Projects per year
Abstract
We prove the Shepp–Olkin conjecture, which states that the entropy of the sum of independent Bernoulli random variables is concave in the parameters of the individual random variables. Our proof refines an argument previously presented by the same authors, which resolved the conjecture in the monotonic case (where all the parameters are simultaneously increasing). In fact, we show that the monotonic case is the worst case, using a careful analysis of concavity properties of the derivatives of the probability mass function. We propose a generalization of Shepp and Olkin’s original conjecture, to consider Rényi and Tsallis entropies.
Original language | English |
---|---|
Pages (from-to) | 3638-3649 |
Number of pages | 12 |
Journal | Bernoulli |
Volume | 23 |
Issue number | 4B |
Early online date | 23 May 2017 |
DOIs | |
Publication status | Published - Nov 2017 |
Keywords
- Bernoulli sums
- concavity
- entropy
- transportation of measure
- Poisson binomial distribution
Fingerprint
Dive into the research topics of 'A proof of the Shepp-Olkin entropy concavity conjecture'. Together they form a unique fingerprint.Projects
- 1 Finished
-
Information geometry of graphs
Johnson, O. T. (Principal Investigator)
1/09/11 → 1/09/13
Project: Research
Profiles
-
Professor Oliver T Johnson
- School of Mathematics - Head of School, Professor of Information Theory
- Statistical Science
- Probability, Analysis and Dynamics
Person: Academic , Member, Professional and Administrative