On the Bias of Traceroute Sampling
... the level at which the Internet Protocol (IP) operates, and the connections between autonomous systems, the level at which the Border Gateway Protocol (BGP) operates. Similar results were obtained in [17, 3], among others. Based on these and other topological studies, it is widely believed that the ...
... the level at which the Internet Protocol (IP) operates, and the connections between autonomous systems, the level at which the Border Gateway Protocol (BGP) operates. Similar results were obtained in [17, 3], among others. Based on these and other topological studies, it is widely believed that the ...
The probability of nontrivial common knowledge
... Pa (n) when the size n of the state space Sn grows large. That is, if two (or more) agents face a large state space and their partition profile is drawn according to the uniform model, what is the asymptotic probability that they can attain common knowledge of a nontrivial event? Perhaps surprisingl ...
... Pa (n) when the size n of the state space Sn grows large. That is, if two (or more) agents face a large state space and their partition profile is drawn according to the uniform model, what is the asymptotic probability that they can attain common knowledge of a nontrivial event? Perhaps surprisingl ...
BROWNIAN MOTION AND THE STRONG MARKOV PROPERTY
... Definition 1.7. Let (S, Σ, µ) be a measure space. When µ(Σ) equals 1, this map is termed a probability measure and the associated measure space is called a probability space. We are now able to use this machinery to re-introduce some familiar concepts within probability theory. First, let us introdu ...
... Definition 1.7. Let (S, Σ, µ) be a measure space. When µ(Σ) equals 1, this map is termed a probability measure and the associated measure space is called a probability space. We are now able to use this machinery to re-introduce some familiar concepts within probability theory. First, let us introdu ...
Learning Sums of Independent Integer Random Variables
... straightforward to show that S must have almost all its probability mass on values in a small interval, and (1) follows easily from this. The more challenging case is when Var(S) is “large.” Intuitively, in order for Var(S) to be large it must be the case that at least one of the k − 1 values 1, 2, ...
... straightforward to show that S must have almost all its probability mass on values in a small interval, and (1) follows easily from this. The more challenging case is when Var(S) is “large.” Intuitively, in order for Var(S) to be large it must be the case that at least one of the k − 1 values 1, 2, ...
Artificial Intelligence, Lecture 6.1, Page 1
... ω |= α ∧ β if ω |= α and ω |= β ω |= α ∨ β if ω |= α or ω |= β ω |= ¬α if ω 6|= α Let Ω be the set of all possible worlds. ...
... ω |= α ∧ β if ω |= α and ω |= β ω |= α ∨ β if ω |= α or ω |= β ω |= ¬α if ω 6|= α Let Ω be the set of all possible worlds. ...
Approximations of upper and lower probabilities by measurable
... shall show, when these two sets are not equal the use of the upper and the lower probability could carry some serious loss of information. The study of the equality P(Γ)(A) = [P∗ (A), P ∗ (A)] can be split into two different subproblems: on the one hand, we need to study the convexity of the set P(Γ ...
... shall show, when these two sets are not equal the use of the upper and the lower probability could carry some serious loss of information. The study of the equality P(Γ)(A) = [P∗ (A), P ∗ (A)] can be split into two different subproblems: on the one hand, we need to study the convexity of the set P(Γ ...
Random projections, marginals, and moments
... the sequel some aspects of a more general approach based on quasi-analytic functions. In the sequel, and unless explicitly mentioned, we consider uniqueness on R, not on R+ . Theorem 2.2 (Hausdorff, [Hau23]). A probability distribution P on [0, 1] is characterized by its moments. Proof. The density ...
... the sequel some aspects of a more general approach based on quasi-analytic functions. In the sequel, and unless explicitly mentioned, we consider uniqueness on R, not on R+ . Theorem 2.2 (Hausdorff, [Hau23]). A probability distribution P on [0, 1] is characterized by its moments. Proof. The density ...
Bayesian Belief Network
... • In general, we write P(A|B) to represent a belief in A under the assumption that B is known. • Strictly speaking, P(A|B) is a shorthand for the expression P(A|B,K) where K represents all other relevant information. • Only when all other information is irrelevant can we really write P(A|B). • The t ...
... • In general, we write P(A|B) to represent a belief in A under the assumption that B is known. • Strictly speaking, P(A|B) is a shorthand for the expression P(A|B,K) where K represents all other relevant information. • Only when all other information is irrelevant can we really write P(A|B). • The t ...
uniform central limit theorems - Assets
... continuous for almost all ω. So the empirical process αn converges in distribution to the Brownian bridge composed with F, namely t 7→ yF (t) , at least when restricted to finite sets. It was then natural to ask whether this convergence extends to infinite sets or the whole interval or line. Kolmogo ...
... continuous for almost all ω. So the empirical process αn converges in distribution to the Brownian bridge composed with F, namely t 7→ yF (t) , at least when restricted to finite sets. It was then natural to ask whether this convergence extends to infinite sets or the whole interval or line. Kolmogo ...