A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
A Bayesian model for local smoothing in kernel density estimation
Statistics and Computing
Instance-based generative biological shape modeling
ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
Incremental one-class learning with bounded computational complexity
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
A flexible extreme value mixture model
Computational Statistics & Data Analysis
Bayesian multiscale smoothing in supervised and semi-supervised kernel discriminant analysis
Computational Statistics & Data Analysis
Bayesian adaptive bandwidth kernel density estimation of irregular multivariate distributions
Computational Statistics & Data Analysis
Algorithms for maximum-likelihood bandwidth selection in kernel density estimators
Pattern Recognition Letters
Synopses for Massive Data: Samples, Histograms, Wavelets, Sketches
Foundations and Trends in Databases
Haptic rendering of variable density point cloud through local kernel bandwidth estimation
Proceedings of the Eighth Indian Conference on Computer Vision, Graphics and Image Processing
Bayesian estimation of adaptive bandwidth matrices in multivariate kernel density estimation
Computational Statistics & Data Analysis
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Kernel density estimation for multivariate data is an important technique that has a wide range of applications. However, it has received significantly less attention than its univariate counterpart. The lower level of interest in multivariate kernel density estimation is mainly due to the increased difficulty in deriving an optimal data-driven bandwidth as the dimension of the data increases. We provide Markov chain Monte Carlo (MCMC) algorithms for estimating optimal bandwidth matrices for multivariate kernel density estimation. Our approach is based on treating the elements of the bandwidth matrix as parameters whose posterior density can be obtained through the likelihood cross-validation criterion. Numerical studies for bivariate data show that the MCMC algorithm generally performs better than the plug-in algorithm under the Kullback-Leibler information criterion, and is as good as the plug-in algorithm under the mean integrated squared error (MISE) criterion. Numerical studies for five-dimensional data show that our algorithm is superior to the normal reference rule. Our MCMC algorithm is the first data-driven bandwidth selector for multivariate kernel density estimation that is applicable to data of any dimension.