کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1146195 1489692 2012 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Bayesian nonlinear regression for large pp small nn problems
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز عددی
پیش نمایش صفحه اول مقاله
Bayesian nonlinear regression for large pp small nn problems
چکیده انگلیسی

Statistical modeling and inference problems with sample sizes substantially smaller than the number of available covariates are challenging. This is known as large pp small nn problem. Furthermore, the problem is more complicated when we have multiple correlated responses. We develop multivariate nonlinear regression models in this setup for accurate prediction. In this paper, we introduce a full Bayesian support vector regression model with Vapnik’s ϵϵ-insensitive loss function, based on reproducing kernel Hilbert spaces (RKHS) under the multivariate correlated response setup. This provides a full probabilistic description of support vector machine (SVM) rather than an algorithm for fitting purposes. We have also introduced a multivariate version of the relevance vector machine (RVM). Instead of the original treatment of the RVM relying on the use of type II maximum likelihood estimates of the hyper-parameters, we put a prior on the hyper-parameters and use Markov chain Monte Carlo technique for computation. We have also proposed an empirical Bayes method for our RVM and SVM. Our methods are illustrated with a prediction problem in the near-infrared (NIR) spectroscopy. A simulation study is also undertaken to check the prediction accuracy of our models.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Multivariate Analysis - Volume 108, July 2012, Pages 28–40
نویسندگان
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