9,099 research outputs found
On nonparametric estimation of a mixing density via the predictive recursion algorithm
Nonparametric estimation of a mixing density based on observations from the
corresponding mixture is a challenging statistical problem. This paper surveys
the literature on a fast, recursive estimator based on the predictive recursion
algorithm. After introducing the algorithm and giving a few examples, I
summarize the available asymptotic convergence theory, describe an important
semiparametric extension, and highlight two interesting applications. I
conclude with a discussion of several recent developments in this area and some
open problems.Comment: 22 pages, 5 figures. Comments welcome at
https://www.researchers.one/article/2018-12-
Modern Coding Theory: The Statistical Mechanics and Computer Science Point of View
These are the notes for a set of lectures delivered by the two authors at the
Les Houches Summer School on `Complex Systems' in July 2006. They provide an
introduction to the basic concepts in modern (probabilistic) coding theory,
highlighting connections with statistical mechanics. We also stress common
concepts with other disciplines dealing with similar problems that can be
generically referred to as `large graphical models'.
While most of the lectures are devoted to the classical channel coding
problem over simple memoryless channels, we present a discussion of more
complex channel models. We conclude with an overview of the main open
challenges in the field.Comment: Lectures at Les Houches Summer School on `Complex Systems', July
2006, 44 pages, 25 ps figure
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