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... example, we may be interested in predicting whether a person is a potential money-launderer based on their bank deposits, international travel, business connections and arrest records of known associates [Jensen, 1997]. In another case, we may be interested in classifying web pages as belonging to a ...
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What Conditional Probability Must (Almost)

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Wed 2012-04-11 - Mathematics

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Bayesian Belief Network

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Function Identification in Neuron Populations via Information

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Bayesian and frequentist approaches

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The Optimal Sample Complexity of PAC Learning

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Mutations of intermediate effect are responsible for adaptation in

... shown by the size of the competitive advantage that evolved genotypes held over the ancestor (mean SZ2.09, tZ16.25, d.f.Z67, p!0.0001). The advantage varied substantially across genotypes (FZ2.71, d.f.Z67, p!0.0001, s.d.Z1.06), with an observed range of 0.20–5.19. The estimated selection coefficient ...
Bayesian Probability
Bayesian Probability

... decision problem, there is no fact as to which option maximizes expected utility with Proposal 4. There are nevertheless rational and irrational choices in many such situations. For example, I think most people’s degree of belief in getting two sixes in 24 tosses of a pair of dice is too vague for t ...
Why should one expect to find long runs of (non)
Why should one expect to find long runs of (non)

2012 ISAC Journal Maximum Likelihood
2012 ISAC Journal Maximum Likelihood

... to this question may not be found in all cases, in the case of random sampling it can be answered with the help of probability theory. In sampling theory, we are primarily concerned with this very question. The process of going from known sample information to an unknown population is called statist ...
The relative frequency interpretation of probability
The relative frequency interpretation of probability

What Conditional Probability Must (Almost) Be
What Conditional Probability Must (Almost) Be

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Weak Convergence

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Predictability of a CD4 Count Predictions Based on CD4 Counts

... and reaction to the drug will be the same, so the blood pressures will form two bell curves that will probably overlap quite a bit. The question that can be asked is whether the two bell curves are statistically different. If they are then it can be concluded that the drug worked. Technically the qu ...
CONDITIONAL EXPECTATION Definition 1. Let (Ω,F,P) be a
CONDITIONAL EXPECTATION Definition 1. Let (Ω,F,P) be a

CONDITIONAL EXPECTATION Definition 1. Let (Ω,F,P) be a
CONDITIONAL EXPECTATION Definition 1. Let (Ω,F,P) be a

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Reasoning with Limited Resources and Assigning Probabilities to

... human being is possessed with an infinite mind, which is able to see all kinds of connections within the corpus of physical data, a mind that can survey all possible patterns and all sorts of theories that can account for the phenomena. This is a creature whose conceptual space, whose goals, beliefs ...
Reasoning with Limited Resources and
Reasoning with Limited Resources and

... human being is possessed with an infinite mind, which is able to see all kinds of connections within the corpus of physical data, a mind that can survey all possible patterns and all sorts of theories that can account for the phenomena. This is a creature whose conceptual space, whose goals, beliefs ...
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Lecture 2: Random variables in Banach spaces

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Probability and Stochastic Processes

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THE FIRST-DIGIT PHENOMENON A century

... are also a very good fit to Benford’s law (Figure 1). The skeptical reader is encouraged to perform a simple experiment such as listing all the numbers occurring on the front pages of several local newspapers, or randomly selecting data from “a Farmer’s Alamack,” as Knuth suggests. In the 60 years s ...
On independent sets in purely atomic probability spaces with
On independent sets in purely atomic probability spaces with

... with s, t ∈ N s, t ≥ 2, one can check that the sets A := {1, 2, 3, . . . , s}, B := {1, s+1, 2s+1 . . . , (t−1)s+1} represent non-trivial independent events. To match the uniform distribution situation it would be interesting if Gn was a dependent space for every prime n. The class of independent se ...
STOCHASTIC PROCESSES Basic notions
STOCHASTIC PROCESSES Basic notions

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Probability box



A probability box (or p-box) is a characterization of an uncertain number consisting of both aleatoric and epistemic uncertainties that is often used in risk analysis or quantitative uncertainty modeling where numerical calculations must be performed. Probability bounds analysis is used to make arithmetic and logical calculations with p-boxes.An example p-box is shown in the figure at right for an uncertain number x consisting of a left (upper) bound and a right (lower) bound on the probability distribution for x. The bounds are coincident for values of x below 0 and above 24. The bounds may have almost any shapes, including step functions, so long as they are monotonically increasing and do not cross each other. A p-box is used to express simultaneously incertitude (epistemic uncertainty), which is represented by the breadth between the left and right edges of the p-box, and variability (aleatory uncertainty), which is represented by the overall slant of the p-box.
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