Use Of Bayesian Models Research Articles

Using the Bayes Probability Model to Evaluate the Risk of Accidents Caused by the Electronic Chart Display and Information System

The obligated implementation of the Electronic Chart Display and Information System (ECDIS) began ten years ago, and during this time, we could observe different types of familiarization with the system through its users. The incorrect use of the ECDIS is a problem recognized by the International Hydrographic Organization (IHO), and it is caused by disparate levels of education and the quality of courses. Another aspect of the recognized problem is the unequal length of the ECDIS specific course training period through which users acquire type-specific familiarization with the system. Switching between different types of ECDISs makes users more prone to errors until they become fully familiar with the new product system. This paper analyzes seafarers’ knowledge and ECDIS usage over a 6-year period. Based on obtained data, models that enable risk analysis based on conditional probability were created. This paper presents the use of Bayesian modeling to reduce errors in maritime accidents caused by inadequate use of the ECDIS.

A unified Bayesian framework for bias adjustment in multiple comparisons from clinical trials.

In clinical trials, multiple comparisons arising from various treatments/doses, subgroups, or endpoints are common. Typically, trial teams focus on the comparison showing the largest observed treatment effect, often involving a specific treatment pair and endpoint within a subgroup. These findings frequently lead to follow-up pivotal studies, many of which do not confirm the initial positive results. Selection bias occurs when the most promising treatment, subgroup, or endpoint is chosen for further development, potentially skewing subsequent investigations. Such bias can be defined as the deviation in the observed treatment effects from the underlying truth. In this article, we propose a general and unified Bayesian framework to address selection bias in clinical trials with multiple comparisons. Our approach does not require a priori specification of a parametric distribution for the prior, offering a more flexible and generalized solution. The proposed method facilitates a more accurate interpretation of clinical trial results by adjusting for such selection bias. Through simulation studies, we compared several methods and demonstrated their superior performance over the normal shrinkage estimator. We recommended the use of Bayesian Model Averaging estimator averaging over Gaussian Mixture Models as the prior distribution based on its performance and flexibility. We applied the method to a multicenter, randomized, double-blind, placebo-controlled study investigating the cardiovascular effects of dulaglutide.

Evaluating scientific confidence in the concordance of in vitro and in vivo protective points of departure

To fulfil the promise of reducing reliance on mammalian in vivo laboratory animal studies, new approach methods (NAMs) need to provide a confident basis for regulatory decision-making. However, previous attempts to develop in vitro NAMs-based points of departure (PODs) have yielded mixed results, with PODs from U.S. EPA's ToxCast, for instance, appearing more conservative (protective) but poorly correlated with traditional in vivo studies. Here, we aimed to address this discordance by reducing the heterogeneity of in vivo PODs, accounting for species differences, and enhancing the biological relevance of in vitro PODs. However, we only found improved in vitro-to-in vivo concordance when combining the use of Bayesian model averaging-based benchmark dose modeling for in vivo PODs, allometric scaling for interspecies adjustments, and human-relevant in vitro assays with multiple induced pluripotent stem cell-derived models. Moreover, the available sample size was only 15 chemicals, and the resulting level of concordance was only fair, with correlation coefficients <0.5 and prediction intervals spanning several orders of magnitude. Overall, while this study suggests several ways to enhance concordance and thereby increase scientific confidence in vitro NAMs-based PODs, it also highlights challenges in their predictive accuracy and precision for use in regulatory decision making.

Use of Bayesian Modeling for Risk Assessment and Robustness Evaluation

Use of Bayesian Modeling for Risk Assessment and Robustness Evaluation

Estimating the US Baseline Distribution of Health Inequalities Across Race, Ethnicity, and Geography for Equity-Informative Cost-Effectiveness Analysis

ObjectivesInformation on how life expectancy, disability-free life expectancy, and quality-adjusted life expectancy varies across equity-relevant subgroups is required to conduct distributional cost-effectiveness analysis. These summary measures are not comprehensively available in the United States, given limitations in nationally representative data across racial and ethnic groups. MethodsThrough linkage of US national survey data sets and use of Bayesian models to address missing and suppressed mortality data, we estimate health outcomes across 5 racial and ethnic subgroups (non-Hispanic American Indian or Alaska Native, non-Hispanic Asian and Pacific Islander, non-Hispanic black, non-Hispanic white, and Hispanic). Mortality, disability, and social determinant of health data were combined to estimate sex- and age-based outcomes for equity-relevant subgroups based on race and ethnicity, as well as county-level social vulnerability. ResultsLife expectancy, disability-free life expectancy, and quality-adjusted life expectancy at birth declined from 79.5, 69.4, and 64.3 years, respectively, among the 20% least socially vulnerable (best-off) counties to 76.8, 63.6, and 61.1 years, respectively, among the 20% most socially vulnerable (worst-off) counties. Considering differences across racial and ethnic subgroups, as well as geography, gaps between the best-off (Asian and Pacific Islander; 20% least socially vulnerable counties) and worst-off (American Indian/Alaska Native; 20% most socially vulnerable counties) subgroups were large (17.6 life-years, 20.9 disability-free life-years, and 18.0 quality-adjusted life-years) and increased with age. ConclusionsExisting disparities in health across geographies and racial and ethnic subgroups may lead to distributional differences in the impact of health interventions. Data from this study support routine estimation of equity effects in healthcare decision making, including distributional cost-effectiveness analysis.

Measuring cognitive effort without difficulty

An important finding in the cognitive effort literature has been that sensitivity to the costs of effort varies between individuals, suggesting that some people find effort more aversive than others. It has been suggested this may explain individual differences in other aspects of cognition; in particular that greater effort sensitivity may underlie some of the symptoms of conditions such as depression and schizophrenia. In this paper, we highlight a major problem with existing measures of cognitive effort that hampers this line of research, specifically the confounding of effort and difficulty. This means that behaviour thought to reveal effort costs could equally be explained by cognitive capacity, which influences the frequency of success and thereby the chance of obtaining reward. To address this shortcoming, we introduce a new test, the Number Switching Task (NST), specially designed such that difficulty will be unaffected by the effort manipulation and can easily be standardised across participants. In a large, online sample, we show that these criteria are met successfully and reproduce classic effort discounting results with the NST. We also demonstrate the use of Bayesian modelling with this task, producing behavioural parameters which can be associated with other measures, and report a preliminary association with the Need for Cognition scale.

Risk preferences, gender effects and Bayesian econometrics

Gender differences in decision making is a topic that has attracted much attention in the literature and the debate seems to be inconclusive. A method that is often used in the economics literature to account for gender effects is by estimating econometric structural models and testing the significance of the estimated parameters. In this paper we focus on estimations of preference models and we show how omitting to account for behavioural heterogeneity can lead to failures in identifying potential differences. Using data from risky choice experiments, we compare the traditional representative agent Maximum Likelihood Estimation approach against two more flexible inference methods that allow for heterogeneity at the individual level, the Maximum Simulated Likelihood Estimation, and the Hierarchical Bayesian modelling. We show how ignoring heterogeneity may lead to failures capturing gender differences and we suggest the use of Bayesian modelling to effectively estimate the underlying parameters.

Profile-likelihood Bayesian model averaging for two-sample summary data Mendelian randomization in the presence of horizontal pleiotropy.

Two‐sample summary data Mendelian randomization is a popular method for assessing causality in epidemiology, by using genetic variants as instrumental variables. If genes exert pleiotropic effects on the outcome not entirely through the exposure of interest, this can lead to heterogeneous and (potentially) biased estimates of causal effect. We investigate the use of Bayesian model averaging to preferentially search the space of models with the highest posterior likelihood. We develop a Metropolis‐Hasting algorithm to perform the search using the recently developed MR‐RAPS as the basis for defining a posterior distribution that efficiently accounts for pleiotropic and weak instrument bias. We demonstrate how our general modeling approach can be extended from a standard one‐component causal model to a two‐component model, which allows a large proportion of SNPs to violate the InSIDE assumption. We use Monte Carlo simulations to illustrate our methods and compare it to several related approaches. We finish by applying our approach to investigate the causal role of cholesterol on the development age‐related macular degeneration.

National Intelligence and Economic Growth: A Bayesian Update

Since Lynn and Vanhanen’s book IQ and the Wealth of Nations (2002), many publications have evidenced a relationship between national IQ and national prosperity. The strongest statistical case for this lies in Jones and Schneider’s (2006) use of Bayesian model averaging to run thousands of regressions on GDP growth (1960-1996), using different combinations of explanatory variables. This generated a weighted average over many regressions to create estimates robust to the problem of model uncertainty. We replicate and extend Jones and Schneider’s work with many new robustness tests, including new variables, different time periods, different priors and different estimates of average national intelligence. We find national IQ to be the “best predictor” of economic growth, with a higher average coefficient and average posterior inclusion probability than all other tested variables (over 67) in every test run. Our best estimates find a one point increase in IQ is associated with a 7.8% increase in GDP per capita, above Jones and Schneider’s estimate of 6.1%. We tested the causality of national IQs using three different instrumental variables: cranial capacity, ancestry-adjusted UV radiation, and 19th-century numeracy scores. We found little evidence for reverse causation, with only ancestry-adjusted UV radiation passing the Wu-Hausman test (p < .05) when the logarithm of GDP per capita in 1960 was used as the only control variable. Key Words: Human capital, National IQ, Economic growth, Bayesian model averaging, Intelligence, Smart fraction

Bayesian Multilateration

Multilateration (MLAT) is the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">de facto</i> technique to localize points of interest (POIs) in navigation and surveillance systems. Despite sensors being inherently noisy, most existing techniques i) are oblivious to noise patterns in sensor measurements; and ii) only provide point estimates of the POI. This often results in unreliable estimates with high variance, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e</i> ., that are highly sensitive to measurement noise. To overcome this caveat, we advocate the use of Bayesian modeling. Using Bayesian statistics, we provide a comprehensive guide to handle uncertainties in MLAT, including principled choices for the likelihood function and the prior distributions. Notably, the resulting model is easy to implement and can leverage off-the-shelf Markov Chain Monte Carlo (MCMC) software for inference. Besides coping with unreliable measurements, our framework can also deal with sensors whose location is not completely known, which is an asset in mobile systems. Our solution also naturally incorporates multiple measurements per reference point, a common practical situation that is usually not handled directly by other approaches. Comprehensive experiments with both synthetic and real-world data indicate that our Bayesian approach to the MLAT task provides better position estimation and uncertainty quantification when compared to the available alternatives.

Bayesian paired comparison with the bpcs package

This article introduces the bpcs R package (Bayesian Paired Comparison in Stan) and the statistical models implemented in the package. This package aims to facilitate the use of Bayesian models for paired comparison data in behavioral research. Bayesian analysis of paired comparison data allows parameter estimation even in conditions where the maximum likelihood does not exist, allows easy extension of paired comparison models, provides straightforward interpretation of the results with credible intervals, has better control of type I error, has more robust evidence towards the null hypothesis, allows propagation of uncertainties, includes prior information, and performs well when handling models with many parameters and latent variables. The bpcs package provides a consistent interface for R users and several functions to evaluate the posterior distribution of all parameters to estimate the posterior distribution of any contest between items and to obtain the posterior distribution of the ranks. Three reanalyses of recent studies that used the frequentist Bradley–Terry model are presented. These reanalyses are conducted with the Bayesian models of the bpcs package, and all the code used to fit the models, generate the figures, and the tables are available in the online appendix.

Bayesian and Maximum-Likelihood Modeling and Higher-Level Scores of Interpersonal Problems With Circumplex Structure.

Difficulties in interpersonal behavior are often measured by the circumplex-based Inventory of Interpersonal Problems. Its eight scales can be represented by a three-factor structure with two circumplex factors, Dominance and Love, and a general problem factor, Distress. Bayesian confirmatory factor analysis is well-suited to evaluate the higher-level structure of interpersonal problems because circumplex loading priors allow for data-driven adjustments and a more flexible investigation of the ideal circumplex pattern than conventional maximum likelihood confirmatory factor analysis. Using a non-clinical sample from an online questionnaire study (N = 822), we replicated the three-factor structure of the IIP by maximum likelihood and Bayesian confirmatory factor analysis and found great proximity of the Bayesian loadings to perfect circumplexity. We found additional support for the validity of the three-factor model of the IIP by including external criteria-Agreeableness, Extraversion, and Neuroticism from the Big Five and subclinical grandiose narcissism-in the analysis. We also investigated higher-level scores for Dominance, Love, and Distress using traditional regression factor scores and weighted sum scores. We found excellent reliability (with Rtt ≥ 0.90) for Dominance, Love, and Distress for the two scoring methods. We found high congruence of the higher-level scores with the underlying factors and good circumplex properties of the scoring models. The correlational pattern with the external measures was in line with theoretical expectations and similar to the results from the factor analysis. We encourage the use of Bayesian modeling when dealing with circumplex structure and recommend the use of higher-level scores for interpersonal problems as parsimonious, reliable, and valid measures.

Supporting adaptive management with ecological forecasting: chronic wasting disease in the Jackson Elk Herd

AbstractAdaptive management has emerged as the prevailing approach for combining environmental research and management to advance science and policy. Adaptive management, as originally formulated by Carl Walters in 1986, depends on the use of Bayesian models to provide a framework to accumulate knowledge. The emergence of ecological forecasting using the Bayesian framework has provided robust tools and supports a new approach to informing adaptive management, which can be particularly useful in developing policy for managing infectious disease in wildlife. We used the potential infection of elk populations with chronic wasting disease in the Jackson Valley of Wyoming and the National Elk Refuge as a model system to show how Bayesian forecasting can support adaptive management in anticipation of management challenges. The core of our approach resembles the sex‐ and age‐structured, discrete time models used to support management decisions on elk harvest throughout western North America. Our model differs by including stages for CWD‐infected and unaffected animals. We used data on population counts, sex and age classification, and CWD testing, as well as results from prior research, in a Bayesian statistical framework to predict model parameters and the number of animals in each age, sex, and disease stage over time. Initial forecasts suggested CWD may reach a mean prevalence in the population of 12%, but uncertainty in this forecast is large and we cannot rule out a mean forecasted prevalence as high as 20%. Using recruitment rates observed during the last two decades, the model predicted that a CWD prevalence of 7% in females would cause the population growth rate () to drop below 1, resulting in population declines even when female harvest was zero. The primary value of this ecological forecasting approach is to provide a framework to assimilate data with understanding of disease processes to enable continuous improvement in understanding the ecology of CWD and its management.

Genomic selection for resistance to Francisellosis in commercial Nile tilapia population: Genetic and genomic parameters, correlation with growth rate and predictive ability

Nile tilapia has become the most important species within freshwater aquaculture worldwide, the global tilapia market being expected to reach US$ 25 billion before the end of 2028. Since on an average 50% of the biomass is being lost during outbreaks of Francisellosis in tilapia farms, this study was undertaken to estimate the genetic parameters for resistance to this economically important disease of Nile tilapia, and calculate the genetic correlation with body weights at different ages. A further aim was to characterize the potential of, and to select the best genomic model for, the implementation of genomic selection for resistance to Francisellosis in the commercial Nile tilapia breeding program. The study revealed moderate to high heritabilities (0.37 ± 0.05 to 0.51 ± 0.06) for resistance to Francisellosis using both pedigree and genomic-based estimates. The genetic correlation between resistance to Francisellosis and five different growth traits at different ages ranged from −0.09 to −0.29. Compared to pedigree-based models, GBLUP was found to increase the predictive ability for resistance to Francisellosis by 57%, and the use of Bayesian models would increase this predictive ability by up to 217% in the practical breeding scenario. Thus, the study shows the potential to increase resistance to Francisellosis by genetic selection in commercial Nile tilapia breeding programs. The genetic correlation between resistance to Francisellosis and growth traits showed negative trends, although they were significantly not different from zero. A very large increase in predictive ability for resistance to Francisellosis can be achieved by using Bayesian models for genomic selection.

A Reassessment of the Chronology of the Iron Age site of Khirbet en-Nahas, Southern Jordan

ABSTRACT The chronology of Khirbet en-Nahas, a large Iron Age archaeological site located in the copper mining region of Faynan, southern Jordan, has been under fierce debate for the last 15 years. Since the site was excavated in 2002–2009, several analyses challenged the excavators’ interpretation of the stratigraphy, the results of the radiocarbon data and its dating. However, so far none of these challenges considered the final report published in 2014, which provided precious information from new areas of excavations and novel series of 14C dates. It is therefore necessary to have an independent reassessment of the archaeological and radiocarbon evidence of each excavated area based on the final report. Reasonable questions raised since the beginning about the 14C dates and the use of Bayesian modelling, the stratigraphic contexts from which they were recovered, and the interpretation of the ceramic assemblage can now be reassessed through a meticulous analysis of the site’s stratigraphy and finds. Considering this re-evaluation of the evidence, it is possible to present a reconstruction of the history of the site somewhat different from the one suggested by the excavators.

A Bayesian Approach to Incorporating Spatiotemporal Variation and Uncertainty Limits into Modeling of Predicted Environmental Concentrations from Chemical Monitoring Campaigns.

Environmental monitoring studies provide key information to assess ecosystem health. Results of chemical monitoring campaigns can be used to identify the exposure scenarios of regulatory concern. In environmental risk assessment (ERA), measured concentrations of chemicals can be used to model predicted environmental concentrations (PECs). As the PEC is, by definition, a predicted variable, it is highly dependent on the underlying modeling approach from which it is derived. We demonstrate the use of Bayesian distributional regression models to derive PECs by incorporating spatiotemporal conditional variances, and limits of quantification (LOQ) and detection (LOD) as de facto data censoring. Model accuracies increase when incorporating spatiotemporal conditional variances, and the inclusion of LOQ and LOD results in potentially more robust PEC distributions. The methodology is flexible, credibly quantifies uncertainty, and can be adjusted to different scientific and regulatory needs. Posterior sampling allows to express PECs as distributions, which makes this modeling procedure directly compatible with other Bayesian ERA approaches. We recommend the use of Bayesian modeling approaches with chemical monitoring data to make realistic and robust PEC estimations and encourage the scientific debate about the benefits and challenges of Bayesian methodologies in the context of ERA.

Estimation of Receiver Operating Characteristic Surface Using Mixtures of Finite Polya Trees (MFPT)

Generalisation of Receiver operating characteristic (ROC) curve has become increasingly useful in evaluating the performance of diagnostic tests that have more than binary outcomes. While parametric approaches have been widely used over the years, the limitations associated with parametric assumptions often make it difficult to modelling the volume under surface for data that do not meet criteria under parametric distributions. As such, estimation of ROC surface using nonparametric approaches have been proposed to obtained insights on available data. One of the common approaches to non-parametric estimation is the use of Bayesian models where assumptions about priors can be made then posterior distributions obtained which can then be used to model the data. This study uses Polya tree priors where mixtures of Polya trees approach was used to model simulated three-way ROC data. The results of VUS estimation which is considered a suitable inference in evaluating performance of a diagnostic test, indicated that the mixtures of Polya trees model fitted well the ROC surface data. Further, the model performed relatively well compared to parametric and semiparametric models under similar assumptions. &amp;nbsp;

Use of Bayesian Model Averaging to Estimate Model Uncertainty for Predicting Strain in a Four-Layered Flexible Pavement

AbstractBecause most of the numerical approaches are intensive in terms of computational effort and time, researchers have resorted to the use of surrogate models. For example, surrogate models for...

Use of Bayesian Modeling to Determine the Effects of Meteorological Conditions, Prescribed Burn Season, and Tree Characteristics on Litterfall of Pinus nigra and Pinus pinaster Stands

Research Highlights: Litterfall biomass after prescribed burning (PB) is significantly influenced by meteorological variables, stand characteristics, and the fire prescription. Some of the fire-adaptive traits of the species under study (Pinus nigra and Pinus pinaster) mitigate the effects of PB on litterfall biomass. The Bayesian approach, tested here for the first time, was shown to be useful for analyzing the complex combination of variables influencing the effect of PB on litterfall. Background and Objectives: The aims of the study focused on explaining the influence of meteorological conditions after PB on litterfall biomass, to explore the potential influence of stand characteristic and tree traits that influence fire protection, and to assess the influence of fire prescription and fire behavior. Materials and Methods: An experimental factorial design including three treatments (control, spring, and autumn burning), each with three replicates, was established at two experimental sites (N = 18; 50 × 50 m2 plots). The methodology of the International Co-operative Program on Assessment and Monitoring of Air Pollution Effects on Forests (ICP forests) was applied and a Bayesian approach was used to construct a generalized linear mixed model. Results: Litterfall was mainly affected by the meteorological variables and also by the type of stand and the treatment. The effects of minimum bark thickness and the height of the first live branch were random. The maximum scorch height was not high enough to affect the litterfall. Time during which the temperature exceeded 60 °C (cambium and bark) did not have an important effect. Conclusions: Our findings demonstrated that meteorological conditions were the most significant variables affecting litterfall biomass, with snowy and stormy days having important effects. Significant effects of stand characteristics (mixed and pure stand) and fire prescription regime (spring and autumn PB) were shown. The trees were completely protected by a combination of low-intensity PB and fire-adaptive tree traits, which prevent direct and indirect effects on litterfall. Identification of important variables can help to improve PB and reduce the vulnerability of stands managed by this method.

Markov chain Monte Carlo sampling for accurate estimation of spatial distribution of naturally occurring radionuclides radiation (232Th, 40K, and 238U) in Senegal

ABSTRACT An inaccurate quantification of the reference level of background radiation introduces an inherent statistical bias. Thus, it is necessary to develop a flexible and easy method for accurate characterization of naturally occurring radionuclides (NOR) reference background level in the mining area. In this paper, we propose the use of Bayesian modeling as an alternative statistics technique to study the spatial distribution of NOR. The Markov chain Monte Carlo (MCMC) approach is used to infer the statistical parameter of naturally occurring gamma-induced radionuclides such as 232Th, 40K and 228Ra. We used a bootstrapping method to obtain an accurate sub-sample and then exclude all potential outliers which are out of the Highest Density Interval (HDI). With the resampled sample, we build a model with a Bayesian statistics method with MCMC to draw an inference of the posterior distribution of the gamma-induced radionuclides.