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Mathematical Finance in discrete time
Mathematical Finance in discrete time

... Assumption. Unless explicitly mentioned, we shall assume that FT = F. We do not assume F0 to be necessarily the trivial σ-algebra (∅, Ω), although in many applications this is the case. For modeling asset prices we consider stochastic processes which are families of random variables, whose definitio ...
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Recurrence vs Transience: An introduction to random walks

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Springer Series in Statistics

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A multi-party protocol for constructing the public parameters
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Chapter 6: Continuous Probability Distributions
Chapter 6: Continuous Probability Distributions

Exponential Families and Mixture Families of Probability Distributions
Exponential Families and Mixture Families of Probability Distributions

When and why do people avoid unknown probabilities in decisions
When and why do people avoid unknown probabilities in decisions

Dynamic `frees: A Structured Variational Method Giving Efficient
Dynamic `frees: A Structured Variational Method Giving Efficient

... where the indicator variables are simply used to pick out the correct probabilities. The nodes (vertices) are split into a set VE and a set VH of evidential and non-evidential (hidden) nodes respectively. Likewise the corresponding node state indicator variables are denoted by XE and XH respectively ...
Epistemic Probability Logic Simplified
Epistemic Probability Logic Simplified

DNA fingerprinting for forensic identification: potential effects on data
DNA fingerprinting for forensic identification: potential effects on data

Bayesian Networks for Logical Reasoning
Bayesian Networks for Logical Reasoning

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Document

1342Lectures1to8.pdf
1342Lectures1to8.pdf

... A score is a datum collected by measurement or observation. Raw scores equal unchanged measurements or observations. This course deals mostly with quantitative samples which are numerical data sets. The data is collected via some measurement, each measurement being a particular datum or score. The s ...
Similarities and Differences in Computing with Words
Similarities and Differences in Computing with Words

(8 pages pdf)
(8 pages pdf)

... If instead of working with the scale-normalized mutual distances, we choose to work with the natural mutual distances, we must take into account the estimated scale parameter ^. The natural mutual distances are useful because these can be used to directly specify where to look for points in the ima ...
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Towards common-sense reasoning via conditional

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RANDOM MATCHING PROBLEMS ON THE COM- PLETE GRAPH

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Introduction to Probability 2nd Edition Problem

Probabilistic graphical models in artificial intelligence
Probabilistic graphical models in artificial intelligence

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Solved Problems - UT Mathematics

The Flawed Probabilistic Foundation of Law and Economics
The Flawed Probabilistic Foundation of Law and Economics

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Existence and construction of edge disjoint paths on

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Line-of-sight percolation

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Inductive probability

Inductive probability attempts to give the probability of future events based on past events. It is the basis for inductive reasoning, and gives the mathematical basis for learning and the perception of patterns. It is a source of knowledge about the world.There are three sources of knowledge: inference, communication, and deduction. Communication relays information found using other methods. Deduction establishes new facts based on existing facts. Only inference establishes new facts from data.The basis of inference is Bayes' theorem. But this theorem is sometimes hard to apply and understand. The simpler method to understand inference is in terms of quantities of information.Information describing the world is written in a language. For example a simple mathematical language of propositions may be chosen. Sentences may be written down in this language as strings of characters. But in the computer it is possible to encode these sentences as strings of bits (1s and 0s). Then the language may be encoded so that the most commonly used sentences are the shortest. This internal language implicitly represents probabilities of statements.Occam's razor says the ""simplest theory, consistent with the data is most likely to be correct"". The ""simplest theory"" is interpreted as the representation of the theory written in this internal language. The theory with the shortest encoding in this internal language is most likely to be correct.
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