Related papers: Optimal linear Bernoulli factories for small mean …
Suppose that $X_1,X_2,\ldots$ are independent identically distributed Bernoulli random variables with mean $p$. A Bernoulli factory for a function $f$ takes as input $X_1,X_2,\ldots$ and outputs a random variable that is Bernoulli with mean…
Given a $p$-coin that lands heads with unknown probability $p$, we wish to produce an $f(p)$-coin for a given function $f: (0,1) \rightarrow (0,1)$. This problem is commonly known as the Bernoulli Factory and results on its solvability and…
The Bernoulli Factory is an algorithm that takes as input a series of i.i.d. Bernoulli random variables with an unknown but fixed success probability $p$, and outputs a corresponding series of Bernoulli random variables with success…
A Bernoulli factory is an algorithmic procedure for exact sampling of certain random variables having only Bernoulli access to their parameters. Bernoulli access to a parameter $p \in [0,1]$ means the algorithm does not know $p$, but has…
We consider the problem of computing with many coins of unknown bias. We are given samples access to $n$ coins with \emph{unknown} biases $p_1,\dots, p_n$ and are asked to sample from a coin with bias $f(p_1, \dots, p_n)$ for a given…
For any discrete probability distributions with bounded entropy, we can generate exactly a random variate using only a finite expected number of perfect coin flips. A perfect coin flip is the outcome of an unbiased Bernoulli random…
Consider a randomized algorithm that draws samples exactly from a distribution using recursion. Such an algorithm is called a perfect simulation, and here a variety of methods for building this type of algorithm are shown to derive from the…
A Bernoulli factory is a model for randomness manipulation that transforms an initial Bernoulli random variable into another Bernoulli variable by applying a predetermined function relating the output bias to the input one. In literature,…
Given a known function $f : [0, 1] \mapsto (0, 1)$ and a random but almost surely finite number of independent, Ber$(x)$-distributed random variables with unknown $x \in [0, 1]$, we construct an unbiased, $[0, 1]$-valued estimator of the…
Assume that one aims to simulate an event of unknown probability $s\in (0,1)$ which is uniquely determined, however only its approximations can be obtained using a finite computational effort. Such settings are often encountered in…
Let $q \in (0,1)$ and $\delta \in (0,1)$ be real numbers, and let $C$ be a coin that comes up heads with an unknown probability $p$, such that $p \neq q$. We present an algorithm that, on input $C$, $q$, and $\delta$, decides, with…
Given a (known) function $f:[0,1] \to (0,1)$, we consider the problem of simulating a coin with probability of heads $f(p)$ by tossing a coin with unknown heads probability $p$, as well as a fair coin, $N$ times each, where $N$ may be…
An algorithm is presented that, taking a sequence of independent Bernoulli random variables with parameter $1/2$ as inputs and using only rational arithmetic, simulates a Bernoulli random variable with possibly irrational parameter $\tau$.…
Probabilistic artificial neural networks offer intriguing prospects for enabling the uncertainty of artificial intelligence methods to be described explicitly in their function; however, the development of techniques that quantify…
The well-know needle experiment of Buffon can be regarded as an analog (i.e., continuous) device that stochastically "computes" the number 2/pi ~ 0.63661, which is the experiment's probability of success. Generalizing the experiment and…
Let S\subset (0,1). Given a known function f:S\to (0,1), we consider the problem of using independent tosses of a coin with probability of heads p (where p\in S is unknown) to simulate a coin with probability of heads f(p). We prove that if…
Suppose that we are given an infinite binary sequence which is random for a Bernoulli measure of parameter $p$. By the law of large numbers, the frequency of zeros in the sequence tends to~$p$, and thus we can get better and better…
Suppose that we are given a function f : (0,1) -> (0,1) and, for some unknown p in (0,1), a sequence of independent tosses of a p-coin (i.e., a coin with probability p of ``heads''). For which functions f is it possible to simulate an…
Consider $n$ independent, biased coins, each with a known probability of heads. Presented with an ordering of these coins, flip (i.e., toss) each coin once, in that order, until we have observed both a *head* and a *tail*, or flipped all…
Here several perfect simulation algorithms are brought under a single framework, and shown to derive from the same probabilistic result, called here the Fundamental Theorem of Perfect Simulation (FTPS). An exact simulation algorithm has…