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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 10 Pith papers
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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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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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Diagrams-to-Dynamics (D2D): Exploring Causal Loop Diagram Leverage Points under Uncertainty
D2D converts causal loop diagrams into exploratory system dynamics models, sampling uncertain link strengths from polarity-constrained ranges to rank intervention targets and guide data collection.
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Granulation signatures in 3D hydrodynamical simulations: evaluating background model performance using a Bayesian nested sampling framework
Multi-component granulation background models are statistically preferred over a single-component model across 27 3D convection simulations, with a tentative third component beyond νmax.
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Bayesian Forecast Combination with Predictive Priors via Particle Filtering
A diversity-based predictive prior added to the latent weight dynamics of a Bayesian forecast combination method (DTVW) improves point and density forecasts in simulations and in oil price and U.S. macro applications,...
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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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Bayesian Inverse Physics for Neuro-Symbolic Robot Learning
A position paper arguing that hybrid neuro-symbolic architectures combining physics, Bayesian inference, and program synthesis are essential for general-purpose robot learning.
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