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Bayesian Workflow
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Bayesian Workflow
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The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit Bayesian models, but this still leaves us with many options regarding constructing, evaluating, and using these models, along with many remaining challenges in computation. Using Bayesian inference to solve real-world problems requires not only statistical skills, subject matter knowledge, and programming, but also awareness of the decisions made in the process of data analysis. All of these aspects can be understood as part of a tangled workflow of applied Bayesian statistics. Beyond inference, the workflow also includes iterative model building, model checking, validation and troubleshooting of computational problems, model understanding, and model comparison. We review all these aspects of workflow in the context of several examples, keeping in mind that in practice we will be fitting many models for any given problem, even if only a subset of them will ultimately be relevant for our conclusions.
Forward citations
Cited by 16 Pith papers
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Calibration, Not Compilation: Detecting and Repairing Misspecified Probabilistic Programs Written by Language Models
Bayesian workflow diagnostics outperform unit tests for detecting and repairing statistically misspecified LLM-generated probabilistic programs across benchmarks and real generation tasks.
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Beyond Empirical Bayes: A Hierarchical Bayesian Approach to Crash Rate Estimation with Missing Traffic Volume
A hierarchical Bayesian model jointly imputes missing ADT and estimates segment crash rates with flexible exposure exponents, outperforming Empirical Bayes by PSIS-LOO Δelpd of 9,394 on Ohio data.
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Toward Joint Prediction of a Longitudinal Marker and a Terminal Event: A bivariate discrete-time framework
A flexible Bayesian bivariate discrete-time model jointly predicts partly-conditional longitudinal trajectories and terminal-event risk without immortal-cohort extrapolation.
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To select or not to select: predictively consistent priors instead of model selection
Predictively consistent priors let complex Bayesian models match or beat the out-of-sample performance of selected simpler models across linear, logistic, and nonlinear examples without explicit selection.
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A nutritionally informed model for Bayesian variable selection with metabolite response variables
A new Bayesian variable selection method for metabolite data, using a skew-normal censored mixture with a Markov random field prior, detects diet-metabolite associations in two cohorts.
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RefineStat: Efficient Exploration for Probabilistic Program Synthesis
RefineStat improves small language model performance on probabilistic program synthesis by adding semantic constraint enforcement and diagnostic-aware refinement, producing syntactically and statistically reliable cod...
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Compositional amortized inference for large-scale hierarchical Bayesian models
A new error-damping estimator for compositional score matching enables stable amortized inference on hierarchical Bayesian models with over 750,000 parameters using fewer than one full model simulation on large problems.
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Toward Joint Prediction of a Longitudinal Marker and a Terminal Event: A bivariate discrete-time framework
A Bayesian discrete-time joint model predicts a patient's partly-conditional longitudinal marker trajectory together with the time to a terminal event, illustrated on ICD patients' quality of life and mortality.
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Bridging electrode preparation and electrocatalyst performance with physics-based causal AI
Physics-based structural causal models are used on n<10 multi-modal datasets to quantitatively disentangle support-to-catalyst ratio and loading effects on manganese-antimony oxide ORR performance in alkaline RDE tests.
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Restricted Multivariate Spatial Modeling
Develops a restricted MCAR model via reparameterization to measure and control informativeness in multivariate spatial modeling of health events across subgroups.
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How Requirements Quality Makes (or Breaks) Traceability Link Recovery
Empirical analysis of 189 annotated use cases shows that some requirements quality defects reduce TLR performance while others improve it, with effects varying by approach type.
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Quantifying Evidential Rigor in Meta-Analytic Corpora: A Simulation-Characterized, Bias-Robust Bayesian Workflow with a Nutrition Case Study
Introduces a corpus-scale Bayesian evidential-audit workflow that defines rigor as combined Bayes-factor evidence for effect or no-effect plus absence of explicit bias components, validated via simulations and applied...
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Bayesian Inference of Discretization Error Means in ODEs via Ensemble Kalman Filtering
A Bayesian state-space model with an Ensemble Kalman Filter infers the mean of ODE discretization errors from noisy observations, using a step-size-dependent Markov prior whose convergence is proven.
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Comparative study of Bayesian and Frequentist methods for epidemic forecasting: Insights from simulated and historical data
Neither Bayesian nor frequentist fitting is uniformly better for epidemic forecasts; performance depends on phase and data, though the paper's own results undercut its phase-specific claims.
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A Tutorial on Bayesian Analysis of Linear Shock Compression Data
Bayesian linear regression yields an analytic t-distribution posterior for C0 and S, which can be sampled and pushed through Rankine-Hugoniot equations to obtain pressure-volume Hugoniot credible intervals.
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An Introduction to Bayesian and Frequentist Simulation-Based Inference with Machine Learning
A structured introduction to ML-based simulation-based inference, contrasting Bayesian and frequentist frameworks and covering parameter inference, unfolding, and validation.
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