Papers compiled in Good (1983) made first attempts at combining attractive aspects of Bayesian and frequentist approaches to statistical inference. While the hybrid inference approach of Yuan (2009) succeeded in leveraging Bayesian point estimators with maximum likelihood estimates, hybrid inference does not yet cover the case of a parameter of interest that has a partially known prior. Since s...

In some applications, the response variable assumes values in the unit interval. The standard linear regression model is not appropriate for modelling this type of data because the normality assumption is not met. Alternatively, the beta regression model has been introduced to analyze such observations. A beta distribution represents a flexible density family on (0, 1) interval that covers symm...

Abstract: The Exponentiated Gumbel (EG) distribution has been proposed to capture some aspects of the data that the Gumbel distribution fails to specify. In this paper, we estimate the EG's parameters in the Bayesian framework. We consider a 2-level hierarchical structure for prior distribution. As the posterior distributions do not admit a closed form, we do an approximated inference by using ...

As Bayesian networks are applied to larger and more complex problem domains, search for exible modeling and more eecient inference methods is an ongoing eeort. Multiply sectioned Bayesian networks (MSBNs) extend the HUGIN inference for Bayesian networks into a coherent framework for exible modeling and distributed inference. Lazy propagation extends the Shafer-Shenoy and HUGIN inference methods...

Bayesian network is a complete model for the variables and their relationships, it can be used to answer probabilistic queries about them. A Bayesian network can thus be considered a mechanism for automatically applying Bayes’ theorem to complex problems. In the application of Bayesian networks, most of the work is related to probabilistic inferences. Any variable updating in any node of Bayesi...

Causal inference in sensory cue combination is the process of determining whether multiple sensory cues have the same cause or different causes. Psychophysical evidence indicates that humans closely follow the predictions of a Bayesian causal inference model. Here, we explore how Bayesian causal inference could be implemented using probabilistic population coding and plausible neural operations...

Causation plays a critical role in many predictive and inference tasks. Bayesian networks (BNs) have been used to construct inference systems for diagnostics and decision making. More recently, fuzzy cognitive maps (FCMs) have gained considerable attention and offer an alternative framework for representing structured human knowledge and causal inference. In this paper I briefly introduce Bayes...

Penalized splines can be viewed as BLUPs in a mixed model framework, which allows the use of mixed model software for smoothing. Thus, software originally developed for Bayesian analysis of mixed models can be used for penalized spline regression. Bayesian inference for nonparametric models enjoys the flexibility of nonparametric models and the exact inference provided by the Bayesian inferenti...

We devise an approach to Bayesian statistics and their applications in the analysis of the Monty Hall problem. We combine knowledge gained through applications of the Maximum Entropy Principle and Nash equilibrium strategies to provide results concerning the use of Bayesian approaches unique to the Monty Hall problem. We use a model to describe Monty’s decision process and clarify that Bayesian...