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Local Privacy and Minimax Bounds: Sharp Rates for Probability Estimation
Local Privacy Minimax Bounds Sharp Rates Probability Estimation
2013/6/14
We provide a detailed study of the estimation of probability distributions---discrete and continuous---in a stringent setting in which data is kept private even from the statistician. We give sharp mi...
Calibration diagnostics for point process models via the probability integral transform
Calibration diagnostics point process models probability integral transform
2013/6/14
We propose the use of the probability integral transform (PIT) for model validation in point process models. The simple PIT diagnostics assess the calibration of the model and can detect inconsistenci...
Constrained probability distributions of correlation functions
cosmology gravitational lensing large scale structure of the Universe galaxies statistics Methods statistical
2011/6/21
Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used
in Bayesian parameter estimation, their likelihood function is usually replac...
Probability & incompressible Navier-Stokes equations: An overview of some recent developments
incompressible Navier-Stokes Fourier transform mild solution multi-type branching random walk multiplicative cascade
2009/5/18
This is largely an attempt to provide probabilists some orientation to an important class of non-linear partial differential equations in applied mathematics, the incompressible Navier-Stokes equation...
Orthogonality and probability: beyond nearest neighbor transitions
beyond nearest Orthogonality
2009/4/22
In this article, we will explore why Karlin-McGregor method of using orthogonal polynomials in the study of Markov processes was so successful for one dimensional nearest neighbor processes, but faile...