift posteriors and overcomes biases in the prior that mimic those happening in spectroscopic samples. The method presented here uses all the information at hand to reduce prior biases and incompleteness. Even in cases where we artificially bias the spectroscopic sample to induce a shift in mean redshift of 0.05 the final biases in the posterior are 0.003. This robustness to flaws in the redshift prior or training samples would constitute a milestone for the control of redshift systematic uncertainties in future weak lensing analyses. ; AA and EG were supported by MINECO grants CSD2007-00060 and AYA2015-71825, LACEGAL Marie Sklodowska-Curie grant 734374 with ERDF funds from the European Union Horizon 2020 Programme. CS and GMB were supported by grants AST-1615555 from the US National Science Foundation, and DE-SC0007901 from the US Department of Energy. IEEC is partially funded by the CERCA program of the Generalitat de Catalunya. The MICE simulations have been developed at the MareNostrum supercomputer (BSC-CNS) thanks to grants AECT-2006-2-0011 through AECT-2015-1-0013.

Abstract. Agricultural drought, which occurs due to a significant reduction in the moisture required for vegetation growth, is the most complex amongst all drought categories. The onset of agriculture drought is slow and can occur over vast areas with varying spatial effects, differing in areas with a particular vegetation land cover or specific agro-ecological sub-regions. These spatial variations imply that monitoring and forecasting agricultural drought require complex models that consider the spatial variations in a given region of interest. Hierarchical Bayesian models are suited for modelling such complex systems. Using partially pooled data with sub-groups that characterise spatial differences, these models can capture the sub-group variation while allowing flexibility and information sharing between these sub-groups. This paper's objective is to improve the accuracy and precision of agricultural drought forecasting in spatially diverse regions with a hierarchical Bayesian model. Results showed that the hierarchical Bayesian model was better at capturing the variability for the different agro-ecological zones and vegetation land covers compared to a regular Bayesian auto-regression distributed lags model. The forecasted vegetation condition and associated drought probabilities were more accurate and precise with the hierarchical Bayesian model at 4- to 10-week lead times. Forecasts from the hierarchical model exhibited higher hit rates with a low probability of false alarms for drought events in semi-arid and arid zones. The hierarchical Bayesian model also showed good transferable forecast skills over counties not included in the training data.

AbstractPer‐ and polyfluoroalkyl substances (PFAS) in U.S. drinking water are currently a significant topic of public health concern. Data collection efforts have been undertaken to better understand PFAS occurrence, though limited data observed above reporting limits leaves considerable uncertainty. This work presents a hierarchical Bayesian model developed to estimate national PFAS occurrence in drinking water with a simple model structure and assumptions. Here the model is limited to the occurrence of perfluorooctanoic acid (PFOA), perfluorooctanesulfonic acid (PFOS), perfluorohexanesulfonic acid (PFHxS), and perfluoroheptanoic acid (PFHpA). This model estimates national PFAS exposure while capturing uncertainty, provides information on system‐level PFAS co‐occurrence, and creates an expandable foundation for generating future national estimates of PFAS occurrence. National estimates based on currently available data and model assumptions indicated population‐weighted mean exposure to the sum of mean PFOS, PFOA, PFHpA, and PFHxS around 4.7–5.2 ppt while all four chemicals generally had moderate‐to‐strong correlations among system‐level means.