Tbea : tools for pre- and post-processing in Bayesian evolutionary analyses

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

Comparison of Bayesian survival analysis and Cox regression analysis in simulated and breast cancer data sets

Strange bayes indeed: uniform topological priors imply non-uniform clade priors

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 statistical methods have recently been combined with conventional methods for fisheries stock assessment (e.g. catch-age analysis) to provide a conceptually elegant approach for providing fishery management advice under uncertainty. Uncertainties in the advice provided can be conveyed using posterior probability distributions (or “posteriors”) for the potential outcomes of each policy option. Posteriors can be estimated using data (e.g. catch-age data and relative abundance indices) for the fish population of interest and prior probability distributions for population model parameters (e.g. stock-recruit function parameters) based on data from similar fish populations. Despite growing interest, Bayesian methods remain accessible to relatively few. To increase the accessibility of these methods, the conceptual basis for Bayesian statistical estimation is reviewed and set in the context of fisheries stock assessment. The use of Bayesian methods is illustrated by fitting a logistic model to relative abundance indices for Namibian hake (Merlucius capensis and M. paradoxus) and presenting a decision analysis of alternative harvest policy options. Some alternative approaches are outlined for constructing prior and posterior probability distributions and some recent applications in fisheries. Some of the problems that can be encountered while implementing Bayesian methods are also discussed.

The objective of this study is to examine the properties of Bayes estimators of the shape parameter of the Power Function Distribution (PFD-I), by using two different prior distributions for the parameter θ and different loss functions that were compared with the maximum likelihood estimators. In many practical applications, we may have two different prior information about the prior distribution for the shape parameter of the Power Function Distribution, which influences the parameter estimation. So, we used two different kinds of conjugate priors of shape parameter θ of the Power Function Distribution (PFD-I) to estimate it. The conjugate prior function of the shape parameter θ was considered as a combination of two different prior distributions such as gamma distribution with Erlang distribution and Erlang distribution with exponential distribution and Erlang distribution with non-informative distribution and exponential distribution with the non-informative distribution. We derived Bayes estimators for shape parameter θ of the Power Function Distribution (PFD-I) according to different loss functions such as the squared error loss function (SELF), the weighted error loss function (WSELF) and modified linear exponential (MLINEX) loss function (MLF), with two different double priors. In addition to the classical estimation (maximum likelihood estimation). We used simulation to get the results of this study, for different cases of the shape parameter of the Power Function Distribution used to generate data for different samples sizes.

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.

In Bayesian phylogenetics, confidence in evolutionary relationships is expressed as posterior probability--the probability that a tree or clade is true given the data, evolutionary model, and prior assumptions about model parameters. Model parameters, such as branch lengths, are never known in advance; Bayesian methods incorporate this uncertainty by integrating over a range of plausible values given an assumed prior probability distribution for each parameter. Little is known about the effects of integrating over branch length uncertainty on posterior probabilities when different priors are assumed. Here, we show that integrating over uncertainty using a wide range of typical prior assumptions strongly affects posterior probabilities, causing them to deviate from those that would be inferred if branch lengths were known in advance; only when there is no uncertainty to integrate over does the average posterior probability of a group of trees accurately predict the proportion of correct trees in the group. The pattern of branch lengths on the true tree determines whether integrating over uncertainty pushes posterior probabilities upward or downward. The magnitude of the effect depends on the specific prior distributions used and the length of the sequences analyzed. Under realistic conditions, however, even extraordinarily long sequences are not enough to prevent frequent inference of incorrect clades with strong support. We found that across a range of conditions, diffuse priors--either flat or exponential distributions with moderate to large means--provide more reliable inferences than small-mean exponential priors. An empirical Bayes approach that fixes branch lengths at their maximum likelihood estimates yields posterior probabilities that more closely match those that would be inferred if the true branch lengths were known in advance and reduces the rate of strongly supported false inferences compared with fully Bayesian integration.

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.

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.

The small genus Murbeckiella from the Brassicaceae family underwent manifold taxonomic changes reflecting morphological uncertainties, but also unusual biogeographic distribution patterns ranging from Spain and northern Africa to Caucasus. Close relationships with Oreophyton have been proposed, and both genera have been placed in the orphan tribe Oreophytoneae. We explore phylogenetic relationships to unravel and revise present-day taxonomic treatments, propose a biogeographic framework and contribute to our understanding of the local endemic Murbeckiella omissa from France. For detecting putative hybrids and reticulate evolutionary patterns on polyploid level the newly introduced Paralog PhyloGenomics (PPG) approach has been tested. Short-read whole-genome-sequencing (WGS) was used to map to a 1,000 nuclear gene target data. In addition, coding sequences from the plastome were extracted for phylogenetic reconstruction and divergence time estimates. The PPG approach was applied for phylogenetic reconstructions and evolutionary inference. The PPG concept resolved phylogenetic relationships among diploids and polyploids successfully. Murbeckiella appeared poly- and paraphyletic and the majority of species have been taxonomically integrated into a newly defined genus Oreophyton. One single species, Murbeckiella sousae, is placed in a clade of distinct tribe Arabideae and is awaiting future taxonomic revision. Biogeographic evidence suggests an origin of the tribe in Anatolia or adjacent Levant with crown group diversification of the different species starting with the early Pleistocene. The genus Murbeckiella is a suitable system to apply WGS methods to unravel reticulate evolutionary histories of young species complexes. Its small genome allows deep sequencing at high quality, which may facilitate future studies illustrating the genomic footprints and genetic backgrounds of range expansion and transcontinental migration as well as adaptation in rapidly changing alpine environments.

Latin America constitutes a large and geographically diverse region of the New World. Physiographically, it is characterized by high precipitous mountain ranges – the Sierras Madres in Central America and the Andes in South America – with narrow Pacific coastal plains. Broad, well-drained, low-lying basins are found on the eastern slopes of the mountains that run into the Atlantic and Gulf of Mexico. There are extensive high, arid plains, such as the altiplano of Mexico and South America and the punas of Peru, Bolivia, and Chile. There are also a number of tropical islands (both humid and arid, depending on prevailing winds and mountains) that extend north from South America, forming an archipelago in the Caribbean Sea that terminates in the Bahamas. A number of large islands – notably Cuba and Hispaniola – form the northwestern arm of this island chain. One distinctive feature of Latin America is that it has a very long north–south axis, with little of the east–west continental area unbroken by the north–south trending mountain ranges. This north–south spine crosscuts latitudes, making it difficult for animals and plants to migrate naturally east to west. Typically, similar climates lie along a common latitude. But in Latin America, the same latitude is dissected by altitudinal gradients that result in incredibly diverse ecosystems with diverse cultures adapting to the patchwork of environmental regimes. Some more extensive and large-scale political systems have taken advantage of the juxtaposition of different environmental and climatic regimes to integrate them into complex economies. In other situations, this extreme dissection resulted in isolated economic systems with political systems unable to expand beyond the boundaries of local economies.

The aging of large concrete structures such as Nuclear Containment Buildings (NCB) or bridges involves a continuous strain evolution in time, which may affect their durability, safety and the safety of their environment. Then, the evaluation of structural integrity requires an accurate assessment of the long-term strain level. When considering probabilistic analysis of the delayed mechanical behavior of large concrete structures, the prediction results may present large uncertainties, which do not provide clear indicators aiming at supporting decisions related to structures’ maintenance. In this context, Bayesian updating enables to reduce uncertainties, by combining a prior state of knowledge with noisy monitoring data of the structure response. It requires the definition of a prior probability distribution, which summarizes all available information before collecting monitoring data. In former work concerning Bayesian approaches applied to the analysis of delayed strains, the prior distribution is usually defined through expert judgement, which constitutes a quite subjective process which may have a significant influence on Bayesian updating results. Moreover, the previously cited work involved strong hypotheses related to observation noise, which is usually assumed to be perfectly known. The present contribution aims at evaluating the influence of prior distributions defined by expert judgement on Bayesian updating results, through an illustrative case study of a well instrumented 1:3 scale NCB. The present work proposes also a Bayesian framework suitable for cases where the observation noise of data is unknown. The influence of the amount of monitoring data on the uncertainty reduction provided by Bayesian updating is also studied. Results underline that the modeling choices of the analyst are of paramount importance in the framework of long-term strains predictions, regardless the quantity of available data. Furthermore, results also suggest that Bayesian updating is well suitable for providing significant uncertainty reduction, even in the case of structures which dispose of a limited amount of monitoring data.

Bayesian approaches have been demonstrated as effective methods for reliability analysis of complex systems with small-amount data, which integrate prior information and sample data using Bayes’ theorem. However, there is an assumption that precise prior probability distributions are available for unknown parameters, yet these prior distributions are sometimes unavailable in practical engineering. A possible way to avoiding this assumption is to generalize Bayesian reliability analysis approach by using imprecise probability theory. In this paper, we adopt a set of imprecise Dirichlet distributions as priors to quantify uncertainty of unknown parameters and extend traditional Bayesian reliability analysis approach by introducing an imprecise Dirichlet model (IDM). When the prior information is rare, the result of imprecise Bayesian analysis method is too rough to support engineering decision-making, so we proposed an optimization model to reduce the imprecision of the new method. Spindles are crucial for machine tools and reliability data related to spindles of new-developed machine tools are often rare. We can then use the imprecise Bayesian reliability analysis method to assess its reliability. In this paper, we mainly investigate the reliability assessment of a motorized spindle to illustrate the effectiveness of the proposed method.

The Generalized Pareto (GP) and Generalized extreme value (GEV) distributions play an important role in extreme value analyses, as models for threshold excesses and block maxima respectively. For each of these distributions we consider Bayesian inference using "reference" prior distributions (in the general sense of priors constructed using formal rules) for the model parameters, specifically a Jeffreys prior, the maximal data information (MDI) prior and independent uniform priors on separate model parameters. We investigate the important issue of whether these improper priors lead to proper posterior distributions. We show that, in the GP and GEV cases, the MDI prior, unless modified, never yields a proper posterior and that in the GEV case this also applies to the Jeffreys prior. We also show that a sample size of three (four) is sufficient for independent uniform priors to yield a proper posterior distribution in the GP (GEV) case.