相关论文: The Probability of a Run
The probability of necessity (PN), which quantifies the probability that an observed event would not have occurred in the absence of the treatment, is a central estimand in attribution analysis. While PN has been extensively studied for…
We study a probabilistic variant of binary session types that relate to a class of Finite-State Markov Chains. The probability annotations in session types enable the reasoning on the probability that a session terminates successfully, for…
We present a nice result on the probability of a cycle occurring in a randomly generated graph. We then provide some extensions and applications, including the proof of the famous Cayley formula, which states that the number of labeled…
A method for computing probabilistic propositions is presented. It assumes the availability of a single external routine for computing the probability of one instantiated variable, given a conjunction of other instantiated variables. In…
This paper examines some methods and ideas underlying the author's successful probabilistic learning systems(PLS), which have proven uniquely effective and efficient in generalization learning or induction. While the emerging principles are…
When presenting forensic evidence, such as a DNA match, experts often use the Likelihood ratio (LR) to explain the impact of evidence . The LR measures the probative value of the evidence with respect to a single hypothesis such as 'DNA…
Based on the probability distribution observed in complex systems and an assumption that the probability distributions of complex systems satisfy a new generalized multiplication, it is proved that the statistical theory of complex systems…
This article presents a concise proof of the famous Benford's law when the distribution has a Riemann integrable probability density function and provides a criterion to judge whether a distribution obeys the law. The proof is intuitive and…
The correctness of most randomized distributed algorithms is expressed by a statement of the form ``some predicate of the executions holds with high probability, regardless of the order in which actions are scheduled''. In this paper, we…
We introduce an algorithm for the uniform generation of infinite traces, i.e., infinite words up to commutation of some letters. The algorithm outputs on-the-fly approximations of a theoretical infinite trace, the latter being distributed…
We propose a sound and complete proof rule ProbTA for quantitative analysis of violation probability of probabilistic programs. Our approach extends the technique of trace abstraction with probability in the control-flow randomness style,…
A probability method is provided to prove three classes of combinatorial identities. The method is extremely simple, only one step after the proper probability setup.
In this short expository article, we describe a mathematical tool called the probabilistic method, and illustrate its elegance and beauty through proving a few well-known results. Particularly, we give an unconventional probabilistic proof…
A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.
We present a method to estimate the provability of a mathematical formula. We adapt the tactical theorem prover TacticToe to factor in these estimations. Experiments over the HOL4 library show an increase in the number of theorems re-proven…
We provide direct elementary proofs of several explicit expressions for Bernoulli numbers and Bernoulli polynomials. As a byproduct of our method of proof, we provide natural definitions for generalized Bernoulli numbers and polynomials of…
We give a reciprocity formula for a two-variable sum where the variables satisfy a linear congruence condition. We also prove that such sum is a measure of how well a rational is approximable from below and show that the reciprocity formula…
A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.
We prove an analogue of the classical ballot theorem that holds for any random walk in the range of attraction of the normal distribution. Our result is best possible: we exhibit examples demonstrating that if any of our hypotheses are…
We settle in the affirmative the Graham-Sloane conjecture.