
	Where results make sense

Topic: Upper and lower probabilities

Related Topics

Lower Saxony

Lower Canada

Lower Silesian Voivodship

Lower Silesia

Lower Austria

Lower Hutt

Lower Peninsula of Michigan

lower house

Lower East Side

Lower Silesian

Lower New York Bay

Lower Mainland

In the News (Fri 17 Feb 12)

EXECUTIVE POWER

Iran

ANALYSIS

Pakistan

Family compact

	Bayesian probability - Wikipedia, the free encyclopedia
		Bayesianism is the philosophical tenet that the mathematical theory of probability applies to the degree of plausibility of a statement.
		This is in contrast to frequentism, which rejects degree-of-belief interpretations of mathematical probability, and assigns probabilities only to random events according to their relative frequencies of occurrence.
		The Bayesian approach is in contrast to the concept of frequency probability where probability is held to be derived from observed or imagined frequency distributions or proportions of populations.
	en.wikipedia.org /wiki/Bayesian_probability (1665 words)

	Info and facts on 'Bayesian probability' (Site not responding. Last check: 2007-10-18)
		The Bayesian approach is in contrast to the concept of frequency probability (additional info and facts about frequency probability) where probability is held to be derived from observed or imagined frequency distributions or proportions of populations.
		According to the frequency probability (additional info and facts about frequency probability) definition, however, the laws of probability (additional info and facts about laws of probability) are not applicable to this problem.
		One criticism which has been levelled at the Bayesian probability interpretation is that the probability itself cannot convey how much evidence ((law) all the means by which any alleged matter of fact whose truth is investigated at judicial trial is established or disproved) one has.
	www.absoluteastronomy.com /encyclopedia/b/ba/bayesian_probability.htm (1663 words)

	Talk:List of probability topics - Wikipedia, the free encyclopedia
		Move up to subsection C any categories which the bot should search for missing articles in the List of probability topics.
		The entries above are meant to be carefully read by a person and put them in the list of probability topics as appropriate.
		If there is probability content to the Law, it ought to be added there, really, before a link from here.
	en.wikipedia.org /wiki/Talk:List_of_probability_topics (427 words)

	[No title]
		Probabilities of upper-tercile flows are diminished in southern California, in the southern Great Basin, in New England, and especially in the upper Mississippi and Ohio River basins.
		Probabilities of upper-tercile flows are diminished from the southwestern states to Iowa, along the western Gulf Coast, in peninsular Florida, and in New England.
		Figure 4: Anomalous probabilities of occurrence of a maximum-daily flow during October 1999 to September 2000 that is among the upper tercile of historical annual maximum-daily flows; same coloring and scaling as in Figure 1.
	grads.iges.org /ellfb/Dec99/dettinger.htm (1646 words)

	Lower Probability, Choquet Capacities and Belief Functions
		The example about lower envelopes shows that not every lower probability is a lower envelope, i.e., not every lower probability is the representation of a set of distributions.
		30] that says that the set of probability distributions that dominates a lower probability is a closed convex polyhedron (possibly empty) in the simplex of all probability measures.
		The set of probability distributions that create the lower envelope is exactly the set of all probability distributions that dominate the 2-monotone lower probability.
	www.cs.cmu.edu /~qbayes/Tutorial/Introduction/node7.html (1124 words)

	INTERFERENCE OF LIGHT - Online Information article about INTERFERENCE OF LIGHT
		The intensity of the resultant will of course depend upon the precise manner in which the phases are distributed, and may vary from n' to zero.
		For example, the probability of intensity less than n is •6321.
		ray, perpendicular to the wave-front, reflected at the upper surface, ABCDE the ray transmitted at B, reflected at C and transmitted at D; and these are accompanied by other rays reflected internally 3, 5, andc., times.
	encyclopedia.jrank.org /I27_INV/INTERFERENCE_OF_LIGHT.html (9560 words)

	Upper and Lower Previsions (Site not responding. Last check: 2007-10-18)
		This is an introduction to the concepts of lower and upper prevision and the mathematical theory of coherence.
		Because upper and lower previsions have a simple behavioural interpretation, it is easy to understand the practical meaning of conclusions that are expressed in terms of them, and to use them in making decisions.
		Choquet integrals) of lower probabilities that are 2-monotone.
	ippserv.rug.ac.be /documentation/upper_lower_prev/upper_lower_prev.html (4329 words)

	RAMAS Constructor
		Probabilities entered must be between zero and one in each row, however the probabilities across rows need not add to one.
		A variant of probability theory in which the elements of the probability space to which nonzero mass is attributed, called focal elements, are not singletons but rather sets which represent the indistinguishability of alternatives within bodies of evidence.
		Theories of imprecise probabilities are often expressed in terms of a lower probability measure giving the lower probability for every possible event from some universal set, or in terms of closed convex sets of probability distributions.
	www.ramas.com /constructor.htm (3927 words)

	Autobiography of Patrick Suppes, p. 9
		The formal theory of such upper and lower probabilities in qualitative terms is very similar to the framework for extensive quantities developed in my first paper in 1951.
		The source of the difficulty is that in the case of expectations we move from the relatively simple properties of subadditive and superadditive upper and lower measures to multiplicative problems as in the characteristic expression for expected utility in which utilities and probabilities are multiplied and then added.
		It is easy to give a simple counterexample to straightforward generalization of the results for upper and lower probabilities, and this is done in Suppes (l975a).
	www.stanford.edu /~psuppes/autobio9.html (679 words)

	6.9 Multiple upper-lower classes
		upper sets exist that satisfy the main conditions, i.e., there are no transitions among sets of the same type (except, of course, through the boundary set), there are transitions only from the upper sets to the lower sets, and communication from the lower sets to the upper sets can occur only through the boundary set
		Observe that the new ``upper'' CTMC is composed by the
		To illustrate the idea of the multiple lower and upper sets, we give an example of applying Algorithm 6.9.
	www.cs.wm.edu /~riska/PhD-thesis-html/node89.html (729 words)

	Upper and Lower Bounds on Overflow Probabilities for a Multiplexer with Multiclass Markovian Sources - Artiges, Nain ... (Site not responding. Last check: 2007-10-18)
		Upper and Lower Bounds on Overflow Probabilities for a Multiplexer with Multiclass Markovian Sources (1995)
		We do not assume that the model is symmetrical: there is an arbitrary number K of different traffic classes, and for each class k, an arbitrary number N k of sources of class k.
		10.6%: Upper and Lower Bounds for the Multiplexing of Multiclass..
	citeseer.ist.psu.edu /293399.html (540 words)

	New SAS Functions for Computing Probabilities
		The PDF function computes probability density and mass functions for continuous and discrete distributions, and the LOGPDF function computes the logarithm of the probability density function.
		The SDF function computes the upper tail of a specified distribution, also known as the survivor distribution function.
		Consider calculating an upper tail probability for a random variable X that is distributed as chi-squared with 100 degrees of freedom.
	support.sas.com /rnd/app/da/new/probabilityfunctions.html (422 words)

	Fine.html (Site not responding. Last check: 2007-10-18)
		He is currently a member of the Executive Committee of the Society for Imprecise Probability: Theory and Applications.
		With the exception of the period 1989 to 1999, when I was concerned with the theory of artificial feedforward neural networks and their applications to problems of forecasting demand for electrical power and emitter location and sensor arrays, I have focussed on issues in the foundations of probability.
		In particular I have been interested in comparative probability that need not have an additive representation, upper and lower probabilities that are not envelopes of a set of measures, and most recently on probability as an arbitrary set of standard probability measures.
	people.ece.cornell.edu /tlfine/bio.html (460 words)

	math lessons - Bayesian probability
		Bayesianism is the philosophical tenet that the mathematical theory of probability applies to the degree of plausibility of statements, or to the degree of belief of rational agents in the truth of statements; when used with Bayes theorem, it then becomes Bayesian inference.
		Whereas a frequentist and a Bayesian might both assign probability 1/2 to the event of getting a head when a coin is tossed, only a Bayesian might assign probability 1/1000 to personal belief in the proposition that there was life on Mars a billion years ago, without intending to assert anything about any relative frequency.
		One criticism which has been levelled at the Bayesian probability interpretation is that the probability itself cannot convey how much evidence one has.
	www.mathdaily.com /lessons/Bayesian_probability (1403 words)

	Graphical Models
		Probability theory provides the glue whereby the parts are combined, ensuring that the system as a whole is consistent, and providing ways to interface models to data.
		Unfortunately, the method of first computing the full joint probability distribution, and then marginalizing out the unwanted nodes, takes time which is exponential in the number of nodes.
		The goal is to infer the posterior probability of each disease given all the symptoms (which can be present, absent or unknown).
	www.cs.ubc.ca /~murphyk/Bayes/bayes.html (6598 words)

	Lower and upper bounds for time-smoothed total transition probabilities and their rates
		A formalism of time-smoothed total transition probabilities and their rates is developed which employs Laplace averages of these quantities.
		Rigorous lower and upper bounds are obtained for the Laplace-averaged quantities which reduce to equalities for two-level systems.
		The lower bounds appear to be potentially useful estimating lower bounds for total cross sections of various processes.
	stacks.iop.org /0305-4470/9/931 (232 words)

	1967
		One suggestion is to take the product of the spaces, form the probability system on the product, and them map the system to S using the diagonal mapping.
		Intuitively, the upper probability measures which points in X could possibly be mapped in the set in S. The lower probability measures, which points in X must be mapped in the set in S. The paper also defines compatible probability measures that are in between the upper and lower probability measures:
		This paper proposed logit to estimate the probability of an Event and a numerical procedure for estimating the function based on Kalman updating.
	www.io.com /~slava/history/1967.htm (556 words)

	SfS - The proper fiducial argument
		It argues that far from being a quaint, little, isolated idea, this was the first attempt to build a bridge between aleatory probabilities (the only ones used by Neyman) and epistemic probabilities (the only ones used by Bayesians), by implicitly introducing, as a new type, frequentist epistemic probabilities.
		Some (partly rather unknown) reactions by other statisticians are discussed, and some rudiments of a new, unifying general theory of statistics are given which uses upper and lower probabilities and puts fiducial probability into a larger framework.
		Then Fisher's pertaining 1930 paper is being reread in the light of present understanding, followed by some short sections on the (legitimate) aposteriori interpretation of confidence intervals, and on fiducial probabilities as limits of lower probabilities.
	stat.ethz.ch /research/research_reports/2003/114 (232 words)

	Amazon.com: Scientific Reasoning: The Bayesian Approach: Books: Colin Howson,Peter Urbach (Site not responding. Last check: 2007-10-18)
		In this clearly reasoned defense of Bayes's Theorem — that probability can be used to reasonably justify scientific theories — Colin Howson and Peter Urbach examine the way in which scientists appeal to probability arguments, and demonstrate that the classical approach to statistical inference is full of flaws.
		Much of this book will strike students of classical probability theory and philosophy of science as very counter-intuitive at first, but it is so well argued and so clear that I think most readers will begin to warm up to the Bayesian view at least to some degree by the time they finish the book.
		If you've ever wondered exactly what the Bayesian approach to probability is, and what it is supposed to offer science, or you've ever been dissatisfied with the traditional answers to the problem of induction, this book will be your welcome friend for a number of evenings.
	www.amazon.com /exec/obidos/tg/detail/-/0812692357?v=glance (1634 words)

	[No title]
		A: An upper bound of two nodes a and b is a third node c such that a
		A: It uses upper and lower probabilities induced by a multivalued mapping.
		Lower probabilities are epistemic probabilities - degrees of belief.
	www-sal.cs.uiuc.edu /~csgso/qual/ai-ref.txt (16602 words)

	Glenn Shafer - A Mathematical Theory of Evidence (Site not responding. Last check: 2007-10-18)
		In the spring of 1971, I attended a course on statistical inference taught by Arthur Dempster at Harvard.
		In the fall of that same year Geoffrey Watson suggested I give a talk expositing Dempster's work on upper and lower probabilities to the Department of Statistics at Princeton.
		It offers a reinterpretation of Dempster's work, a reinterpretation that identifies his "lower probabilities" as epistemic probabilities or degrees of belief, takes the rule for combining such degrees of belief as fundamental, and abandons the idea that they arise as lower bounds over classes of Bayesian probabilities.
	www.glennshafer.com /books/amte.html (348 words)

	Combination Calculi for Uncertainty Reasoning: Representing Uncertainty Using Distributions (ResearchIndex) (Site not responding. Last check: 2007-10-18)
		A common component to these methods is the use of additional values, other than conditional probabilities, to assert current degrees of belief and certainties in propositions.
		Beginning with the viewpoint that these values can be associated with statistics of multiple opinions in an evidential reasoning system, we categorize the choices that are available in updating and tracking these multiple...
		154 Upper and lower probabilities induced by a multivalued mappi..
	citeseer.lcs.mit.edu /67084.html (574 words)

	[No title] (Site not responding. Last check: 2007-10-18)
		Next, NSL was modified by requiring that each HCP assertion be scaled; this means that to each HCP assertion was associated a bound on the deviation from 1 of the conditional probability that is the subject of the assertion.
		This paper describes a new approach to bounding the results of arithmetic operations on random variables when the dependency relationship between the variables is unspecified.
		Three replies are advanced: that priors are imprecise or of little weight, that it is possible to distinguish reasonable from unreasonable priors on logical grounds; and that disagreement about priors can usually be explained by differences in background information.
	ippserv.rug.ac.be /biblio/ipp.bib (731 words)

	Upper Probabilities Based Only on the Likelihood Function - Walley, Moral (ResearchIndex) (Site not responding. Last check: 2007-10-18)
		Abstract: In the problem of parametric statistical inference with a finite parameter space, we study some simple rules for defining posterior upper and lower probabilities directly from the observed likelihood function, without using any prior probabilities.
		The rules satisfy the likelihood principle and a basic consistency principle ("avoiding sure loss"), they produce vacuous inferences when the likelihood function is constant, and they have other symmetry, monotonicity and continuity properties.
		Walley, P., and Moral, S. Upper probabilities based only on the likelihood function.
	citeseer.ist.psu.edu /226204.html (562 words)

	ME290M, Spring 1999, Week 5a (Site not responding. Last check: 2007-10-18)
		In the 1960’s Dempster [1967] introduced the notions of upper and lower probabilities, which were not additive, for dealing with incomplete data.
		Shafer built on the Dempster model and interpreted these upper and lower probabilities as degrees of plausibility and belief, respectively and introduced the approach to uncertainty management sometimes referred to as "Dempster-Shafer" theory.
		One distinction of this theory is that it does not require a prior probability for each individual event, but a prior measure of "belief" to classes of events.
	best.me.berkeley.edu /~aagogino/me290m/s99/Week7a/Week7a.html (2332 words)

	Decision Analysis Society - Working Paper Abstract Archive (Site not responding. Last check: 2007-10-18)
		Suppose that a probability measure P is known to lie in a set of probability measures M. Upper and lower bounds on the probability of any event may then be computed.
		Sometimes, the bounds on the probability of an event A conditional on an event B may strictly contain the bounds on the unconditional probability of A. Surprisingly, this might happen for every B in a partition B. If so, we say that dilation has occurred.
		In addition to being an interesting statistical curiosity, this counterintuitive phenomenon has important implications in robust Bayesian inference and in the theory of upper and lower probabilities.
	faculty.fuqua.duke.edu /daweb/wp920820.htm (154 words)

	watson_system science
		Introduction to basic concepts of probability theory, Bayes theorem, probability distributions, point estimation and confidence interval inference from data, and test of hypothesis.
		Prerequisites: SSIE 561 and probability and statistics, or consent of department chair.
		Some useful models and strategies for assessing imprecise probability are introduced, and some applications to probabilistic reasoning, statistical inference and decision are discussed.
	www.binghamton.edu /bulletin/2000-2001/watson-ss.html (4897 words)

	Uncertainty and Vagueness in Knowledge Based Systems (Site not responding. Last check: 2007-10-18)
		The problem in learning inference networks is to decompose a multi-dimensional probability or possibility distribution in distributions on lower-dimensional spaces, which approximate the overall distribution as good as possible.
		In classical methods, measures from probability or information theory are used to select relevant features.
		Therefore we also analyze approaches that are based on Shafer´s evidence theory (belief functions), on possibility theory, or on the theory on upper and lower probabilities.
	fuzzy.cs.uni-magdeburg.de /uncert.html (350 words)

Try your search on: Qwika (all wikis)