Selecting a Biased-Coin Design

Tossing a Biased Coin

When we talk about a coin toss, we think of it as unbiased: with probability one-half it comes up heads, and with probability one-half it comes up tails. An ideal unbiased coin might not correctly model a real coin, which could be biased slightly one way or another. After all, real life is rarely fair. This possibility leads us to an interesting mathematical and computational question. Is there...

UNBIASED COIN TOSSING WITH A BIASED COIN by

PrQcedures are exhibited and analyzed for converting a sequence of iid Bernoulli variables with unknown mean p into a Bernoulli variable with mean 1/2. The efficiency of several procedures is studied.

Ecient Simulations by a Biased Coin

A Remark on Sieving in Biased Coin

In this work, we establish a nontrivial level of distribution for densities on {1, . . . , N} obtained by a biased coin convolution. As a consequence of sieving theory, one then derives the expected lower bound for the weight of such densities on sets of pseudo-primes. At the end, we make a comment on the recent paper of Peled, Sen and Zeitouni (which largely motivated this work) and show how s...

Finding a most biased coin with fewest flips

We study the problem of learning the most biased coin among a set of coins by tossing the coins adaptively. The goal is to minimize the number of tosses to identify a coin i∗ such that Pr (coin i∗ is most biased) is at least 1 − δ for any given δ. Under a particular probabilistic model, we give an optimal algorithm, i.e., an algorithm that minimizes the expected number of tosses, to learn a mos...