Related papers: Bayesian Analysis
We introduce a few of the key ideas of statistical analysis using two real-world examples to illustrate how these ideas are used in practice.
We provide four case studies that use Bayesian machinery to making inductive reasoning. Our main motivation relies in offering several instances where the Bayesian approach to data analysis is exploited at its best to perform complex tasks,…
This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes…
Total probability and Bayes formula are two basic tools for using prior information in the Bayesian statistics. In this paper we introduce an alternative tool for using prior information. This new toold enables us to improve some…
The two key issues of modern Bayesian statistics are: (i) establishing principled approach for distilling statistical prior that is consistent with the given data from an initial believable scientific prior; and (ii) development of a…
The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…
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…
Bayesian predictive probabilities are commonly used for interim monitoring of clinical trials through efficacy and futility stopping rules. Despite their usefulness, calculation of predictive probabilities, particularly in pre-experiment…
The author revisits the Blue Bus Problem, a famous thought-experiment in law involving probabilistic proof, and presents simple Bayesian solutions to different versions of the blue bus hypothetical. In addition, the author expresses his…
Artificial Intelligence (AI), and in particular, the explainability thereof, has gained phenomenal attention over the last few years. Whilst we usually do not question the decision-making process of these systems in situations where only…
A product of two Gaussians (or normal distributions) is another Gaussian. That's a valuable and useful fact! Here we use it to derive a refactoring of a common product of multivariate Gaussians: The product of a Gaussian likelihood times a…
Theory testing in the physical sciences has been revolutionized in recent decades by Bayesian approaches to probability theory. Here, I will consider Bayesian approaches to theory extensions, that is, theories like inflation which aim to…
A new method is developed to represent probabilistic relations on multiple random events. Where previously knowledge bases containing probabilistic rules were used for this purpose, here a probability distribution over the relations is…
We provide an introductory review of Bayesian data analytical methods, with a focus on applications for linguistics, psychology, psycholinguistics, and cognitive science. The empirically oriented researcher will benefit from making Bayesian…
In this paper, we are concerned with attributing meaning to the results of a Bayesian analysis for a problem which is sufficiently complex that we are unable to assert a precise correspondence between the expert probabilistic judgements of…
In this paper, we propose an explicit closed-form Bayes factor for the problem of two-sample hypothesis testing. The proposed approach can be regarded as a Bayesian version of the pooled-variance t-statistic and has various appealing…
In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate…
Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…
After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…
The design of an experiment can be always be considered at least implicitly Bayesian, with prior knowledge used informally to aid decisions such as the variables to be studied and the choice of a plausible relationship between the…