This paper proposes a new approach to sparsity, called the horseshoe estimator, which arises from a prior based on multivariate-normal scale mixtures. We describe the estimator's advantages over existing approaches, including its robustness, adaptivity to different sparsity patterns and...

A Bayesian perspective is taken to quantify the amount of information learned from observing a stochastic process, Xt, on the interval [0, T] which satisfies the stochastic differential equation, dXt = S([theta], t, Xt)dt+[sigma](t, Xt)dBt. Information is defined as a change in expected utility...

We propose a new data-augmentation strategy for fully Bayesian inference in models with binomial likelihoods. The approach appeals to a new class of Pólya--Gamma distributions, which are constructed in detail. A variety of examples are presented to show the versatility of the method, including...

type="main" xml:id="rssb12042-abs-0001" <title type="main">Summary</title> <p>We propose the Bayesian bridge estimator for regularized regression and classification. Two key mixture representations for the Bayesian bridge model are developed: a scale mixture of normal distributions with respect to an α-stable random...</p>

Standard financial models predict that investors who are willing to hold an investment in the short‐run will hold the same investment for the long‐run. It is well known that a leveraged investment's expected excess return is equal to the unlevered excess return scaled by the leverage factor....

An optimal investment strategy is “memoryless,” because it depends on present and expected future conditions, but not on the past. This article discusses the conditions required for a single, optimal investment strategy which the authors refer to as the memoryless trading rule. As a...