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Physical Sciences and Mathematics Commons™
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- 13P10 Commutative Rings and Algebras/Computational Aspects/Grobner Bases (1)
- 60C05 Combinatorial Probability (1)
- 60E15 Inequalities; stochastic orderings (1)
- 60G42 Martingales with Discrete Parameters (1)
- 60J20 Probability theory and stochastic processes/Markov processes/Applications of Markov chains and discrete-time Markov processes on general state spaces (1)
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Markov Bases For Noncommutative Harmonic Analysis Of Partially Ranked Data, Ann Johnston
Markov Bases For Noncommutative Harmonic Analysis Of Partially Ranked Data, Ann Johnston
HMC Senior Theses
Given the result $v_0$ of a survey and a nested collection of summary statistics that could be used to describe that result, it is natural to ask which of these summary statistics best describe $v_0$. In 1998 Diaconis and Sturmfels presented an approach for determining the conditional significance of a higher order statistic, after sampling a space conditioned on the value of a lower order statistic. Their approach involves the computation of a Markov basis, followed by the use of a Markov process with stationary hypergeometric distribution to generate a sample.This technique for data analysis has become an accepted tool …
Martingale Couplings And Bounds On Tails Of Probability Distributions, Kyle Luh
Martingale Couplings And Bounds On Tails Of Probability Distributions, Kyle Luh
HMC Senior Theses
Wassily Hoeffding, in his 1963 paper, introduces a procedure to derive inequalities between distributions. This method relies on finding a martingale coupling between the two random variables. I have developed a construction that establishes such couplings in various urn models. I use this construction to prove the inequality between the hypergeometric and binomial random variables that appears in Hoeffding's paper. I have then used and extended my urn construction to create new inequalities.