950 research outputs found
A Universal Scheme for Transforming Binary Algorithms to Generate Random Bits from Loaded Dice
In this paper, we present a universal scheme for transforming an arbitrary
algorithm for biased 2-face coins to generate random bits from the general
source of an m-sided die, hence enabling the application of existing algorithms
to general sources. In addition, we study approaches of efficiently generating
a prescribed number of random bits from an arbitrary biased coin. This
contrasts with most existing works, which typically assume that the number of
coin tosses is fixed, and they generate a variable number of random bits.Comment: 2 columns, 10 page
Minimalist design of a robust real-time quantum random number generator
We present a simple and robust construction of a real-time quantum random
number generator (QRNG). Our minimalist approach ensures stable operation of
the device as well as its simple and straightforward hardware implementation as
a stand-alone module. As a source of randomness the device uses measurements of
time intervals between clicks of a single-photon detector. The obtained raw
sequence is then filtered and processed by a deterministic randomness
extractor, which is realized as a look-up table. This enables high speed
on-the-fly processing without the need of extensive computations. The overall
performance of the device is around 1 random bit per detector click, resulting
in 1.2 Mbit/s generation rate in our implementation
Post-Election Audits: Restoring Trust in Elections
With the intention of assisting legislators, election officials and the public to make sense of recent literature on post-election audits and convert it into realistic audit practices, the Brennan Center and the Samuelson Law, Technology and Public Policy Clinic at Boalt Hall School of Law (University of California Berkeley) convened a blue ribbon panel (the "Audit Panel") of statisticians, voting experts, computer scientists and several of the nation's leading election officials. Following a review of the literature and extensive consultation with the Audit Panel, the Brennan Center and the Samuelson Clinic make several practical recommendations for improving post-election audits, regardless of the audit method that a jurisdiction ultimately decides to adopt
Induced Distributions from Generalized Unfair Dice
In this paper we analyze the probability distributions associated with
rolling (possibly unfair) dice infinitely often. Specifically, given a
-sided die, if denotes the outcome of the
toss, then the distribution function is , where . We show that is singular and
establish a piecewise linear, iterative construction for it. We investigate two
ways of comparing to the fair distribution -- one using supremum norms and
another using arclength. In the case of coin flips, we also address the case
where each independent flip could come from a different distribution. In part,
this work aims to address outstanding claims in the literature on Bernoulli
schemes. The results herein are motivated by emerging needs, desires, and
opportunities in computation to leverage physical stochasticity in
microelectronic devices for random number generation.Comment: 18 pages, 1 figur
Seventh-grade curriculum in probability (a guide for teachers)
A review of the literature indicates that teachers try to make connections between experimental and theoretical probabilities while teaching their students, but these connections are often not very clear. This greatly increases misconceptions students have about probability. This thesis presents a treatment of teaching probability that is geared for seventh grade and intended to minimize the misconceptions that both teachers and students may have. We present a concise mathematical exposition of finite probability models as well as collection of examples and activities, so as to help teachers and students organize their thinking and minimize misconceptions. The various examples and activities suggested in this thesis hopefully will increase the quality of instruction in probability and ultimately motivate the students in this important field of mathematics
The Bayesian sampler : generic Bayesian inference causes incoherence in human probability
Human probability judgments are systematically biased, in apparent tension with Bayesian models of cognition. But perhaps the brain does not represent probabilities explicitly, but approximates probabilistic calculations through a process of sampling, as used in computational probabilistic models in statistics. Naïve probability estimates can be obtained by calculating the relative frequency of an event within a sample, but these estimates tend to be extreme when the sample size is small. We propose instead that people use a generic prior to improve the accuracy of their probability estimates based on samples, and we call this model the Bayesian sampler. The Bayesian sampler trades off the coherence of probabilistic judgments for improved accuracy, and provides a single framework for explaining phenomena associated with diverse biases and heuristics such as conservatism and the conjunction fallacy. The approach turns out to provide a rational reinterpretation of “noise” in an important recent model of probability judgment, the probability theory plus noise model (Costello & Watts, 2014, 2016a, 2017; Costello & Watts, 2019; Costello, Watts, & Fisher, 2018), making equivalent average predictions for simple events, conjunctions, and disjunctions. The Bayesian sampler does, however, make distinct predictions for conditional probabilities and distributions of probability estimates. We show in 2 new experiments that this model better captures these mean judgments both qualitatively and quantitatively; which model best fits individual distributions of responses depends on the assumed size of the cognitive sample
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