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On direct and indirect probabilistic reasoning in legal proof1
On direct and indirect probabilistic reasoning in legal proof1

NBER WORKING PAPER SERiES THE DISTRIBUTION OF EXCHANGE RATES IN THE EMS
NBER WORKING PAPER SERiES THE DISTRIBUTION OF EXCHANGE RATES IN THE EMS

... rate is described by a mixture of normal distributions. The parameters of the distribution are the mean and variance in the stable state, p anda, and the mean and variance in the volatile state, p and o. In addition, there are ...
cowan_DESY_1 - Centre for Particle Physics
cowan_DESY_1 - Centre for Particle Physics

... frequentist analysis has to decide how many parameters are justified. In a Bayesian analysis we can insert as many parameters as we want, but constrain them with priors. Suppose e.g. based on a theoretical bias for things not too bumpy, that a certain parametrization ‘should hold to 2%’. How to tran ...
Chapter 4: Simple random samples and their properties
Chapter 4: Simple random samples and their properties

A Joint Characterization of Belief Revision Rules
A Joint Characterization of Belief Revision Rules

... Even under a pure ‘as if’interpretation of ascribed beliefs, highly sophisticated beliefs are dubious given the complexity of their behavioural implications (which may be hard to test empirically). ...
De Finetti and Savage on the normative relevance of imprecise
De Finetti and Savage on the normative relevance of imprecise

methods of the mathematical morphology of landscape
methods of the mathematical morphology of landscape

Inferences on the means of lognormal distributions using
Inferences on the means of lognormal distributions using

A POSSIBILITY THEOREM ON INFORMATION AGGREGATION IN
A POSSIBILITY THEOREM ON INFORMATION AGGREGATION IN

pdf
pdf

... via an active attack, and succeeding with probability ε(k). We will prove that ε(k) is negligible. We can view the adversary’s attack as follows: first, the adversary receives a public key y, where y = f (x) for random x ∈ {0, 1} k . Next, the adversary — playing the role of a verifier who may act i ...
Chapter 6 of notes  file
Chapter 6 of notes file

EM Demystified: An Expectation-Maximization
EM Demystified: An Expectation-Maximization

... Expectation-maximization (EM) is a method to find the maximum likelihood estimator of a parameter θ of a probability distribution. Let’s start with an example. Say that the probability of the temperature outside your window for each of the 24 hours of a day x ∈ R24 depends on the season θ ∈ {summer, ...
Bayesian Belief Network (BBN)
Bayesian Belief Network (BBN)

Bounding Bloat in Genetic Programming
Bounding Bloat in Genetic Programming

... is to always prefer the smaller of two trees, given equal fitness. Introducing this simple bloat control, [Neu12] was able to give tight bounds on the optimization time in the case of k = 1: in this setting, no new redundant leaves can be introduced. The hard part is now to give an analysis when k = ...
MODEL UNCERTAINTY
MODEL UNCERTAINTY

Lecture Notes - Kerala School of Mathematics
Lecture Notes - Kerala School of Mathematics

... Consider two isolated containers labeled as body A and body B, containing two different fluids. Let the total number of molecules of the two fluids, distributed in the containers A and B, be d, labeled as {1, 2, ..., d}. Let the observation be made on the number of the molecules in A. To start with, ...
I can`t define the niche but I know it when I see it: a formal link
I can`t define the niche but I know it when I see it: a formal link

... Figure 1. (A) Conceptual model of presence data. We may observe our study organism in the set of environments given by: NSM SR. From this we can infer that an environment occupied by the organism is a part of the niche, while a species may be absent because an environment is unsuitable, or unavailab ...
Introduction - ODU Computer Science
Introduction - ODU Computer Science

... – The boundary conditions may be complicated and no analytical techniques are available ...
Notes 17 - Wharton Statistics
Notes 17 - Wharton Statistics

Frequentism as a positivism: a three-tiered interpretation of probability
Frequentism as a positivism: a three-tiered interpretation of probability

Random Variables
Random Variables

Bayes` theorem
Bayes` theorem

... that there are just 10 balls in the machine. This is because the probability that “3” comes out given that balls 1-10 are in the machine is 10%, whereas the probability that this ball comes out given that balls numbered 1-10,000 are in the machine is only 0.01%. (Note that, whichever hypothesis you ...
Aristotle`s Logic Computed by Parametric Probability and Linear
Aristotle`s Logic Computed by Parametric Probability and Linear

... The problems in Aristotle’s Prior Analytics involve three categorical terms, called ‘major’, ‘middle’, and ‘minor’, each of which can be either true or false. Let us use A for the major term, B for the middle term, and C for the minor term. We abbreviate truth as T and falsity as F. The major and mi ...
Conditionals, Conditional Probabilities, and
Conditionals, Conditional Probabilities, and

Hypothesis Testing: How to Discriminate between Two Alternatives
Hypothesis Testing: How to Discriminate between Two Alternatives

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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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