Random Constraint Satisfaction
... CSP problems such as SAT and graph colorability (see [10]). Especially, for random instances of SAT, Mitchell, Selman and Levesque [29] pointed out that some distributions that are commonly used in such experiments are uninteresting since they generate formulas that are almost always very easy to sa ...
... CSP problems such as SAT and graph colorability (see [10]). Especially, for random instances of SAT, Mitchell, Selman and Levesque [29] pointed out that some distributions that are commonly used in such experiments are uninteresting since they generate formulas that are almost always very easy to sa ...
Test Martingales, Bayes Factors and p-Values
... The increasing importance of Bayesian philosophy and practice starting in the 1960s has made the likelihood ratio P (y)/Q(y) even more important. This ratio is now often called the Bayes factor for P against Q, because by Bayes’s theorem, we obtain the ratio of P ’s posterior probability to Q’s post ...
... The increasing importance of Bayesian philosophy and practice starting in the 1960s has made the likelihood ratio P (y)/Q(y) even more important. This ratio is now often called the Bayes factor for P against Q, because by Bayes’s theorem, we obtain the ratio of P ’s posterior probability to Q’s post ...
Conditionals, indeterminacy, and triviality
... (§1.1–1.2). In §1.3, I sketch my favored semantics for indicative conditionals and in §1.4 show how it resolves this indeterminacy problem. In §2, I turn to the various triviality proofs, splitting them into two kinds, and show how our semantics handles the resulting two problems of triviality. Perh ...
... (§1.1–1.2). In §1.3, I sketch my favored semantics for indicative conditionals and in §1.4 show how it resolves this indeterminacy problem. In §2, I turn to the various triviality proofs, splitting them into two kinds, and show how our semantics handles the resulting two problems of triviality. Perh ...
Introductory lecture notes on Markov chains and random walks
... generalisation takes us into the realm of Randomness. We will be dealing with random variables, instead of deterministic objects. Other examples of dynamical systems are the algorithms run, say, by the software in your computer. Some of these algorithms are deterministic, but some are stochastic.1 T ...
... generalisation takes us into the realm of Randomness. We will be dealing with random variables, instead of deterministic objects. Other examples of dynamical systems are the algorithms run, say, by the software in your computer. Some of these algorithms are deterministic, but some are stochastic.1 T ...
Contrast Functions for Blind Separation and Deconvolution of Sources
... in the case of instantaneous mixtures or a convolution in the case of convolutive mixtures. Thus, separation is always understood with the above indeterminacy attached, not in the sense of having extracted exactly the sources. Following Comon [1], we call a contrast function discriminating if it att ...
... in the case of instantaneous mixtures or a convolution in the case of convolutive mixtures. Thus, separation is always understood with the above indeterminacy attached, not in the sense of having extracted exactly the sources. Following Comon [1], we call a contrast function discriminating if it att ...
http://www.york.ac.uk/depts/maths/histstat/normal_history.pdf
... (2) J C Burkill and H Burkill, A Second Course in Mathematical Analysis, Cambridge: University Press 1970. (3) R Courant, Differential and Integral Calculus (2 volumes), London and Glasgow: Blackie 1934–6. (4) Copson, Theory of Functions of a Complex Variable, Oxford: Clarendon Press 1935. (5) A De ...
... (2) J C Burkill and H Burkill, A Second Course in Mathematical Analysis, Cambridge: University Press 1970. (3) R Courant, Differential and Integral Calculus (2 volumes), London and Glasgow: Blackie 1934–6. (4) Copson, Theory of Functions of a Complex Variable, Oxford: Clarendon Press 1935. (5) A De ...
Test martingales, Bayes factors, and p-values
... for which the reciprocal likelihood ratio Q(y)/P (y) is largest. (Here P (y) and Q(y) represent either probabilities assigned to y by the two hypotheses or, more generally, probability densities relative to a common reference measure.) If the observation y is a vector, say y1 . . . yt , where t con ...
... for which the reciprocal likelihood ratio Q(y)/P (y) is largest. (Here P (y) and Q(y) represent either probabilities assigned to y by the two hypotheses or, more generally, probability densities relative to a common reference measure.) If the observation y is a vector, say y1 . . . yt , where t con ...
Objective probability and the assessment of
... Just as it is a physical property of a glass that it will break when dropped, so it seems to be a physical property of a coin that it lands heads as often as tails. The suggestive terms ‘would be’ and ‘habit’ were used by C. S. Peirce to describe such characteristics.21 Things are a little more comp ...
... Just as it is a physical property of a glass that it will break when dropped, so it seems to be a physical property of a coin that it lands heads as often as tails. The suggestive terms ‘would be’ and ‘habit’ were used by C. S. Peirce to describe such characteristics.21 Things are a little more comp ...
Probability box
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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.