Browsing by Author "Wolpert, RL"

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Open Access
Bayesian Nonparametric Function Estimation Using Overcomplete Representations and Levy Random Field Priors
(Oberwolfach Reports, 2005) Clyde, M; House, L; Tu, C; Wolpert, RL
Open Access
Bayesian nonparametric models for peak identification in maldi-tof mass spectroscopy
(Annals of Applied Statistics, 2011-06-01) House, LL; Clyde, MA; Wolpert, RL
We present a novel nonparametric Bayesian approach based on Lévy Adaptive Regression Kernels (LARK) to model spectral data arising from MALDI-TOF (Matrix Assisted Laser Desorption Ionization Time-of-Flight) mass spectrometry. This model-based approach provides identification and quantification of proteins through model parameters that are directly interpretable as the number of proteins, mass and abundance of proteins and peak resolution, while having the ability to adapt to unknown smoothness as in wavelet based methods. Informative prior distributions on resolution are key to distinguishing true peaks from background noise and resolving broad peaks into individual peaks for multiple protein species. Posterior distributions are obtained using a reversible jump Markov chain Monte Carlo algorithm and provide inference about the number of peaks (proteins), their masses and abundance. We show through simulation studies that the procedure has desirable true-positive and false-discovery rates. Finally, we illustrate the method on five example spectra: a blank spectrum, a spectrum with only the matrix of a low-molecular-weight substance used to embed target proteins, a spectrum with known proteins, and a single spectrum and average of ten spectra from an individual lung cancer patient. © 2013 Institute of Mathematical Statistics.
Open Access
Stochastic expansions using continuous dictionaries: Lévy adaptive regression kernels
(Annals of Statistics, 2011-08-01) Wolpert, RL; Clyde, MA; Tu, C
This article describes a new class of prior distributions for nonparametric function estimation. The unknown function is modeled as a limit of weighted sums of kernels or generator functions indexed by continuous parameters that control local and global features such as their translation, dilation, modulation and shape. Lévy random fields and their stochastic integrals are employed to induce prior distributions for the unknown functions or, equivalently, for the number of kernels and for the parameters governing their features. Scaling, shape, and other features of the generating functions are location-specific to allow quite different function properties in different parts of the space, as with wavelet bases and other methods employing overcomplete dictionaries. We provide conditions under which the stochastic expansions converge in specified Besov or Sobolev norms. Under a Gaussian error model, this may be viewed as a sparse regression problem, with regularization induced via the Lévy random field prior distribution. Posterior inference for the unknown functions is based on a reversible jump Markov chain Monte Carlo algorithm. We compare the Lévy Adaptive Regression Kernel (LARK) method to wavelet-based methods using some of the standard test functions, and illustrate its flexibility and adaptability in nonstationary applications. © Institute of Mathematical Statistics, 2011.