Unreliable probabilities, risk taking, and decision making
... Kolmogoroff's axioms, i.e., there is a unique probability measure that describes these degrees of belief. However, a presupposition of this theorem is that the agent be willing to take either side of a bet, i.e., if the agent is not willing to bet on the state sj at odds of a:b, then he should be wi ...
... Kolmogoroff's axioms, i.e., there is a unique probability measure that describes these degrees of belief. However, a presupposition of this theorem is that the agent be willing to take either side of a bet, i.e., if the agent is not willing to bet on the state sj at odds of a:b, then he should be wi ...
Uncertainty171
... e.g., P(Cavity = true) = 0.1 and P(Weather = sunny) = 0.72 correspond to belief prior to arrival of any (new) evidence ...
... e.g., P(Cavity = true) = 0.1 and P(Weather = sunny) = 0.72 correspond to belief prior to arrival of any (new) evidence ...
Uncertainty
... probability density functions • Probability distributions for continuous variables are called probability density functions. • For continuous variables, it is not possible to write out the entire distribution as a table. (infinitely many values!) • defines the probability that a random variable tak ...
... probability density functions • Probability distributions for continuous variables are called probability density functions. • For continuous variables, it is not possible to write out the entire distribution as a table. (infinitely many values!) • defines the probability that a random variable tak ...
Approximations for Probability Distributions and
... 1.1 Definition. A semi-distance on P is a function d(·, ·) on P ×P, which satisfies (i) and (ii) below. (i) Nonnegativity. For all P1 , P2 ∈ P d(P1 , P2 ) ≥ 0. (ii) Triangle Inequality. For all P1 , P2 , P3 ∈ P d(P1 , P2 ) ≤ d(P1 , P3 ) + d(P3 , P2 ). If a semi-distance satisfies the strictness prop ...
... 1.1 Definition. A semi-distance on P is a function d(·, ·) on P ×P, which satisfies (i) and (ii) below. (i) Nonnegativity. For all P1 , P2 ∈ P d(P1 , P2 ) ≥ 0. (ii) Triangle Inequality. For all P1 , P2 , P3 ∈ P d(P1 , P2 ) ≤ d(P1 , P3 ) + d(P3 , P2 ). If a semi-distance satisfies the strictness prop ...
MATHEMATICS WITHOUT BORDERS 2015
... We can place the first apple in the second place, in which case the places available for the second apple would be 4 to 8, i.e. 5 possibilities. We can place the first apple in the third place, in which case the places available for the second apple would be 5 to 8, i.e. 4 possibilities. We can plac ...
... We can place the first apple in the second place, in which case the places available for the second apple would be 4 to 8, i.e. 5 possibilities. We can place the first apple in the third place, in which case the places available for the second apple would be 5 to 8, i.e. 4 possibilities. We can plac ...
Doob: Half a century on - Imperial College London
... or stochastic processes remains what it was half a century ago – how to handle measure theory. (The present writer met an echo of this when examining recently in the University of Cambridge. Both measure theory and stochastic processes are in the curriculum - but, the numbers taking the first are ti ...
... or stochastic processes remains what it was half a century ago – how to handle measure theory. (The present writer met an echo of this when examining recently in the University of Cambridge. Both measure theory and stochastic processes are in the curriculum - but, the numbers taking the first are ti ...
![arXiv:math/0610716v2 [math.PR] 16 Feb 2007](http://s1.studyres.com/store/data/014486155_1-5585348474c4e163d9225232ca2e759f-300x300.png)
