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1. Assessing the Impact of Precision Parameter Prior in Bayesian Non-parametric Growth Curve Modeling

   https://doi.org/10.3389/fpsyg.2021.624588  

   Tong, Xin; Ke, Zijun (March 2021, Frontiers in Psychology)

   null (Ed.)

   Bayesian non-parametric (BNP) modeling has been developed and proven to be a powerful tool to analyze messy data with complex structures. Despite the increasing popularity of BNP modeling, it also faces challenges. One challenge is the estimation of the precision parameter in the Dirichlet process mixtures. In this study, we focus on a BNP growth curve model and investigate how non-informative prior, weakly informative prior, accurate informative prior, and inaccurate informative prior affect the model convergence, parameter estimation, and computation time. A simulation study has been conducted. We conclude that the non-informative prior for the precision parameter is less preferred because it yields a much lower convergence rate, and growth curve parameter estimates are not sensitive to informative priors. 

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2. Prior choice and data requirements of Bayesian multivariate hierarchical models fit to tag‐recovery data: The need for power analyses

   https://doi.org/10.1002/ece3.9847  

   Deane, Cody E; Carlson, Lindsay G; Cunningham, Curry J; Doak, Pat; Kielland, Knut; Breed, Greg A (March 2023, Ecology and Evolution)

   Abstract Recent empirical studies have quantified correlation between survival and recovery by estimating these parameters as correlated random effects with hierarchical Bayesian multivariate models fit to tag‐recovery data. In these applications, increasingly negative correlation between survival and recovery has been interpreted as evidence for increasingly additive harvest mortality. The power of these hierarchal models to detect nonzero correlations has rarely been evaluated, and these few studies have not focused on tag‐recovery data, which is a common data type. We assessed the power of multivariate hierarchical models to detect negative correlation between annual survival and recovery. Using three priors for multivariate normal distributions, we fit hierarchical effects models to a mallard (Anas platyrhychos) tag‐recovery data set and to simulated data with sample sizes corresponding to different levels of monitoring intensity. We also demonstrate more robust summary statistics for tag‐recovery data sets than total individuals tagged. Different priors led to substantially different estimates of correlation from the mallard data. Our power analysis of simulated data indicated most prior distribution and sample size combinations could not estimate strongly negative correlation with useful precision or accuracy. Many correlation estimates spanned the available parameter space (−1,1) and underestimated the magnitude of negative correlation. Only one prior combined with our most intensive monitoring scenario provided reliable results. Underestimating the magnitude of correlation coincided with overestimating the variability of annual survival, but not annual recovery. The inadequacy of prior distributions and sample size combinations previously assumed adequate for obtaining robust inference from tag‐recovery data represents a concern in the application of Bayesian hierarchical models to tag‐recovery data. Our analysis approach provides a means for examining prior influence and sample size on hierarchical models fit to capture–recapture data while emphasizing transferability of results between empirical and simulation studies. 

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3. Expert elicitation and data noise learning for material flow analysis using Bayesian inference

   Dong, Jiayuan; Liao, Jiankan; Huan, Xun; Cooper, Daniel (May 2023, Journal of industrial ecology)

   Bayesian inference allows the transparent communication and systematic updating of model uncertainty as new data become available. When applied to material flow analysis (MFA), however, Bayesian inference is undermined by the difficulty of defining proper priors for the MFA parameters and quantifying the noise in the collected data. We start to address these issues by first deriving and implementing an expert elicitation procedure suitable for generating MFA parameter priors. Second, we propose to learn the data noise concurrent with the parametric uncertainty. These methods are demonstrated using a case study on the 2012 US steel flow. Eight experts are interviewed to elicit distributions on steel flow uncertainty from raw materials to intermediate goods. The experts’ distributions are combined and weighted according to the expertise demonstrated in response to seeding questions. These aggregated distributions form our model parameters’ informative priors. Sensible, weakly informative priors are adopted for learning the data noise. Bayesian inference is then performed to update the parametric and data noise uncertainty given MFA data collected from the United States Geological Survey and the World Steel Association. The results show a reduction in MFA parametric uncertainty when incorporating the collected data. Only a modest reduction in data noise uncertainty was observed using 2012 data; however, greater reductions were achieved when using data from multiple years in the inference. These methods generate transparent MFA and data noise uncertainties learned from data rather than pre-assumed data noise levels, providing a more robust basis for decision-making that affects the system. 

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4. Diversification Models Conflate Likelihood and Prior, and Cannot be Compared Using Conventional Model-Comparison Tools

   https://doi.org/10.1093/sysbio/syad010  

   May, Michael R.; Rothfels, Carl J.; Hoehna, ed., Sebastian (March 2023, Systematic Biology)

   Abstract Time-calibrated phylogenetic trees are a tremendously powerful tool for studying evolutionary, ecological, and epidemiological phenomena. Such trees are predominantly inferred in a Bayesian framework, with the phylogeny itself treated as a parameter with a prior distribution (a “tree prior”). However, we show that the tree “parameter” consists, in part, of data, in the form of taxon samples. Treating the tree as a parameter fails to account for these data and compromises our ability to compare among models using standard techniques (e.g., marginal likelihoods estimated using path-sampling and stepping-stone sampling algorithms). Since accuracy of the inferred phylogeny strongly depends on how well the tree prior approximates the true diversification process that gave rise to the tree, the inability to accurately compare competing tree priors has broad implications for applications based on time-calibrated trees. We outline potential remedies to this problem, and provide guidance for researchers interested in assessing the fit of tree models. [Bayes factors; Bayesian model comparison; birth-death models; divergence-time estimation; lineage diversification] 

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5. Graph Structure Learning with Interpretable Bayesian Neural Networks

   Wasserman, Max; Mateos, Gonzalo (September 2024, Transactions on machine learning research)

   Graphs serve as generic tools to encode the underlying relational structure of data. Often this graph is not given, and so the task of inferring it from nodal observations becomes important. Traditional approaches formulate a convex inverse problem with a smoothness promoting objective and rely on iterative methods to obtain a solution. In supervised settings where graph labels are available, one can unroll and truncate these iterations into a deep network that is trained end-to-end. Such a network is parameter efficient and inherits inductive bias from the optimization formulation, an appealing aspect for data constrained settings in, e.g., medicine, finance, and the natural sciences. But typically such settings care equally about \textit{uncertainty} over edge predictions, not just point estimates. Here we introduce novel iterations with independently interpretable parameters, i.e., parameters whose values - independent of other parameters' settings - proportionally influence characteristics of the estimated graph, such as edge sparsity. After unrolling these iterations, prior knowledge over such graph characteristics shape prior distributions} over these independently interpretable network parameters to yield a Bayesian neural network (BNN) capable of graph structure learning (GSL) from smooth signal observations. Fast execution and parameter efficiency allow for high-fidelity posterior approximation via Markov Chain Monte Carlo (MCMC) and thus uncertainty quantification on edge predictions. Informative priors unlock modeling tools from Bayesian statistics like prior predictive checks. Synthetic and real data experiments corroborate this model's ability to provide well-calibrated estimates of uncertainty, in test cases that include unveiling economic sector modular structure from S&P500 data and recovering pairwise digit similarities from MNIST images. Overall, this framework enables GSL in modest-scale applications where uncertainty on the data structure is paramount 

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