232,974 research outputs found
A Cubic Algorithm for Computing Gaussian Volume
We present randomized algorithms for sampling the standard Gaussian
distribution restricted to a convex set and for estimating the Gaussian measure
of a convex set, in the general membership oracle model. The complexity of
integration is while the complexity of sampling is for
the first sample and for every subsequent sample. These bounds
improve on the corresponding state-of-the-art by a factor of . Our
improvement comes from several aspects: better isoperimetry, smoother
annealing, avoiding transformation to isotropic position and the use of the
"speedy walk" in the analysis.Comment: 23 page
Metropolized Randomized Maximum Likelihood for sampling from multimodal distributions
This article describes a method for using optimization to derive efficient
independent transition functions for Markov chain Monte Carlo simulations. Our
interest is in sampling from a posterior density for problems in which
the dimension of the model space is large, is multimodal with regions
of low probability separating the modes, and evaluation of the likelihood is
expensive. We restrict our attention to the special case for which the target
density is the product of a multivariate Gaussian prior and a likelihood
function for which the errors in observations are additive and Gaussian
Boosted Beta regression.
Regression analysis with a bounded outcome is a common problem in applied statistics. Typical examples include regression models for percentage outcomes and the analysis of ratings that are measured on a bounded scale. In this paper, we consider beta regression, which is a generalization of logit models to situations where the response is continuous on the interval (0,1). Consequently, beta regression is a convenient tool for analyzing percentage responses. The classical approach to fit a beta regression model is to use maximum likelihood estimation with subsequent AIC-based variable selection. As an alternative to this established - yet unstable - approach, we propose a new estimation technique called boosted beta regression. With boosted beta regression estimation and variable selection can be carried out simultaneously in a highly efficient way. Additionally, both the mean and the variance of a percentage response can be modeled using flexible nonlinear covariate effects. As a consequence, the new method accounts for common problems such as overdispersion and non-binomial variance structures
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