Bayesian stock assessment: a review and example application using the logistic model

Bayesian methods have been proposed as a way of synthesizing all available evidence to inform decision making. However, few practical applications of the use of Bayesian methods for combining patient-level data (i.e., trial) with additional evidence (e.g., literature) exist in the cost-effectiveness literature. The objective of this study was to compare a Bayesian cost-effectiveness analysis using informative priors to a standard non-Bayesian nonparametric method to assess the impact of incorporating additional information into a cost-effectiveness analysis. Patient-level data from a previously published nonrandomized study were analyzed using traditional nonparametric bootstrap techniques and bivariate normal Bayesian models with vague and informative priors. Two different types of informative priors were considered to reflect different valuations of the additional evidence relative to the patient-level data (i.e., "face value" and "skeptical"). The impact of using different distributions and valuations was assessed in a sensitivity analysis. Models were compared in terms of incremental net monetary benefit (INMB) and cost-effectiveness acceptability frontiers (CEAFs). The bootstrapping and Bayesian analyses using vague priors provided similar results. The most pronounced impact of incorporating the informative priors was the increase in estimated life years in the control arm relative to what was observed in the patient-level data alone. Consequently, the incremental difference in life years originally observed in the patient-level data was reduced, and the INMB and CEAF changed accordingly. The results of this study demonstrate the potential impact and importance of incorporating additional information into an analysis of patient-level data, suggesting this could alter decisions as to whether a treatment should be adopted and whether more information should be acquired.

Thermodynamic modeling and uncertainty quantification of CO2-loaded aqueous MEA solutions

BackgroundBayesian phylogenetic inference holds promise as an alternative to maximum likelihood, particularly for large molecular-sequence data sets. We have investigated the performance of Bayesian inference with empirical and simulated protein-sequence data under conditions of relative branch-length differences and model violation.ResultsWith empirical protein-sequence data, Bayesian posterior probabilities provide more-generous estimates of subtree reliability than does the nonparametric bootstrap combined with maximum likelihood inference, reaching 100% posterior probability at bootstrap proportions around 80%. With simulated 7-taxon protein-sequence datasets, Bayesian posterior probabilities are somewhat more generous than bootstrap proportions, but do not saturate. Compared with likelihood, Bayesian phylogenetic inference can be as or more robust to relative branch-length differences for datasets of this size, particularly when among-sites rate variation is modeled using a gamma distribution. When the (known) correct model was used to infer trees, Bayesian inference recovered the (known) correct tree in 100% of instances in which one or two branches were up to 20-fold longer than the others. At ratios more extreme than 20-fold, topological accuracy of reconstruction degraded only slowly when only one branch was of relatively greater length, but more rapidly when there were two such branches. Under an incorrect model of sequence change, inaccurate trees were sometimes observed at less extreme branch-length ratios, and (particularly for trees with single long branches) such trees tended to be more inaccurate. The effect of model violation on accuracy of reconstruction for trees with two long branches was more variable, but gamma-corrected Bayesian inference nonetheless yielded more-accurate trees than did either maximum likelihood or uncorrected Bayesian inference across the range of conditions we examined. Assuming an exponential Bayesian prior on branch lengths did not improve, and under certain extreme conditions significantly diminished, performance. The two topology-comparison metrics we employed, edit distance and Robinson-Foulds symmetric distance, yielded different but highly complementary measures of performance.ConclusionsOur results demonstrate that Bayesian inference can be relatively robust against biologically reasonable levels of relative branch-length differences and model violation, and thus may provide a promising alternative to maximum likelihood for inference of phylogenetic trees from protein-sequence data.

Bayesian Analysis of the Pragmatic Airway Resuscitation Trial

Weibull distribution is one of the continous probability density function. This distribution is known as a flexible distribution. One of it’s flexibility is can be transformed into other distributions such as exponential distribution depends on parameter selected. Similar to other distribution, Weibull distribution also characterized by cumulative distribution function, mean, variance and moment generating function. One of the well-known application of this distribution is in the field of quality control utilizing reliability data and the well-known tool in quality control is control chart. Therefore, reliability data is not follow normal distribution then Shewhart control chart cannot be applied. To solve this problem, control chart can be formed with the control limit is obtained by Bayesian method. In applying Bayesian method, prior distribution of shape parameter is assumed to be uniform distribution and variables for reliability is assumed to be invers of Weibull distribution. The prior distribution is combine with likelihood function then posterior distribution is obtained which in then used as the control limits by find it’s mean.

To evaluate the usefulness of the Bayesian method for hepatic fibrosis staging with magnetic resonance elastography (MRE). The sample of this retrospective study comprised patients with chronic liver disease (n = 309), in whom histopathological fibrosis staging and MRE using either a 1.5T (n = 214) or a 3T magnetic resonance imaging (MRI) system (n = 95) had been performed. The optimal cutoff stiffness value was determined and used to calculate the discrimination ability of fibrosis staging by the cutoff method. The Bayesian method calculated post-MRE probability of each fibrosis stage, yielding MRE-based fibrosis staging without a cutoff value as well as the confidence of staging. We compared the discrimination ability in all patients and in a subgroup of patients with high (≥90%) posterior probability. The discrimination ability for hepatic fibrosis staging was comparable between the Bayesian method and the cutoff method in all patients because the accuracy of staging with the Bayesian method and the cutoff method in all patients was not different (P = 1.0000). However, in patients with high posterior probability by the Bayesian method, the accuracy of staging with the Bayesian method was significantly improved compared with that of the cutoff method in all patients; for discriminating stage ≥F2 from F0-F1 (98.9% vs. 94.8%, P = 0.0069); for ≥F3 (99.6% vs. 92.6%, P < 0.0001); and for F4 (100% vs. 94.2%, P = 0.0002). The Bayesian method has a highly accurate discrimination ability for noninvasive hepatic fibrosis staging using MRE, if the posterior probability is high. 3 Technical Efficacy: Stage 2 J. MAGN. RESON. IMAGING 2017;46:375-382.

Accounting for the failure sample size decreasing along with stages for large complex systems, a multi-stage Bayesian evaluation method of system reliability growth is proposed, which considers available information transfer across the stages. First, a reliability growth model for a stage of single subsystem is established by the non-homogeneous Poisson process. Its growth information is obtained by an improved means of equivalent transformation in this paper, and then prior expectations of parameters in this stage are gained by predicting failure rate of the post stage. Second, prior distribution of parameters is gained by the maximum entropy method and the moment equivalence method. Then, based on the prior distribution and a likelihood function of fewer failure samples, its posterior distribution and posterior Bayesian inference results can be achieved for the sake of evaluation of reliability growth of the whole system. Finally, a case study is illustrated that the information transfer across the stages of complex systems contributes to correct and economical evaluation of system reliability growth. The findings reveal that the proposed method is suitable for evaluation of reliability growth for large complex systems with small sample size, and has high value of popularization.

Over the past 20years, there has been increasing interest in the use of Bayesian statistical methods for the analysis of clinical trials used to support regulatory decisions. Bayesian methods for the analysis of clinical trials are an attractive option when good prior information is available. Yet, in many cases, prior information is scarce and only tentative or proprietary prior information exists. In these situations, it is necessary to use noninformative type or skeptical-type priors. We undertook a systematic study of Bayesian methods and applied them to 13 randomized clinical trials in metastatic breast cancer submitted to the U.S. Food and Drug Administration for registrational purposes. Across all 13 studies, there were a total of 10,521 patients using 10 experimental agents. Our results demonstrated that Bayesian analyses with noninformative priors provided similar results to more traditional analyses. We also found that early interim looks at the study results can vary widely based upon the type of prior used. Finally, we found that pre-defined threshold stopping rules need to be relatively strong to prevent trials from stopping very early. Our results suggest that, when prior information is limited and a noninformative prior is used, there is little numerical difference between Bayesian methods and more traditional analysis methods. Bayesian methods, however, may provide additional summaries of the data that are more easily interpretable than means and confidence intervals.

This study was conducted to estimate the genetic parameters influencing egg quality in Khorasan Razavi native fowl. (Co)Variance components were estimated by the Bayesian statistical method via Gibbs sampling in GIBBS3F90 software. 1000 eggs (28-29 weeks old) were collected from 775 hens of the ninth generation of Khorasan-Razavi Province native fowl breeding center. External (egg weight,specific gravity, long length, short length, shape index, shell strength, shell weight, shell thickness) and internal (yolk diameter, yolk height, yolk weight, yolk index, albumen diameter, albumen height, albumen weight, albumen index, Haugh unit) egg quality traits were measured. Six univariate animal models were used for estimation of genetic parameters and the best model for each trait was determined by deviance information criterion (DIC). Genetic and phenotypic correlations between traits were estimated using bivariate animal model. Direct heritability estimates ranged from 0.10 (egg width) to 0.39 (yolk index). For all traits except albumen diameter and albumen index, the inclusion of maternal effects in the model resulted in considerable reduction in direct heritability. Genetic correlations of egg weight with shell strength and shell thickness were negative. In conclusion, due to genetic correlations among external and internal egg quality traits, selection based on egg weight and shell thickness may improve external and internal egg quality traits. Also, including maternal effects in the form of genetic or permanent environment in the statistical model resulted in more accurate estimates for most traits.

Bayesian inference plays an essential role in the development of mathematical theory, as an important component of statistical methods. The prior distribution, the likelihood function and the posterior distribution are used in Bayesian inference. A combination of the prior distribution and the likelihood function will represent the posterior distribution, where the background information decides the prior distribution, and the background information and the observed data together form the likelihood function. This paper presents the background of Bayesian inference, the main developments, and the challenges of computing the posterior distribution. It focuses on six MCMC-based methods, such as the Metropolis-Hastings algorithm, Gibbs sampler, Reversible Jump MCMC, Hamiltonian Monte Carlo, Adaptive Metropolis, and preconditioned Crank-Nicolson. The advantages, limitations and applications of each algorithm are also briefly described.

Previous research showed that employing results from meta-analyses of relevant previous fMRI studies can improve the performance of voxelwise Bayesian second-level fMRI analysis. In this process, prior distributions for Bayesian analysis can be determined by information acquired from the meta-analyses. However, only image-based meta-analysis, which is not widely accessible to fMRI researchers due to the lack of shared statistical images, was tested in the previous study, so the applicability of the prior determination method proposed by the previous study might be limited. In the present study, whether determining prior distributions based on coordinate-based meta-analysis, which is widely accessible to researchers, can also improve the performance of Bayesian analysis, was examined. Three different types of coordinate-based meta-analyses, BrainMap and Ginger ALE, and NeuroQuery, were tested as information sources for prior determination. Five different datasets addressing three task conditions, i.e., working memory, speech, and face processing, were analyzed via Bayesian analysis with a meta-analysis informed prior distribution, Bayesian analysis with a default Cauchy prior adjusted for multiple comparisons, and frequentist analysis with familywise error correction. The findings from the aforementioned analyses suggest that use of coordinate-based meta-analysis also significantly enhanced performance of Bayesian analysis as did image-based meta-analysis.

Stock assessment methods vary among regions, reflecting local conditions, fishery management systems, available data, and historical developments. Contributions from the scientific community of the International Council for the Exploration of the Sea (ICES) had global impact on the advancement of stock assessment methods and applications. In the early to mid-1900s, single species demographic models were applied to industrial fisheries throughout the northern hemisphere. In this period, ICES played a central role by contributing foundational concepts and developing conventional methods for stock assessment. In the late 1900s, trends in assessment methods diverged among regions because of differences in fisheries, available data, exploitation histories, management systems, cultural factors, and previously applied methods in each region. Monitoring programs were established for many commercial fisheries in the North Atlantic by the mid-1900s, including collection of fishery statistics, port samples of size and age composition, and fishery-independent surveys, which supported development and application of virtual population analysis (VPA) with yield-per-recruit reference points. In contrast to early deterministic models, integrated statistical models were developed in the 1980s for fisheries in the Pacific and southern hemisphere, many of which had insufficient data to support VPA approaches. The general differences in assessment methods between the North Atlantic and other regions persisted for decades, despite the exchange of ideas and people. In the 21st century, with broader inter-regional collaborations and the evolution of management systems, integrated statistical models were more commonly adopted as best practice for stock assessment throughout the world, primarily for their statistical advantages and flexibility to represent a wide range of fisheries and the available data. The history of stock assessment offers lessons for promoting the communication of advancements and application of appropriate methods for meeting the needs of fishery management.

This paper proposed a Bayesian method-based structural equation model (SEM) of miners’ work injury for an underground coal mine in India. The environmental and behavioural variables for work injury were identified and causal relationships were developed. For Bayesian modelling, prior distributions of SEM parameters are necessary to develop the model. In this paper, two approaches were adopted to obtain prior distribution for factor loading parameters and structural parameters of SEM. In the first approach, the prior distributions were considered as a fixed distribution function with specific parameter values, whereas, in the second approach, prior distributions of the parameters were generated from experts’ opinions. The posterior distributions of these parameters were obtained by applying Bayesian rule. The Markov Chain Monte Carlo sampling in the form Gibbs sampling was applied for sampling from the posterior distribution. The results revealed that all coefficients of structural and measurement model parameters are statistically significant in experts’ opinion-based priors, whereas, two coefficients are not statistically significant when fixed prior-based distributions are applied. The error statistics reveals that Bayesian structural model provides reasonably good fit of work injury with high coefficient of determination (0.91) and less mean squared error as compared to traditional SEM.

Bayesian system reliability assessment method with maximum entropy as prior distribution is developed in the present analysis. The system reliability assessment model is established, and the method and process of system reliability assessment are put forward. The method is based on the theory of information entropy. The probability density function and distribution function of system reliability parameters are given by using maximum entropy method. Prior distribution of Bayesian analysis method is the distribution function. Likelihood function is given by a small amount of field test data. According to Bayesian methods, posterior distribution is determined by using prior distribution and likelihood function. The point estimation and interval estimation of system reliability parameters are calculated in order to evaluate the system reliability. The method solves better the problem of system reliability assessment for small sample cases, and is an optimum method for reliability assessment of large and complex systems.

Stock–recruit functions are important in fisheries stock assessment, but there is often uncertainty surrounding the appropriate stock–recruit model and its parameter values. Combining different stock–recruit data sets of related species through Bayesian hierarchical analysis can decrease these uncertainties and help to characterize appropriate stock–recruit forms and ranges of plausible parameter values. Two different stock–recruit functions (Beverton–Holt and Ricker) have been parameterized in terms of the steepness, which is a parameter that is comparable between populations. In the hierarchical analysis, the prior probability distribution of parameters for the cross-population variation in steepness is determined through a concise model structure. By calculating the Bayes' posteriors for alternative model forms, model uncertainty is accounted for. This methodology has been applied to Atlantic salmon (Salmo salar) stock–recruit data to provide predictions for the steepness of the stock–recruit function for Baltic salmon for which no stock–recruit data exist.