Bayesian Thinking Research Articles

Heterogeneity, Bayesian thinking, and phenotyping in critical care: A primer.

To familiarize clinicians with the emerging concepts in critical care research of Bayesian thinking and personalized medicine through phenotyping and explain their clinical relevance by highlighting how they address the issues of frequent negative trials and heterogeneity of treatment effect. The past decades have seen many negative (effect-neutral) critical care trials of promising interventions, culminating in calls to improve the field's research through adopting Bayesian thinking and increasing personalization of critical care medicine through phenotyping. Bayesian analyses add interpretive power for clinicians as they summarize treatment effects based on probabilities of benefit or harm, contrasting with conventional frequentist statistics that either affirm or reject a null hypothesis. Critical care trials are beginning to include prospective Bayesian analyses, and many trials have undergone reanalysis with Bayesian methods. Phenotyping seeks to identify treatable traits to target interventions to patients expected to derive benefit. Phenotyping and subphenotyping have gained prominence in the most syndromic and heterogenous critical care disease states, acute respiratory distress syndrome and sepsis. Grouping of patients has been informative across a spectrum of clinically observable physiological parameters, biomarkers, and genomic data. Bayesian thinking and phenotyping are emerging as elements of adaptive clinical trials and predictive enrichment, paving the way for a new era of high-quality evidence. These concepts share a common goal, sifting through the noise of heterogeneity in critical care to increase the value of existing and future research. The future of critical care medicine will inevitably involve modification of statistical methods through Bayesian analyses and targeted therapeutics via phenotyping. Clinicians must be familiar with these systems that support recommendations to improve decision-making in the gray areas of critical care practice.

Research on Bayesian Statistics Teaching with R

Bayesian statistics uses the mathematical rules of probability to combine data with prior information to yield inferences which are always more precise than would be obtained by either source of information alone. The current Bayesian education has not yet attracted enough attention from the education community in China. The rise of MCMC and probabilistic programming languages has profoundly reshaped Bayesian statistics. Compared to precise mathematical analysis, the simulation-based teaching can help students to avoid tedious statistical calculations and cultivate Bayesian thinking.

Contributed Session III: Identifying Specific Neural Substrates for Bayesian-like Computations in Binocular Vision and Multisensory Processing.

Bayesian thinking is influential in vision but the grounding of Bayesian computation in wetware is poorly understood. Bayesian reliability (inverse variance) weighting of inputs is predicted by Maximum Likelihood Estimation Theory and has some psychophysical support, but evidence for neural reliability weighting is sparse and neural modeling of reliability weighting is tricky. However, reliability averaging is just one possible perceptual weighted average. An alternative - nonlinear magnitude-weighted averaging - was suggested by Schrodinger in 1926 to account for suprathreshold binocular perception and is available to repurpose for other sensory cue combinations. We identified macaque suppressive binocular neurons that implement nonlinear magnitude-weighted averaging and approximate Bayesian averaging, without suffering the computational difficulties that Bayesian averaging implies. We then applied the binocular modeling to suppressive multisensory (visual-tactile, audio-tactile, and audio-visual) neurons. Although magnitude-weighting is a better fit than reliability-weighted averaging for cortical firing rates (in all four cases and in three different species), nonlinear magnitude-weighted averaging is well correlated with reliability averaging. Magnitude-weighted averaging could serve as a surrogate for Bayesian calculations; mildly suppressive binocular and multisensory bimodal neurons could be neural correlates of Bayesian-like computation in the brain.

A special issue on Bayesian inference: challenges, perspectives and prospects.

A special issue on Bayesian inference: challenges, perspectives and prospects.

Statistical inference with exchangeability and martingales.

In this paper, we start by reviewing exchangeability and its relevance to the Bayesian approach. We highlight the predictive nature of Bayesian models and the symmetry assumptions implied by beliefs of an underlying exchangeable sequence of observations. By taking a closer look at the Bayesian bootstrap, the parametric bootstrap of Efron and a version of Bayesian thinking about inference uncovered by Doob based on martingales, we introduce a parametric Bayesian bootstrap. Martingales play a fundamental role. Illustrations are presented as is the relevant theory. This article is part of the theme issue 'Bayesian inference: challenges, perspectives, and prospects'.

2021 Terzaghi Lecture: Geotechnical Systems, Uncertainty, and Risk

Risk assessment for large engineered systems involving geotechnical uncertainties—such as dams, coastal works, industrial facilities, and offshore structures—has matured in recent decades. This capability is becoming an ever more pressing concern considering increasing natural hazards and the effects of climate change. This progress and the current state of practice are reviewed by considering four projects. An underlying theme is what we have learned about how geoprofessionals should think about uncertainty, judgment, and risk. The organizing key is Bayesian thinking, which is neither new nor unintuitive to most geoprofessionals. However, this way of thinking and analyzing data is powerful, even when dealing with the sparse data of geotechnical projects. The presentation builds on the past Terzaghi Lectures of Casagrande, Whitman, and Christian. It uses examples of infrastructure systems for which geotechnical considerations were important. Reliability concepts developed in this earlier practice provide a window into the processes of integrating site characterization data, judgment, engineering models, and predictions to achieve tolerable levels of risk. Along the way, arguments are made on the nature of uncertainty and on the benefits of processing data, judgment, and inferences through a consistent lens.

Conceptual Grounding for Bayesian Inference for Latent Variables in Factor Analysis

ABSTRACT Obtaining values for latent variables in factor analysis models, also referred to as factor scores, has long been of interest to researchers. However, many treatments of factor analysis do not focus on inference about the latent variables, and even fewer do so from a Bayesian perspective. Researchers may therefore be ill-acquainted with Bayesian thinking on this issue, despite the fact that certain existing procedures may be seen as Bayesian to some extent. The focus of this paper is to provide a conceptual grounding for Bayesian inference for latent variables, articulating not only what Bayesian inference has to say about values for latent variables, but why Bayesian inference is suited for this problem. As to why, it is argued that the notion of exchangeability motivates the form of factor analysis, as well as Bayesian inference for latent variables. The argument is supported by documenting the widespread use of Bayesian inference in analogous settings, including latent variables in other measurement models, multilevel models, and missing data. As to what, this work describes a Bayesian analysis when other parameters are known, as well as partially and fully Bayesian analyses when other parameters are unknown. This facilitates a discussion of various choices researchers have when adopting Bayesian approaches to inference about latent variables.

A simple consistent Bayes factor for testing the Kendall rank correlation coefficient

In this paper, we propose a simple and easy-to-implement Bayesian hypothesis test for the presence of an association, described by Kendall's τ coefficient, between two variables measured on at least an ordinal scale. Owing to the absence of the likelihood functions for the data, we employ the asymptotic sampling distributions of the test statistic as the working likelihoods and then specify a truncated normal prior distribution on the noncentrality parameter of the alternative hypothesis, which results in the Bayes factor available in closed form in terms of the cumulative distribution function of the standard normal distribution. Investigating the asymptotic behaviour of the Bayes factor we find the conditions of the priors so that it is consistent to whichever the hypothesis is true. Simulation studies and a real-data application are used to illustrate the effectiveness of the proposed Bayes factor. It deserves mentioning that the proposed method can be easily covered in undergraduate and graduate courses in nonparametric statistics with an emphasis on students' Bayesian thinking for data analysis.

A Bayesian approach to nested data analysis: A primer for strategic management research

Bayesian analysis offers strategy scholars numerous benefits. In addition to aligning empirical and theoretical endeavors by incorporating prior knowledge, the Bayesian approach allows researchers to estimate and visualize relationships that reflect the probability distributions many strategy researchers mistakenly interpret from conventional techniques. Yet, strategy scholars have proven hesitant to adopt Bayesian methods. We suggest that this is because there is no accessible template for employing the technique with the types of data strategy researchers tend to encounter. The central objective of our research is to synthesize disparate contributions from the Bayesian literature that are relevant for strategy scholarship, especially for nested data. We provide an intuitive overview of Bayesian thinking and illustrate how scholars can employ Bayesian techniques to analyze nested data using an example dataset involving CEO compensation. Our results show how using Bayesian models may lead to substantively different interpretations and conclusions compared to traditional approaches based on frequentist techniques.

Learning the Art and Science of Diagnosis

This Viewpoint discusses key tenets of developing diagnostic acumen, including gathering and integrating data, applying iterative bayesian thinking, choosing the format of communication, and determining the urgency of diagnosis.

An ethically-motivated, Bayesian, adaptive design clinical trial bringing hope to women with menorrhagia…and warmth to statisticians' hearts.

An ethically-motivated, Bayesian, adaptive design clinical trial bringing hope to women with menorrhagia…and warmth to statisticians' hearts.

Philosophical or empirical incommensurability of frequentist versus Bayesian thinking

Frequentists and Bayesians disagree about the soundness of performing calculations based, in an important part, on prior information. The disagreement goes back to a basic philosophical disagreement about how to conceptualize the meaning of probability. As frequentists and Bayesians use the term differently, there is a basic philosophical incommensurability. However, this philosophical incommensurability need not imply an empirical incommensurability. It is possible for there to be, simultaneously, philosophical incommensurability and empirical commensurability. This possibility implies consequences that this article discusses

Beyond the p-value: Bayesian Statistics and Causation

ABSTRACT Statistical paradigms limit the perspective and tools social work researchers use to study the world and answer questions impacting people and policy. Currently, quantitative social work researchers overwhelmingly rely on the frequentist paradigm of statistics. This paper discusses foundational differences between the frequentist and Bayesian statistical paradigms, describes basic concepts of Bayesian analysis, compares Bayesian and frequentist statistical analysis for a sample social work problem, and introduces two types of causal analyses built on Bayesian statistical thinking: counterfactual causality, and causality based on work by computer scientist Judea Pearl. Implications for social work research are discussed.

A Bayesian Statistics Course for Undergraduates: Bayesian Thinking, Computing, and Research

We propose a semester-long Bayesian statistics course for undergraduate students with calculus and probability background. We cultivate students’ Bayesian thinking with Bayesian methods applied to real data problems. We leverage modern Bayesian computing techniques not only for implementing Bayesian methods, but also to deepen students’ understanding of the methods. Collaborative case studies further enrich students’ learning and provide experience to solve open-ended applied problems. The course has an emphasis on undergraduate research, where accessible academic journal articles are read, discussed, and critiqued in class. With increased confidence and familiarity, students take the challenge of reading, implementing, and sometimes extending methods in journal articles for their course projects. Supplementary materials for this article are available online.

Why Bayesian Ideas Should Be Introduced in the Statistics Curricula and How to Do So

While computing has become an important part of the statistics field, course offerings are still influenced by a legacy of mathematically centric thinking. Due to this legacy, Bayesian ideas are not required for undergraduate degrees and have largely been taught at the graduate level; however, with recent advances in software and emphasis on computational thinking, Bayesian ideas are more accessible. Statistics curricula need to continue to evolve and students at all levels should be taught Bayesian thinking. This article advocates for adding Bayesian ideas for three groups of students: intro-statistics students, undergraduate statistics majors, and graduate student scientists; and furthermore, provides guidance and materials for creating Bayesian-themed courses for these audiences. Supplementary files for this article are available on line.

Scenarios, Probability, and Evidence Scholarship, Old and New.

Scenarios, Probability, and Evidence Scholarship, Old and New.

The Limits of Bayesian Thinking in Court.

We comment on the contributions of Dahlman and of Fenton et al., who both suggested a Bayesian approach to analyze the Simonshaven case. We argue that analyzing a full case with a Bayesian approach is not feasible, and that there are serious problems with assigning actual numbers to probabilities and priors. We also discuss the nature of Bayesian thinking in court, and the nature and interpretation of the likelihood ratio. In particular, we discuss what it could mean that a likelihood ratio is in some sense uncertain.

Infusing High Value Care Education Directly into Patient Care on the Medicine Wards.

This article was migrated. The article was marked as recommended. Background: Multiple national initiatives have been implemented to promote cost-conscious care. Yet, there remains a deficiency of formal high value care (HVC) curricula among internal medicine residency programs.We aimedto develop a curriculum that teaches HVC material that can be utilized at the point of care and to assess the curriculum's impact on the participants' attitudes, knowledge, and practice patterns pertaining to HVC. Methods: We conducted our study on the inpatient internal medicine service over two-week rotations at Johns Hopkins Bayview Medical Center. Internal medicine residentsparticipated in two collaborative educational sessions that incorporated an introduction of important concepts in HVC, Bayesian thinking, clinical cases, and a review of a hospital bill of one of the patients under the team's care. Participants were also encouraged to reflect on their practice patterns and incorporate the HVC principles taught into their daily clinical work. We administered pre- and post-curriculum surveys to assess change in reported HVC-related practice behaviors, knowledge, and attitudes. Results: Forty-seven residents participated in the study. We included the twenty participants who completed both a pre- and post-curriculum survey in the data analysis. After participation in the curriculum, there was a significant increase in the use of pre-test probabilities in clinical decision making ( p=0.005). There was also a trend toward improvement in HVC knowledge and practice patterns after the rotation. Conclusion: We implemented a curriculum that may have improved high-value practice patterns through point-of-care education on the inpatient medicine wards.

De-Biasing Legal Fact-Finders With Bayesian Thinking.

This article shows how Bayesian thinking can help legal fact-finders to avoid some common fallacies and biases in the evaluation of legal evidence (false dichotomy, dependence neglect, and miss rate neglect).

Frequentist, Bayes, or Other?

ABSTRACT Both philosophically and in practice, statistics is dominated by frequentist and Bayesian thinking. Under those paradigms, our courses and textbooks talk about the accuracy with which true model parameters are estimated or the posterior probability that they lie in a given set. In nonparametric problems, they talk about convergence to the true function (density, regression, etc.) or the probability that the true function lies in a given set. But the usual paradigms' focus on learning the true model and parameters can distract the analyst from another important task: discovering whether there are many sets of models and parameters that describe the data reasonably well. When we discover many good models we can see in what ways they agree. Points of agreement give us more confidence in our inferences, but points of disagreement give us less. Further, the usual paradigms’ focus seduces us into judging and adopting procedures according to how well they learn the true values. An alternative is to judge models and parameter values, not procedures, and judge them by how well they describe data, not how close they come to the truth. The latter is especially appealing in problems without a true model.