Related papers: Combining Evidence
We consider the Jeffreys-Lindley paradox from an objective Bayesian perspective by attempting to find priors representing complete indifference to sample size in the problem. This means that we ensure that the prior for the unknown mean and…
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…
The forensic science community has increasingly sought quantitative methods for conveying the weight of evidence. Experts from many forensic laboratories summarize their findings in terms of a likelihood ratio. Several proponents of this…
Notwithstanding various attempts to construct a Partial Information Decomposition (PID) for multiple variables by defining synergistic, redundant, and unique information, there is no consensus on how one ought to precisely define either of…
The multinomial model is one of the simplest statistical models. When constraints are placed on the possible values for the probabilities, however, it becomes much more difficult to deal with. Model checking and checking for prior-data…
Incomplete observability of data generates an identification problem. There is no panacea for missing data. What one can learn about a population parameter depends on the assumptions one finds credible to maintain. The credibility of…
Three different inferential problems related to a two dimensional categorical data from a Bayesian perspective have been discussed in this article. Conjugate prior distribution with symmetric and asymmetric hyper parameters are considered.…
Bayesian inference provides a rigorous framework to encapsulate our knowledge and uncertainty regarding various physical quantities in a well-defined and self-contained manner. Utilising modern tools, such Bayesian models can be constructed…
In this paper we explore the application of methods for classical judgment aggregation in pooling probabilistic opinions on logically related issues. For this reason, we first modify the Boolean judgment aggregation framework in the way…
The combination of evidence in Dempster-Shafer theory is compared with the combination of evidence in probabilistic logic. Sufficient conditions are stated for these two methods to agree. It is then shown that these conditions are minimal…
Dempster-Shafer evidence theory is a powerful tool in information fusion. When the evidence are highly conflicting, the counter-intuitive results will be presented. To adress this open issue, a new method based on evidence distance of…
When using complex Bayesian models to combine information, the checking for consistency of the information being combined is good statistical practice. Here a new method is developed for detecting prior-data conflicts in Bayesian models…
(l) I have enough evidence to render the sentence S probable. (la) So, relative to what I know, it is rational of me to believe S. (2) Now that I have more evidence, S may no longer be probable. (2a) So now, relative to what I know, it is…
I propose a normative updating rule, extended Bayesianism, for the incorporation of probabilistic information arising from the process of becoming more aware. Extended Bayesianism generalizes standard Bayesian updating to allow the…
Methods are described for the solution of linear inference problems subject to deterministic constraints. The approach builds on work by Backus (1970a,b,c) and Parker (1977), but a range useful advances are suggested to address both…
Bayesian methods are increasingly applied in these days in the theory and practice of statistics. Any Bayesian inference depends on a likelihood and a prior. Ideally one would like to elicit a prior from related sources of information or…
We introduce a Bayesian solution for the problem in forensic speaker recognition, where there may be very little background material for estimating score calibration parameters. We work within the Bayesian paradigm of evidence reporting and…
A reliable modeling of uncertain evidence in Bayesian networks based on a set-valued quantification is proposed. Both soft and virtual evidences are considered. We show that evidence propagation in this setup can be reduced to standard…
The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…
Eliciting informative prior distributions for Bayesian inference can often be complex and challenging. While popular methods rely on asking experts probability based questions to quantify uncertainty, these methods are not without their…