Use Of Bayesian Analysis Research Articles

A Bayesian approach to analyzing long-term agricultural experiments

Effective and flexible statistical analyses are key to getting the most out of long-term experiments (LTEs). Here, we aim to introduce Bayesian analysis to the wider LTE community and show how the modelling process differs from traditional statistical analyses. Bayesian methods have become increasingly popular due to more flexibility in model development with better access to statistical software and sampling algorithms. Using Bayes' Theorem, model coefficients are estimated by incorporating any prior knowledge we may have on model terms. Including prior knowledge in this way requires a different estimating procedure for a fitted model. Bayesian model coefficients are usually sampled from thousands of samples from one or more runs of a Markov Chain. We present the use of Bayesian analyses through three examples. Example 1 illustrates a single regression with and without factors using the Broadbalk Long-Term Experiment, showing how the estimated model changes with more uncertainty in our prior knowledge of model coefficients. Example 2 demonstrates the use of multiple regression, predicting grain yield from factor variables and seasonal weather variables. Example 3 shows an estimation of soil carbon changes under crop rotation and fertilization treatments with a hierarchical time series model using a Swedish soil fertility experiment.

Expressing uncertainty in information systems analytics research: A demonstration of Bayesian analysis applied to binary classification problems

The measures typically used to assess binary classification problems fail to incorporate the uncertainty inherent to many contexts into the results. We propose using a Bayesian model to express the uncertainty in binary classification problems. This study identified 10 previous studies that provided sufficient data to demonstrate the use of Bayesian analysis in Information Systems (IS) contexts with varying levels of uncertainty. The analysis and user study show that the addition of Bayesian analysis is most useful in high uncertainty contexts with a wide interval for positive predictive value. Such an interval will lead to high uncertainty, even with very certain sensitivity and specificity. The usefulness of Bayesian analysis in conditions of medium uncertainty depends on the context. In conditions of low uncertainty, Bayesian analysis does not add much value. The user study showed that presenting models with uncertainty changed researcher perception of which model performed the best with 18 of 21 researchers changing their opinion. We recommend that authors estimate the uncertainty in their models and provide confusion matrices and prevalence estimates in their results to enable Bayesian analysis as research in a domain matures.

How Can We Quantify and Compare Harm in Surgical Trials?

To describe methods that can be used to quantify and compare harm caused by surgical interventions in ophthalmology trials. Perspective study. A published landmark glaucoma trial was used as an exemplar. A consensus-derived classification system of severity of complications was applied to published data of the Tube Versus Trabeculectomy glaucoma trial. The severity grade of each complication was multiplied to the number of patients who incurred that complication to estimate a total harm score for each intervention. Graphical tools were also used to display the differences in complications between trial arms. A review of literature on best practice for reporting harm data was also conducted. Analyzing treatment harm is challenging with the relatively small number of events and sample sizes used in randomized controlled trials. However, quantification and graphical representation of harm after surgery is possible. Reframing the research question to one for detecting signals of adverse reactions and use of Bayesian analyses can be useful. Analysis of harm data in clinical trials needs further attention. A severity classification system and a total harm score can be used to quantify harm after glaucoma surgery. Graphical tools can also help interpret complication data.

A Bayesian perspective on Biogen's aducanumab trial.

This perspective is a companion to a recent editorial on the use of Bayesian analysis in clinical research. We aim to introduce and highlight the relevance and advantages that Bayesian inference offers to clinical trials using the data on the amyloid antibody aducanumab presented at a Food and Drug Administration hearing in November 2020 as an applied example. We apply Bayesian analysis of model plausibility and effect sizes based on simulated data of the two phase 3 trials of aducanumab in prodromal and mild dementia stages of Alzheimer's disease (AD). Bayesian analysis can quantify evidence in favor of, or against, the presence of an effect (i.e., provide evidence of absence), as well as assess the strength of the effect. This is in contrast to the binary conclusions provided by frequentist tests.

Improving the analysis of adverse event data in randomized controlled trials

Analyzing treatment harm is vital but problematic with the relatively small sample sizes afforded in randomized controlled trials (RCTs). Good analysis practice for efficacy outcomes are well established but there has been minimal progress for the analysis of adverse events (AEs). In this commentary we examine four key issues for AE analysis. Namely, why harm data in RCTs is undervalued, why AE analysis is difficult, what aspects of current analysis practice are unsatisfactory, and the challenges for selection and interpretation of AEs results in publications. We discuss how the value of harm data from RCTs could be better realized by reframing the research question to one for detecting signals of adverse reactions. We align established good statistical practice to current unsatisfactory practice. We encourage use of Bayesian analyses to enable cumulative assessment of harm across trial research phases and discourage selecting AEs to report based on arbitrary rules. We propose comprehendible summaries to be based on core outcome sets, serious and pre-specified events, and events leading to discontinuation. Analysis of AEs in contemporary clinical trials needs attention to progress. In the following we have outlined immediate, mid and longer-term strategies for trialists to adopt to support a change in practice

Bayesian mark–recapture–resight–recovery models: increasing user flexibility in the BUGS language

AbstractEstimating demographic parameters of interest is a critical component of applied conservation biology and evolutionary ecology, where demographic models and demographic data have become increasingly complex over the last several decades. These advances have been spurred by the development and use of information theoretic approaches, programs such as MARK and SURGE, and Bayesian inference. The use of Bayesian analyses has also become increasingly popular, where WinBUGS, JAGS, Stan, and NIMBLE provide increased user flexibility. Despite recent advances in Bayesian demographic modeling, some capture–recapture models that have been implemented in Program MARK remain unavailable to quantitative ecologists that wish to use Bayesian modeling approaches. We provide novel parameterizations of capture–mark–recapture–resight–recovery models implemented in Program MARK that have not yet been implemented in the BUGS language. Simulations show that the models described herein provide accurate parameter estimates. Our parameterizations of these models can easily be extended to estimate additional parameters such as entry probability, additional live states, or cause‐specific mortality rates. Additionally, implementing these models in a Bayesian framework allows users to readily estimate parameters as mixtures, incorporate random individual or temporal variation, and use informative priors to assist with parameter estimation.

Bayesian inference of thermodynamic models from vapor flow experiments

The present work concerns the inference of the coefficients of fluid-dependent thermodynamic models, applicable to complex molecular compounds with non-ideal effects. The main objective is to numerically assess the potential of using experimental measurements of some expansion flows to infer the model parameters. The Bayesian formulation incorporates uncertainties in the flow conditions and measurement errors and compares the measurements with the predictions of Computational Fluid Dynamics (CFD) simulations which depend on the parameter values. The resulting parameters posterior distribution is sampled using a Markov-Chain Monte-Carlo method. Polynomial-Chaos (PC) surrogates substitute the CFD predictions in the definition of the Bayesian posterior, in order to alleviate the computational burden of solving multiple CFD problems. We rely on synthetic data i.e., generated numerically, to assess the potential of expansion flow experiments. Using synthetic data prevents experimental bias, enables the control of model errors (thermodynamic and flow models) and permits the measurement of quantities in conditions that would be hardly achievable in practice. We test three expansion flows with increasing non-ideal effects. Our analyses reveal that the considered experiments have limited potential for the inference of the thermodynamic coefficients. Measuring the temperature, in addition to pressure, improves the posterior knowledge of the specific heat ratio, but other parameters remain highly uncertain. Also, the selection of an expansion condition yielding higher non-ideal effects somehow improves the inference, but the trend is limited, and experimenting with these conditions may be challenging. Our work also supports the use of Bayesian analysis with synthetic data to investigate, analyze, and design new experiments in the future.

Bayesian Analysis for Assessing Risks of Rotating Equipment and Its Financial Loss

The petrochemical industry is equipped with major and rotating equipment, such as storage tanks and pumps, to produce the required outputs. The equipment could pose a high level of risks should the organization failed to provide control and mitigation measures. Risk analysis is a conventional and practical technique in identifying hazards and assessing risks associated with equipment. The risk analysis can be integrated with the Bayes’s theorem to assess risks of major and rotating equipment. Therefore, this paper presents the use of Bayesian analysis for assessing risks of rotating equipment and its financial loss, specifically in the petrochemical industry. The study begins with developing a cause-and-effect relationship using a Bayesian network. The probability of failure of equipment and its financial loss can be analyzed based on the Bayesian network. The cause-and-effect relationship could also reveal human factors contributing to the probability of failure of equipment. This paper focuses on an accident involving pumps during maintenance activity in the petrochemical plant. The human factors issues contributing to the accident and the financial loss are inadequate procedures and poor work processes.

Nonperturbative potential for the study of quarkonia in QGP

A thermal potential can be defined to facilitate understanding the behavior of quarkonia in quark-gluon plasma. A nonperturbative evaluation of this potential from lattice QCD is difficult, as it involves real-time corelation function, and has often involved the use of Bayesian analysis, with its associated systematics. In this work we show that using the properties of the static quarkonia thermal correlation functions, one can directly extract a thermal potential for quarkonia from Euclidean Wilson loop data. This leads to a controlled extraction, and allows us to judge the suitability of various model potentials. We also discuss the phenomenology of quarkonia in the gluonic plasma.

Bayesian multiple membership multiple classification logistic regression model on student performance with random effects in university instructors and majors.

Educational success measured by retention leading to graduation is an essential component of any academic institution. As such, identifying the factors that contribute significantly to success and addressing those factors that result in poor performances are important exercises. By success, we mean obtaining a semester GPA of 3.0 or better and a GPA of 2.0 or better. We identified these factors and related challenges through analytical models based on student performance. A large dataset obtained from a large state university over three consecutive semesters was utilized. At each semester, GPAs were nested within students and students were taking classes from multiple instructors and pursuing a specific major. Thus, we used multiple membership multiple classification (MMMC) Bayesian logistic regression models with random effects for instructors and majors to model success. The complexity of the analysis due to multiple membership modeling and a large number of random effects necessitated the use of Bayesian analysis. These Bayesian models identified factors affecting academic performance of college students while accounting for university instructors and majors as random effects. In particular, the models adjust for residency status, academic level, number of classes, student athletes, and disability residence services. Instructors and majors accounted for a significant proportion of students’ academic success, and served as key indicators of retention and graduation rates. They are embedded within the processes of university recruitment and competition for the best students.

The Interpretation of Mesolithic Structures in Britain: New Evidence from Criet Dubh, Isle of Mull, & Alternative Approaches to Chronological Analysis for Inferring Occupation Tempos & Settlement Patterns

The number of Mesolithic structures known in Britain has significantly increased since 2000, providing new opportunities for economic and social interpretations of this period. We describe a further structure, represented by features from the Mesolithic site of Criet Dubh, Isle of Mull. We compare the inferred Criet Dubh structure to other Mesolithic structures from Britain, notably those described as ‘pit-houses’. We then consider the implications of the radiocarbon dates from such structures for the tempo of occupation and past settlement patterns. While the use of Bayesian analysis of radiocarbon dates has encouraged interpretations of prolonged occupation and sedentism, we propose alternative interpretations with patterns of intermittent occupation for Criet Dubh and the pit-houses, involving their re-use after extended periods of abandonment within a sparsely populated landscape. The ability to debate such interpretations reflects the transformation in Mesolithic research made possible by the discovery of such structures, the use of multiple radiocarbon determinations, the application of Bayesian analysis, and the exploration of associations between cultural and environmental change. These developments have made the Mesolithic a particularly innovative period of study.

A Bayesian Framework for Exoplanet Direct Detection and Non-detection

Abstract Rigorously quantifying the information in high-contrast imaging data is important for informing follow-up strategies to confirm the substellar nature of a point source, constraining theoretical models of planet–disk interactions, and deriving planet occurrence rates. However, within the exoplanet direct imaging community, non-detections have almost exclusively been defined using a frequentist detection threshold (i.e., contrast curve) and associated completeness. This can lead to conceptual inconsistencies when included in a Bayesian framework. A Bayesian upper limit is such that the true value of a parameter lies below this limit with a certain probability. The associated probability is the integral of the posterior distribution with the upper limit as the upper bound. In summary, a frequentist upper limit is a statement about the detectability of planets while a Bayesian upper limit is a statement about the probability of a parameter to lie in an interval given the data. The latter is therefore better suited for rejecting hypotheses or theoretical models based on their predictions. In this work we emphasize that Bayesian statistics and upper limits are more easily interpreted and typically more constraining than the frequentist approach. We illustrate the use of Bayesian analysis in two different cases: (1) with a known planet location where we also propose to use model comparison to constrain the astrophysical nature of the point source and (2) gap-carving planets in TW Hya. To finish, we also mention the problem of combining radial velocity and direct imaging observations.

A Patient-Centered Proposal for Bayesian Analysis of Self-Experiments for Health.

The rise of affordable sensors and apps has enabled people to monitor various health indicators via self-tracking. This trend encourages self-experimentation, a subset of self-tracking in which a person systematically explores potential causal relationships to try to answer questions about their health. Although recent research has investigated how to support the data collection necessary for self-experiments, less research has considered the best way to analyze data resulting from these self-experiments. Most tools default to using traditional frequentist methods. However, the US Agency for Healthcare Research and Quality recommends using Bayesian analysis for n-of-1 studies, arguing from a statistical perspective. To develop a complementary patient-centered perspective on the potential benefits of Bayesian analysis, this paper describes types of questions people want to answer via self-experimentation, as informed by 1) our experiences engaging with irritable bowel syndrome patients and their healthcare providers and 2) a survey investigating what questions individuals want to answer about their health and wellness. We provide examples of how those questions might be answered using 1) frequentist null hypothesis significance testing, 2) frequentist estimation, and 3) Bayesian estimation and prediction. We then provide design recommendations for analyses and visualizations that could help people answer and interpret such questions. We find the majority of the questions people want to answer with self-tracking data are better answered with Bayesian methods than with frequentist methods. Our results therefore provide patient-centered support for the use of Bayesian analysis for n-of-1 studies.

How proper are Bayesian models in the astronomical literature?

The well-known Bayes theorem assumes that a posterior distribution is a probability distribution. However, the posterior distribution may no longer be a probability distribution if an improper prior distribution (non-probability measure) such as an unbounded uniform prior is used. Improper priors are often used in the astronomical literature to reflect a lack of prior knowledge, but checking whether the resulting posterior is a probability distribution is sometimes neglected. It turns out that 23 articles out of 75 articles (30.7%) published online in two renowned astronomy journals (ApJ and MNRAS) between Jan 1, 2017 and Oct 15, 2017 make use of Bayesian analyses without rigorously establishing posterior propriety. A disturbing aspect is that a Gibbs-type Markov chain Monte Carlo (MCMC) method can produce a seemingly reasonable posterior sample even when the posterior is not a probability distribution (Hobert and Casella, 1996). In such cases, researchers may erroneously make probabilistic inferences without noticing that the MCMC sample is from a non-existing probability distribution. We review why checking posterior propriety is fundamental in Bayesian analyses, and discuss how to set up scientifically motivated proper priors.

In silico evaluation of limited blood sampling strategies for individualized recombinant factor IX prophylaxis in hemophilia B patients

Background Patients with severe hemophilia B regularly administer prophylactic intravenous doses of clotting factor IX concentrate to maintain a trough level of at least 0.01 IU mL-1 in order to prevent joint bleeds. Assessment of individual pharmacokinetic (PK) parameters allows individualization of the recombinant factor IX (rFIX) dose. Aim To evaluate the predictive performance of limited sampling strategies (LSSs) with one to three samples to estimate individual PK parameters of rFIX. Methods Monte Carlo simulations were performed to obtain 5000 concentration-time profiles by the use of population PK parameters for rFIX from literature. Eleven LSSs were developed with one, two or three samples taken within an 80-h interval following administration of 100 IU kg-1 rFIX. Clearance (CL), half-life (t1/2 ), time to 1% and steady-state distribution volume (Vss ) were estimated for each simulated individual by the use of Bayesian analysis. Results For each LSS, average bias was small for CL (range - 1.5% to 1.4%), t1/2 (range - 4.5% to - 0.7%), time to 1% (range - 2.9% to 0%), and Vss (range - 3.7% to 0.3%). Imprecision for these parameters ranged from 6.4% to 11.9%, from 10.3% to 15.6%, from 7.3% to 10.9%, and from 9% to 20.1%, respectively. The best predictive performance was achieved with one sample taken between 10 min and 3 h and two samples taken between 48 h and 56 h after administration of rFIX. Conclusions This study demonstrates that limited sampling strategies, used for individualized dosing of rFIX in hemophilia B patients, can be developed and evaluated by in silico simulation.

Forecast of Large Earthquakes Through Semi-periodicity Analysis of Labeled Point Processes

Large earthquakes have semi-periodic behavior as a result of critically self-organized processes of stress accumulation and release in seismogenic regions. Hence, large earthquakes in a given region constitute semi-periodic sequences with recurrence times varying slightly from periodicity. In previous papers, it has been shown that it is possible to identify these sequences through Fourier analysis of the occurrence time series of large earthquakes from a given region, by realizing that not all earthquakes in the region need belong to the same sequence, since there can be more than one process of stress accumulation and release in the region. Sequence identification can be used to forecast earthquake occurrence with well determined confidence bounds. This paper presents improvements on the above mentioned sequence identification and forecasting method: the influence of earthquake size on the spectral analysis, and its importance in semi-periodic events identification are considered, which means that earthquake occurrence times are treated as a labeled point process; a revised estimation of non-randomness probability is used; a better estimation of appropriate upper limit uncertainties to use in forecasts is introduced; and the use of Bayesian analysis to evaluate the posterior forecast performance is applied. This improved method was successfully tested on synthetic data and subsequently applied to real data from some specific regions. As an example of application, we show the analysis of data from the northeastern Japan Arc region, in which one semi-periodic sequence of four earthquakes with M ≥ 8.0, having high non-randomness probability was identified. We compare the results of this analysis with those of the unlabeled point process analysis.

Use of Bayesian analysis with individual‐based modeling to project outcomes of coral restoration

AbstractVarious approaches to coral restoration have been developed to help increase rate of reef recovery from perturbations, among the most common of which is coral transplantation. Success is often evaluated based on short‐term observations that capture only the initial phase of space colonization by coral transplants. Here, an individual‐based model is developed to quantify uncertainty in future trajectories in experimental plots given past observations. Empirical data were used to estimate probabilistic growth, survival, and fission rates of Acropora pulchra and A. intermedia (order Scleractinia) in a sandy reef flat (Bolinao, Philippines). Simulations were initialized with different densities (25 or 50 transplants per species per 16 m2) to forecast possible coral cover trajectories over a 5‐year period. Given current conditions, there is risk of local extinction which is higher in low‐density plots for both species, and higher for A. intermedia compared to A. pulchra regardless of density. While total coral cover is projected to increase, species composition in the future is more likely to be highly uneven. The model was used to quantify effect on recovery rate of protection from pulse anthropogenic disturbances, given different initial transplantation densities. When monitoring data are limited in time, stochastic models may be used to assess whether the restoration trajectory is heading toward the desired state and at what rate, and foresee system response to various adaptive interventions.

Estimation of expected number of accidents and workforce unavailability through Bayesian population variability analysis and Markov-based model

Occupational accidents pose several negative consequences to employees, employers, environment and people surrounding the locale where the accident takes place. Some types of accidents correspond to low frequency-high consequence (long sick leaves) events, and then classical statistical approaches are ineffective in these cases because the available dataset is generally sparse and contain censored recordings. In this context, we propose a Bayesian population variability method for the estimation of the distributions of the rates of accident and recovery. Given these distributions, a Markov-based model will be used to estimate the uncertainty over the expected number of accidents and the work time loss. Thus, the use of Bayesian analysis along with the Markov approach aims at investigating future trends regarding occupational accidents in a workplace as well as enabling a better management of the labor force and prevention efforts. One application example is presented in order to validate the proposed approach; this case uses available data gathered from a hydropower company in Brazil.

System Priors for Econometric Time Series

The paper introduces “system priors”, their use in Bayesian analysis of econometric time series, and provides a simple and illustrative application. System priors were devised by Andrle and Benes (2013) as a tool to incorporate prior knowledge into an economic model. Unlike priors about individual parameters, system priors offer a simple and efficient way of formulating well-defined and economically-meaningful priors about high-level model properties. The generality of system priors are illustrated using an AR(2) process with a prior that most of its dynamics comes from business-cycle frequencies.

Some Remarks on the Application of Bayesian Analysis in Law

This paper discusses the use of Bayesian analysis in law. It introduces the key concepts of Bayesian analysis by giving some common examples of criminal cases. It focuses on the advantages of Bayesian analysis over some other probability interpretations (mainly the frequentist one). The last part of the text discusses the general notion of truth in legal proceedings and its possible interpretations within the probabilistic framework – given the Bayesian subjectivists-objectivists discussion.