(2015) On Bayesian problem-solving: helping Bayesians solve simple Bayesian word problems. Resolving the " Bayesian Paradox " —Bayesians Who Failed to Solve Bayesian Problems A well-supported conclusion a reader would draw from the vast amount of research on Bayesian inference could be distilled into one sentence: " People are profoundly Bayesians, but they fail to solve Bayesian word problems....

Abstract: Probabilistic inference models (e.g. Bayesian models) are often cast as being rational and at odds with simple heuristic approaches. We show that prominent decision heuristics, take-the-best and tallying, are special cases of Bayesian inference. We developed two Bayesian learning models by extending two popular regularized regression approaches, lasso and ridge regression. The priors ...

In this paper we present a simple hierarchical Bayesian treatment of the sparse kernel logistic regression (KLR) model based MacKay’s evidence approximation. The model is re-parameterised such that an isotropic Gaussian prior over parameters in the kernel induced feature space is replaced by an isotropic Gaussian prior over the transformed parameters, facilitating a Bayesian analysis using stan...

Naive Bayesian classifiers tend to perform very well on a large number of problem domains, although their representation power is quite limited compared to more sophisticated machine learning algorithms. In this paper we study combining multiple naive Bayesian classifiers by using the hierarchical mixtures of experts system. This novel system, which we call hierarchical mixtures of naive Bayesi...

In typical applications of Bayesian optimization, minimal assumptions are made about the objective function being optimized. This is true even when researchers have prior information about the shape of the function with respect to one or more argument. We make the case that shape constraints are often appropriate in at least two important application areas of Bayesian optimization: (1) hyperpar...

D. Trafimow (2003) presented an analysis of null hypothesis significance testing (NHST) using Bayes's theorem. Among other points, he concluded that NHST is logically invalid, but that logically valid Bayesian analyses are often not possible. The latter conclusion reflects a fundamental misunderstanding of the nature of Bayesian inference. This view needs correction, because Bayesian methods ha...