Bayesian Procedure Research Articles

Adolescent individual, school, and neighborhood influences on young adult hypertension risk.

Geographic and contextual socioeconomic risk factors in adolescence may be more strongly associated with young adult hypertension than individual-level risk factors. This study examines the association between individual, neighborhood, and school-level influences during adolescence on young adult blood pressure. Data were analyzed from the National Longitudinal Study of Adolescent to Adult Health (1994-1995 aged 11-18 and 2007-2008 aged 24-32). We categorized hypertension as systolic blood pressure ≥140 mm Hg and/or diastolic blood pressure ≥90 mm Hg. Secondary outcomes included continuous systolic and diastolic blood pressure. We fit a series of cross-classified multilevel models to estimate the associations between young adulthood hypertension with individual-level, school-level, and neighborhood-level factors during adolescence (i.e., fixed effects) and variance attributable to each level (i.e., random effects). Models were fit using Bayesian estimation procedures. For linear models, intra-class correlations (ICC) are reported for random effects. The final sample included 13,911 participants in 128 schools and 1,917 neighborhoods. Approximately 51% (7,111) young adults were hypertensive. Individual-level characteristics-particularly older ages, Non-Hispanic Black race, Asian race, male sex, BMI, and current smoking-were associated with increased hypertension. Non-Hispanic Black (OR = 1.21; 95% CI: 1.03-1.42) and Asian (OR = 1.28; 95% CI: 1.02-1.62) students had higher odds of hypertension compared to non-Hispanic White students. At the school level, hypertension was associated with the percentage of non-Hispanic White students (OR for 10% higher = 1.06; 95% CI: 1.01-1.09). Adjusting for individual, school, and neighborhood predictors attenuated the ICC for both the school (from 1.4 null to 0.9 fully-adjusted) and neighborhood (from 0.4 to 0.3). We find that adolescents' schools and individual-level factors influence young adult hypertension, more than neighborhoods. Unequal conditions in school environments for adolescents may increase the risk of hypertension later in life. Our findings merit further research to better understand the mechanisms through which adolescents' school environments contribute to adult hypertension and disparities in hypertension outcomes later in life.

Bayesian Kernel Two-Sample Testing

In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where applications are often restricted to univariate cases. Here, we propose a Bayesian kernel two-sample testing procedure based on modeling the difference between kernel mean embeddings in the reproducing kernel Hilbert space using the framework established by Flaxman et al. The use of kernel methods enables its application to random variables in generic domains beyond the multivariate Euclidean spaces. The proposed procedure results in a posterior inference scheme that allows an automatic selection of the kernel parameters relevant to the problem at hand. In a series of synthetic experiments and two real data experiments (i.e., testing network heterogeneity from high-dimensional data and six-membered monocyclic ring conformation comparison), we illustrate the advantages of our approach. Supplementary materials for this article are available online.

Sequential Bayesian bandwidth selection for multivariate kernel regression with applications

A new Bayesian bandwidth selection procedure is proposed for nonparametric kernel estimates based on the sequential Monte Carlo method. Compared with the existing Bayesian bandwidth selector of Zhang et al. (2009), this new method can enhance the convergence to the global optimum with a substantially faster computation speed. In particular, the method offers an improved out-of-sample performance as shown by simulations. The bandwidth selector is applied to the option state price density, production function, and nonparametric relationship between oil and stock index returns; results indicate that our proposed method outperforms other methods in terms of the mean square error and log-likelihood in all applications.

Regularized Bayesian calibration and scoring of the WD-FAB IRT model improves predictive performance over marginal maximum likelihood.

Item response theory (IRT) is the statistical paradigm underlying a dominant family of generative probabilistic models for test responses, used to quantify traits in individuals relative to target populations. The graded response model (GRM) is a particular IRT model that is used for ordered polytomous test responses. Both the development and the application of the GRM and other IRT models require statistical decisions. For formulating these models (calibration), one needs to decide on methodologies for item selection, inference, and regularization. For applying these models (test scoring), one needs to make similar decisions, often prioritizing computational tractability and/or interpretability. In many applications, such as in the Work Disability Functional Assessment Battery (WD-FAB), tractability implies approximating an individual’s score distribution using estimates of mean and variance, and obtaining that score conditional on only point estimates of the calibrated model. In this manuscript, we evaluate the calibration and scoring of models under this common use-case using Bayesian cross-validation. Applied to the WD-FAB responses collected for the National Institutes of Health, we assess the predictive power of implementations of the GRM based on their ability to yield, on validation sets of respondents, ability estimates that are most predictive of patterns of item responses. Our main finding indicates that regularized Bayesian calibration of the GRM outperforms the regularization-free empirical Bayesian procedure of marginal maximum likelihood. We also motivate the use of compactly supported priors in test scoring.

Modeling realized covariance measures with heterogeneous liquidity: A generalized matrix-variate Wishart state-space model

We propose to generalize the Wishart state-space model for realized covariance matrices of asset returns in order to capture complex measurement error structures induced by modern robust and data efficient realized covariance estimators and heterogeneous liquidity across assets. Our model assumes that the latent covariance matrix of the assets is observed through their realized covariance matrix with a Riesz measurement density, which generalizes the Wishart to monotone missing data. The Riesz alleviates the Wishart-implied attenuation of measurement errors and translates into a convenient likelihood factorization which facilitates inference using simple Bayesian MCMC procedures. The state-space approach allows for a flexible description of the covariance dynamics implied by the data and an empirical application shows that the model performs very well in- and out-of-sample.

Cosmic ray spectrum of protons plus helium nuclei between 6 and 158 TeV from HAWC data

A measurement with high statistics of the differential energy spectrum of light elements in cosmic rays, in particular, of primary H plus He nuclei, is reported. The spectrum is presented in the energy range from 6 to 158 TeV per nucleus. Data was collected with the High Altitude Water Cherenkov (HAWC) Observatory between June 2015 and June 2019. The analysis was based on a Bayesian unfolding procedure, which was applied on a subsample of vertical HAWC data that was enriched to 82% of events induced by light nuclei. To achieve the mass separation, a cut on the lateral age of air shower data was set guided by predictions of CORSIKA/QGSJET-II-04 simulations. The measured spectrum is consistent with a broken power-law spectrum and shows a kneelike feature at around E=24.0−3.1+3.6 TeV, with a spectral index γ=−2.51±0.02 before the break and with γ=−2.83±0.02 above it. The feature has a statistical significance of 4.1σ. Within systematic uncertainties, the significance of the spectral break is 0.8σ.17 MoreReceived 22 June 2021Accepted 15 February 2022DOI:https://doi.org/10.1103/PhysRevD.105.063021© 2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCosmic ray composition & spectraGravitation, Cosmology & Astrophysics

Bayesian model selection for structural equation models for myopia data

Structural equation models (SEMs) are extensively used in behavioral, social, and psychological research to model relationships between latent variables and observations. However, most models include redundant variables that are not important to relationships within the model. This study uses a Bayesian model selection procedure with mixture priors for SEMs to determine variables that have a meaningful relationship. The posterior probabilities for all possible models are calculated through the MCMC algorithm and the model with the largest probability is selected. The predictors of non-zero fixed-effect coefficients and/or non-zero random-effect variance components in the MCMC procedure are determined without the need for complex model selection criteria. The proposed methodologies are illustrated in a simulation and applied to a multidimensional longitudinal myopia data set in which the dimensionality of the parameter space is reduced and a more parsimonious model is selected.

Estimating the effectiveness of permanent price reductions for competing products using multivariate Bayesian structural time series models

The Florence branch of an Italian supermarket chain recently implemented a strategy that permanently lowered the price of numerous store brands in several product categories. To quantify the impact of such a policy change, researchers often use synthetic control methods for estimating causal effects when a subset of units receive a single persistent treatment and the rest are unaffected by the change. In our applications, however, competitor brands not assigned to treatment are likely impacted by the intervention because of substitution effects; more broadly, this type of interference occurs whenever the treatment assignment of one unit affects the outcome of another. This paper extends the synthetic control methods to accommodate partial interference, allowing interference within predefined groups but not between them. Focusing on a class of causal estimands that capture the effect both on the treated and control units, we develop a multivariate Bayesian structural time series model for generating synthetic controls that would have occurred in the absence of an intervention, enabling us to estimate our novel effects. In a simulation study we explore our Bayesian procedures’ empirical properties and show that it achieves good frequentists coverage, even when the model is misspecified. We use our new methodology to make causal statements about the impact on sales of the affected store brands and their direct competitors. Our proposed approach is implemented in the CausalMBSTS R package.

Extreme Sea Level Estimation Combining Systematic Observed Skew Surges and Historical Record Sea Levels

AbstractThe estimation of sea levels corresponding to high return periods is crucial for coastal planning and for the design of coastal defenses. This paper deals with the use of historical observations, that is, events that occurred before the beginning of the systematic tide gauge recordings, to improve the estimation of design sea levels. Most of the recent publications dealing with statistical analyses applied to sea levels suggest that astronomical high tide levels and skew surges should be analyzed and modeled separately. Historical samples generally consist of observed record sea levels. Some extreme historical skew surges can easily remain unnoticed if they occur at low or moderate astronomical high tides and do not generate extreme sea levels. The exhaustiveness of historical skew surge series, which is an essential criterion for an unbiased statistical inference, can therefore not be guaranteed. This study proposes a model combining, in a single Bayesian inference procedure, information of two different natures for the calibration of the statistical distribution of skew surges: measured skew surges for the systematic period and extreme sea levels for the historical period. A data‐based comparison of the proposed model with previously published approaches is presented based on a large number of Monte Carlo simulations. The proposed model is applied to four locations on the French Atlantic and Channel coasts. Results indicate that the proposed model is more reliable and accurate than previously proposed methods that aim at the integration of historical records in coastal sea level or surge statistical analyses.

Bayesian-based decipherment of in-depth information in bacterial chemical sensing beyond pleasant/unpleasant responses

Chemical sensing is vital to the survival of all organisms. Bacterial chemotaxis is conducted by multiple receptors that sense chemicals to regulate a single signalling system controlling the transition between the direction (clockwise vs. counterclockwise) of flagellar rotation. Such an integrated system seems better suited to judge chemicals as either favourable or unfavourable, but not for identification purposes though differences in their affinities to the receptors may cause difference in response strength. Here, an experimental setup was developed to monitor behaviours of multiple cells stimulated simultaneously as well as a statistical framework based on Bayesian inferences. Although responses of individual cells varied substantially, ensemble averaging of the time courses seemed characteristic to attractant species, indicating we can extract information of input chemical species from responses of the bacterium. Furthermore, two similar, but distinct, beverages elicited attractant responses of cells with profiles distinguishable with the Bayesian procedure. These results provide a basis for novel bio-inspired sensors that could be used with other cell types to sense wider ranges of chemicals.

A hierarchical model for analyzing multisite individual-level disease surveillance data from multiple systems.

Passive surveillance systems are widely used to monitor diseases occurrence over wide spatial areas due to their cost-effectiveness and integration into broadly distributed healthcare systems. However, such systems are generally associated with imperfect ascertainment of disease cases and with heterogeneous capture probabilities arising from factors such as differential access to care. Augmenting passive surveillance systems with other surveillance efforts provides a way to estimate the true number of incident cases. We develop a hierarchical modeling framework for analyzing data from multiple surveillance systems that allows for individual-level covariate-dependent heterogeneous capture probabilities, and borrows information across surveillance sites to improve estimation of the true number of incident cases. Inference is carried out via a two-stage Bayesian procedure. Simulation studies illustrated superior performance of the proposed approach with respect to bias, root mean square error, and coverage compared to a model that does not borrow information across sites. We applied the proposed model to data from three surveillance systems reporting pulmonary tuberculosis (PTB) cases in a major center of ongoing transmission in China. The analysis yielded bias-corrected estimates of PTB cases from the passive system and led to the identification of risk factors associated with PTB rates, as well as factors influencing the operating characteristics of the implemented surveillance systems.

Bayesian Inference for Estimating Subset Proportions using Differentially Private Counts

Abstract Recently, several organizations have considered using differentially private algorithms for disclosure limitation when releasing count data. The typical approach is to add random noise to the counts sampled from, for example, a Laplace distribution or symmetric geometric distribution. One advantage of this approach, at least for some differentially private algorithms, is that analysts know the noise distribution and hence have the opportunity to account for it when making inferences about the true counts. In this article, we present Bayesian inference procedures to estimate the posterior distribution of a subset proportion, that is, a ratio of two counts, given the released values. We illustrate the methods under several scenarios, including when the released counts come from surveys or censuses. Using simulations, we show that the Bayesian procedures can result in accurate inferences with close to nominal coverage rates.

Estimation of Heritability of Karan Fries Cattle using Bayesian Procedure

  The Bayesian model was applied for analyzing the first lactation in Karan Fries cattle. First lactation data of production (305-day or less milk yield and daily milk yield) were collected from the history-cum pedigree sheet and daily milk yield registers of the division of Dairy Cattle Breeding (DCB), National Dairy Research Institute (NDRI), Karnal. In the Bayesian paradigm, MCMC methods are applied to solve complex mathematical problems to estimate a large number of unknown parameters. Assuming linear mixed model and using the different prior set up, diagnostic of MCMC (Markov Chain Monte Carlo) was carried out graphically as well as by Heidelberg stationarity test. Variance estimates of the random effects (VA) and residual variance estimation (VR) and Variance estimate location effects i.e. fixed effects were calculated along with effective sample size. Finally, heritability (h2) estimates for First lactation 305 days or less milk yield (FL305DMY) was estimated along with its credible interval.

Bayesian set of best dynamic treatment regimes: Construction and sample size calculation for SMARTswithbinary outcomes.

Sequential, multiple assignment, randomized trials (SMARTs) compare sequences of treatment decision rules called dynamic treatment regimes (DTRs). In particular, the Adaptive Treatment for Alcohol and Cocaine Dependence (ENGAGE) SMART aimed to determine the best DTRs for patients with a substance use disorder. While many authors have focused on a single pairwise comparison, addressing the main goal involves comparisons of >2 DTRs. For complex comparisons, there is a paucity of methods for binary outcomes. We fill this gap by extending the multiple comparisons with the best (MCB) methodology to the Bayesian binary outcome setting. The set of best is constructed based on simultaneous credible intervals. A substantial challenge for power analysis is the correlation between outcome estimators for distinct DTRs embedded in SMARTs due to overlapping subjects. We address this using Robins' G-computation formula to take a weighted average of parameter draws obtained via simulation from the parameter posteriors. We use non-informative priors and work with the exact distribution of parameters avoiding unnecessary normality assumptions and specification of the correlation matrix of DTR outcome summary statistics. We conduct simulation studies for both the construction of a set of optimal DTRs using the Bayesian MCB procedure and the sample size calculation for two common SMART designs. We illustrate our method on the ENGAGE SMART. The R package SMARTbayesR for power calculations is freely available on the Comprehensive R Archive Network (CRAN) repository. An RShiny app is available at https://wilart.shinyapps.io/shinysmartbayesr/.

Frequentist test in Bayesian two-stage designs applied in experimental trials

Prediction provides discipline and pragmatic importance to empirical research. The design with the predictive probability approach provides an excellent alternative for conducting multi-stage phase II trials; it is efficient and flexible and possesses desirable statistical properties. . In this paper we consider the Bayesian predictive procedures within the experimental design, for this, we define indices of satisfaction related to a test as a decreasing function of the p-value and satisfaction is higher than the null hypothesis is rejected wider. This design possesses good frequentist properties and allows early termination of the trial. We treated our applications by simulation and real data in experimental planning and sequential designs with binary outcomes.

Estimation of stress–strength reliability based on censored data and its evaluation for coating processes

ABSTRACT In this paper, the classical and Bayesian estimation procedures for stress–strength reliability parameter (SSRP) have been considered based on two independent adaptive Type II progressive hybrid censored samples from inverted exponentiated Rayleigh distributions with different shape parameters. The maximum likelihood estimate of SSRP and its asymptotic confidence interval are attained. The Bayes estimate of SSRP is obtained under two loss functions using the Lindley’s approximation and Metropolis–Hastings algorithm. The highest posterior density credible interval is successively constructed. The behavior of suggested estimators is assessed using a simulation study. Finally, the droplet splashing data under two surface wettabilities are considered to illustrate the application of the stress–strength reliability model to the engineering data.

The chronology of archaeological assemblages based on an automatic Bayesian procedure: Eastern Iberia as study case

The purpose of this work is to show an automatic Bayesian procedure to obtain accurate chronological information of archaeological assemblages characterized by palimpsest or without radiocarbon dates and whose temporal information comes only from bifacial flint arrowheads.In this paper, a classification method based on the Dirichlet-multinomial inferential process and its posterior predictive probability distribution is discussed. Its purpose is to predict the chronological period of undated archaeological assemblages (levels or sites) by means of a Bayesian predictive process based on the posterior distribution of each bifacial flint arrowhead types in the Eastern Iberia during the 4th and 3rd millennium cal. BC. The results obtained suggest that this approach is very useful to achieve an accurate chronology when other archaeological information is not available, or it is not conclusive.

Bayes Posterior Convergence for Loss Functions via Almost Additive Thermodynamic Formalism.

Statistical inference can be seen as information processing involving input information and output information that updates belief about some unknown parameters. We consider the Bayesian framework for making inferences about dynamical systems from ergodic observations, where the Bayesian procedure is based on the Gibbs posterior inference, a decision process generalization of standard Bayesian inference (see [7, 37]) where the likelihood is replaced by the exponential of a loss function. In the case of direct observation and almost-additive loss functions, we prove an exponential convergence of the a posteriori measures to a limit measure. Our estimates on the Bayes posterior convergence for direct observation are related and extend those in [47] to a context where loss functions are almost-additive. Our approach makes use of non-additive thermodynamic formalism and large deviation properties [39, 40, 57] instead of joinings.

Gibbs posterior convergence and the thermodynamic formalism

In this paper we consider the posterior consistency of Bayesian inference procedures when the family of models consists of appropriate stochastic processes. Specifically, we suppose that one observes an unknown ergodic process and one has access to a family of models consisting of dependent processes. In this context, we consider Gibbs posterior inference, which is a loss-based generalization of standard Bayesian inference. Our main results characterize the asymptotic behavior of the Gibbs posterior distributions on the space of models. Furthermore, we show that in the case of properly specified models our convergence results may be used to establish posterior consistency. Our model processes are defined via the thermodynamic formalism for dynamical systems, and they allow for a large degree of dependence, including both Markov chains of unbounded orders and processes that are not Markov of any order. This work establishes close connections between Gibbs posterior inference and the thermodynamic formalism for dynamical systems, which we hope will lead to new questions and results in both nonparametric Bayesian analysis and the thermodynamic formalism.

Handling EEG artifacts and searching individually optimal experimental parameter in real time: a system development and demonstration

Objective. Neuroadaptive paradigms that systematically assess event-related potential (ERP) features across many different experimental parameters have the potential to improve the generalizability of ERP findings and may help to accelerate ERP-based biomarker discovery by identifying the exact experimental conditions for which ERPs differ most for a certain clinical population. Obtaining robust and reliable ERPs online is a prerequisite for ERP-based neuroadaptive research. One of the key steps involved is to correctly isolate electroencephalography artifacts in real time because they contribute a large amount of variance that, if not removed, will greatly distort the ERP obtained. Another key factor of concern is the computational cost of the online artifact handling method. This work aims to develop and validate a cost-efficient system to support ERP-based neuroadaptive research. Approach. We developed a simple online artifact handling method, single trial PCA-based artifact removal (SPA), based on variance distribution dichotomies to distinguish between artifacts and neural activity. We then applied this method in an ERP-based neuroadaptive paradigm in which Bayesian optimization was used to search individually optimal inter-stimulus-interval (ISI) that generates ERP with the highest signal-to-noise ratio. Main results. SPA was compared to other offline and online algorithms. The results showed that SPA exhibited good performance in both computational efficiency and preservation of ERP pattern. Based on SPA, the Bayesian optimization procedure was able to quickly find individually optimal ISI. Significance. The current work presents a simple yet highly cost-efficient method that has been validated in its ability to extract ERP, preserve ERP effects, and better support ERP-based neuroadaptive paradigm.