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Examining how well a hypothesized model fits observed data is pivotal in Bayesian structural equation modeling (SEM). Recent efforts have aimed to formulate Bayesian SEM fit indices akin to those used in frequentist SEM. However, the assessment of these fit indices in Bayesian SEM has been limited in scope. This research entailed two simulation studies to explore the impact of various factors, including prior choices, model misspecification, model size, and sample size, on the sensitivity of fit indices. The first study delved into the prior sensitivity of Bayesian SEM fit indices (BRMSEA [Bayesian root mean square error of approximation], BCFI [Bayesian comparative fit index], BTLI [Bayesian Tucker–Lewis index], and PP p [posterior predictive p -value]) under latent factor and cross-loading misspecifications. The second study explored how alterations in model complexity influenced the prior sensitivity of these fit indices to model misspecifications. The findings indicate a robust performance of Bayesian fit indices under relatively severe model misspecification, suggesting a preference for highly informative priors when prior knowledge is certain. As model size increased, PP p exhibited a balanced performance between true and false positive rates, whereas BRMSEA was less reliable in the presence of latent factor misspecification. Implications for applied research are discussed.

Previous studies have shown a surprising amount of between-subjects variability in the strength of interactions between sensory modalities. For the same set of stimuli, some subjects exhibit strong interactions, whereas others exhibit weak interactions. To date, little is known about what underlies this variability. Sensory integration in the brain could be governed by a global mechanism or by task-specific mechanisms that could be either stable or variable across time. We used a rigorous quantitative tool (Bayesian causal inference) to investigate whether integration (i.e., binding) tendencies generalize across tasks and are stable across time. We report for the first time that individuals' binding tendencies are stable across time but are task-specific. These results provide evidence against the hypothesis that sensory integration is governed by a single, global parameter in the brain.

Expectations are known to greatly affect our experience of the world. A growing theory in computational neuroscience is that perception can be successfully described using Bayesian inference models and that the brain is \"Bayes-optimal\" under some constraints. In this context, expectations are particularly interesting, because they can be viewed as prior beliefs in the statistical inference process. A number of questions remain unsolved, however, for example: How fast do priors change over time? Are there limits in the complexity of the priors that can be learned? How do an individual's priors compare to the true scene statistics? Can we unlearn priors that are thought to correspond to natural scene statistics? Where and what are the neural substrate of priors? Focusing on the perception of visual motion, we here review recent studies from our laboratories and others addressing these issues. We discuss how these data on motion perception fit within the broader literature on perceptual Bayesian priors, perceptual expectations, and statistical and perceptual learning and review the possible neural basis of priors.

Expert knowledge is used widely in the science and practice of conservation because of the complexity of problems, relative lack of data, and the imminent nature of many conservation decisions. Expert knowledge is substantive information on a particular topic that is not widely known by others. An expert is someone who holds this knowledge and who is often deferred to in its interpretation. We refer to predictions by experts of what may happen in a particular context as expert judgments. In general, an expert-elicitation approach consists of five steps: deciding how information will be used, determining what to elicit, designing the elicitation process, performing the elicitation, and translating the elicited information into quantitative statements that can be used in a model or directly to make decisions. This last step is known as encoding. Some of the considerations in eliciting expert knowledge include determining how to work with multiple experts and how to combine multiple judgments, minimizing bias in the elicited information, and verifying the accuracy of expert information. We highlight structured elicitation techniques that, if adopted, will improve the accuracy and information content of expert judgment and ensure uncertainty is captured accurately. We suggest four aspects of an expert elicitation exercise be examined to determine its comprehensiveness and effectiveness: study design and context, elicitation design, elicitation method, and elicitation output. Just as the reliability of empirical data depends on the rigor with which it was acquired so too does that of expert knowledge. El conocimiento de expertos es utilizado ampliamente en la ciencia y práctica de la conservación por la complejidad de los problemas, la falta relativa de datos y la naturaleza inminente de muchas decisiones de conservación. El conocimiento de expertos es información sustancial sobre un tópico particular que no es conocido ampliamente por otros. Un experto es alguien que tiene ese conocimiento y a quien se recurre a menudo para su interpretación. Nos referimos a las predicciones de expertos de lo que puede suceder en un contexto particular como juicio de expertos. En general, un método de obtención de expertos consiste en cinco pasos: decidir como se utilizará la información, determinar que se va a obtener, diseñar el proceso de obtención, llevar a cabo la obtención y traducir la información obtenida en datos cuantitativos que puedan ser utilizados directamente o en un modelo para tomar decisiones. Este último paso es conocido como codificación. Algunas de las consideraciones en la obtención de conocimiento de expertos incluyen determinar como trabajar con múltiples expertos y como combinar múltiples juicios, minimizando el sesgo en la información obtenida, y verificando la precisión de la información de expertos. Resaltamos técnicas estructuradas de obtención que, de ser adoptadas, mejorarán la precisión y contenido de información del juicio de expertos y asegurarán que la incertidumbre sea capturada con precisión. Sugerimos que se examinen cuatro aspectos de un ejercicio de obtención de expertos para determinar su amplitud y efectividad: estudiar el diseño y el contexto, diseño de la obtención, método de obtención y resultado de la obtención. Tal como la confiabilidad de los datos empíricos depende del rigor con que fueron obtenidos, también lo es para el conocimiento de expertos.

We use the language of uninformative Bayesian prior choice to study the selection of appropriately simple effective models. We advocate for the prior which maximizes the mutual information between parameters and predictions, learning as much as possible from limited data. When many parameters are poorly constrained by the available data, we find that this prior puts weight only on boundaries of the parameter space. Thus, it selects a lower-dimensional effective theory in a principled way, ignoring irrelevant parameter directions. In the limit where there are sufficient data to tightly constrain any number of parameters, this reduces to the Jeffreys prior. However, we argue that this limit is pathological when applied to the hyperribbon parameter manifolds generic in science, because it leads to dramatic dependence on effects invisible to experiment.

A catalytic prior distribution is designed to stabilize a high-dimensional “working model” by shrinking it toward a “simplified model.” The shrinkage is achieved by supplementing the observed data with a small amount of “synthetic data” generated from a predictive distribution under the simpler model. We apply this framework to generalized linear models, where we propose various strategies for the specification of a tuning parameter governing the degree of shrinkage and study resultant theoretical properties. In simulations, the resulting posterior estimation using such a catalytic prior outperforms maximum likelihood estimation from the working model and is generally comparable with or superior to existing competitive methods in terms of frequentist prediction accuracy of point estimation and coverage accuracy of interval estimation. The catalytic priors have simple interpretations and are easy to formulate.

When a stimulus is presented, its encoding is known to progress from low- to high-level features. How these features are decoded to produce perception is less clear, and most models assume that decoding follows the same low- to high-level hierarchy of encoding. There are also theories arguing for global precedence, reversed hierarchy, or bidirectional processing, but they are descriptive without quantitative comparison with human perception. Moreover, observers often inspect different parts of a scene sequentially to form overall perception, suggesting that perceptual decoding requires working memory, yet few models consider how working-memory properties may affect decoding hierarchy. We probed decoding hierarchy by comparing absolute judgments of single orientations and relative/ordinal judgments between two sequentially presented orientations. We found that lower-level, absolute judgments failed to account for higher-level, relative/ordinal judgments. However, when ordinal judgment was used to retrospectively decode memory representations of absolute orientations, striking aspects of absolute judgments, including the correlation and forward/backward aftereffects between two reported orientations in a trial, were explained. We propose that the brain prioritizes decoding of higher-level features because they are more behaviorally relevant, and more invariant and categorical, and thus easier to specify and maintain in noisy working memory, and that more reliable higher-level decoding constrains less reliable lower-level decoding.

Groundwater recharge plays a vital role in replenishing aquifers, sustaining demand, and reducing adverse effects (e.g. land subsidence). In order to manage climate change-induced effects on groundwater dynamics, climate models are increasingly being used to predict current and future recharges. Even though there has been a number of hydrological studies that have averaged climate models’ predictions in a Bayesian framework, few studies have been related to the groundwater recharge. In this study, groundwater recharge estimates from 10 regional climate models (RCMs) are averaged in 12 different Bayesian frameworks with variations of priors. A recession-curve-displacement method was used to compute recharge from measured streamflow data. Two basins of different sizes located in the same water resource region in the USA, the Cedar River Basin and the Rainy River Basin, are selected to illustrate the approach and conduct quantitative analysis. It has been shown that groundwater recharge prediction is affected by the Bayesian priors. The non-Empirical Bayes g-Local-based Bayesian priors result in posterior inclusion probability values that are consistent with the performance of the climate models outside the Bayesian framework. With the proper choice of priors, the Bayesian frameworks can produce good results of groundwater recharge with R2, percent bias error, and Willmott's index of agreement of >0.97, <2%, and >0.97, respectively, in the two basins. The Bayesian framework with an appropriate prior provides opportunity to estimate recharge from multiple climate models.

Application of Bayesian methods is one the tools that can be used to face the multiple challenges that are met when clinical trials must be conducted in rare diseases. We propose in this work to use a dynamic Bayesian borrowing approach, based on a mixture prior, to complement the control arm of a comparative trial and estimate the mixture parameter by an Empirical Bayes approach. The method is compared, using simulations, with an approach based on a pre-specified (non-adaptive) informative prior. The simulation study shows that the proposed method exhibits similar power as the non-adaptive prior and drastically reduce type I error in case of severe discrepancy between the informative prior and the study control arm data. In case of limited discrepancy between the informative prior and the study control arm data, then our proposed adaptive prior does not reduce the inflation of the type I error.

Recent studies suggest that apex predators play a pivotal role in maintaining healthy, balanced ecosystems. However, a criticism of studies investigating the ecological role of apex predators is that understanding does not come from manipulative experiments. Here, we use a before-after-control-impact-paired design to test predictions generated from trophic cascade theory (TCT) and mesopredator release hypothesis (MRH) by experimentally introducing dingoes into a 37-km² paddock and measuring the resultant effects on mammal assemblages. To increase precision of parameter estimates generated by our experiment, we used a Bayesian framework which included prior information recorded from a mensurative study located in a comparable ecosystem that contrasted indices of mammal abundance where dingoes were common and rare. Results of the mensurative study were consistent with TCT and MRH. When using an uninformative prior, results of the experiment showed that dingo addition only had a negative effect on kangaroo activity. Use of an informative prior reduced uncertainty of the posterior mean parameter estimates from the experiment and suggested that red foxes were affected negatively and small mammals and rabbits were affected positively by dingo introduction. However, the prior had a strong influence on the posterior mean effect sizes for small mammals, rabbits and foxes. Opposite polarity of uninformed and prior parameter estimates for rabbits suggests that the prior was incompatible with the uninformed estimates from the manipulative experiment. Our study shows how use of logical informative priors can help to overcome statistical issues associated with low-replication in large-scale experiments, but the strong influence of the prior means that our findings were driven largely by the mensurative study.