Bayesian revision of a prior given prior-data conflict,expert opinion,or a similar insight: a large-deviation approach

Learning from model diagnostics that a prior distribution must be replaced by one that conflicts less with the data raises the question of which prior should instead be used for inference and decision. The same problem arises when a decision maker learns that one or more reliable experts express unexpected beliefs. In both cases, coherence of the solution would be guaranteed by applying Bayes's theorem to a distribution of prior distributions that effectively assigns the initial prior distribution a probability arbitrarily close to 1. The new distribution for inference would then be the distribution of priors conditional on the insight that the prior distribution lies in a closed convex set that does not contain the initial prior. A readily available distribution of priors needed for such conditioning is the law of the empirical distribution of sufficiently large number of independent parameter values drawn from the initial prior. According to the Gibbs conditioning principle from the theory of large deviations, the resulting new prior distribution minimizes the entropy relative to the initial prior. While minimizing relative entropy accommodates the necessity of going beyond the initial prior without departing from it any more than the insight demands, the large-deviation derivation also ensures the advantages of Bayesian coherence. This approach is generalized to uncertain insights by allowing the closed convex set of priors to be random.     

A weakly informative prior for Bayesian dynamic model selection with applications in fMRI

In recent years, Bayesian statistics methods in neuroscience have been showing important advances. In particular, detection of brain signals for studying the complexity of the brain is an active area of research. Functional magnetic resonance imagining (fMRI) is an important tool to determine which parts of the brain are activated by different types of physical behavior. According to recent results, there is evidence that the values of the connectivity brain signal parameters are close to zero and due to the nature of time series fMRI data with high-frequency behavior, Bayesian dynamic models for identifying sparsity are indeed far-reaching. We propose a multivariate Bayesian dynamic approach for model selection and shrinkage estimation of the connectivity parameters. We describe the coupling or lead-lag between any pair of regions by using mixture priors for the connectivity parameters and propose a new weakly informative default prior for the state variances. This framework produces one-step-ahead proper posterior predictive results and induces shrinkage and robustness suitable for fMRI data in the presence of sparsity. To explore the performance of the proposed methodology, we present simulation studies and an application to functional magnetic resonance imaging data.     

A dynamic power prior for borrowing historical data in noninferiority trials with binary endpoint

Traditionally, noninferiority hypotheses have been tested using a frequentist method with a fixed margin. Given that information for the control group is often available from previous studies, it is interesting to consider a Bayesian approach in which information is “borrowed” for the control group to improve efficiency. However, construction of an appropriate informative prior can be challenging. In this paper, we consider a hybrid Bayesian approach for testing noninferiority hypotheses in studies with a binary endpoint. To account for heterogeneity between the historical information and the current trial for the control group, a dynamic P value–based power prior parameter is proposed to adjust the amount of information borrowed from the historical data. This approach extends the simple test‐then‐pool method to allow a continuous discounting power parameter. An adjusted α level is also proposed to better control the type I error. Simulations are conducted to investigate the performance of the proposed method and to make comparisons with other methods including test‐then‐pool and hierarchical modeling. The methods are illustrated with data from vaccine clinical trials.     

优先权基本问题研究

优先权制度发端于古老的罗马法,各个国家在继承的过程中形成了各具特色的制度。我国学者在讨论这一制度时,应当首先明确优先权含义和性质。优先权制度是对特殊债权人赋予的特权,这种权利的内容是债权人享有的债权得以优先受偿,其具有的效力至为强大,不仅优先于普通债权,还可以对抗担保物权,具有物权效力。