Modelling Noise and Imprecision in Individual Decisions Graham
... Most theories of decision making under risk are expressed in deterministic form, as if an individual’s preferences are precise, stable and consistent with some ‘core’ of axioms or well-defined components (such as a utility function and/or a probability weighting function). Interpreted literally, the ...
... Most theories of decision making under risk are expressed in deterministic form, as if an individual’s preferences are precise, stable and consistent with some ‘core’ of axioms or well-defined components (such as a utility function and/or a probability weighting function). Interpreted literally, the ...
A simple D2-sampling based PTAS for k-means
... this problem turns out to be NP-hard even for k = 2 [13]. One very popular heuristic for solving the k-means problem is the Lloyd’s algorithm [22]. The heuristic is as follows : start with an arbitrary set of k centers as seeds. Based on these k centers, partition the set of points into k clusters, ...
... this problem turns out to be NP-hard even for k = 2 [13]. One very popular heuristic for solving the k-means problem is the Lloyd’s algorithm [22]. The heuristic is as follows : start with an arbitrary set of k centers as seeds. Based on these k centers, partition the set of points into k clusters, ...
(pdf)
... = P (Xi = −ej ). That is, each step of given by ∀j ∈ {1, . . . , d}, P (Xi = ej ) = 2d the random walk has an equal chance of moving 1 unit in any of the 2d cardinal directions and never moves anywhere else. In this case, given any x ∈ Zd , there is at least one possible path from the origin to x in ...
... = P (Xi = −ej ). That is, each step of given by ∀j ∈ {1, . . . , d}, P (Xi = ej ) = 2d the random walk has an equal chance of moving 1 unit in any of the 2d cardinal directions and never moves anywhere else. In this case, given any x ∈ Zd , there is at least one possible path from the origin to x in ...
Reducing belief simpliciter to degrees of belief
... operator for belief. So the closure of the set of believed propositions under logical consequence is taken as a given; in particular, if A is a logical truth, then A is believed; if A is believed, and A logically implies B, then B is believed; and if both A and B are believed, then also A ∧ B is bel ...
... operator for belief. So the closure of the set of believed propositions under logical consequence is taken as a given; in particular, if A is a logical truth, then A is believed; if A is believed, and A logically implies B, then B is believed; and if both A and B are believed, then also A ∧ B is bel ...
LAB1
... Shaped Curve" or Normal distribution) applies to areas as far ranging as economics and physics. Below are two statements of the Central Limit Theorem (C.L.T.). I) "If an overall random variable is the sum of many random variables, each having its own arbitrary distribution law, but all of them being ...
... Shaped Curve" or Normal distribution) applies to areas as far ranging as economics and physics. Below are two statements of the Central Limit Theorem (C.L.T.). I) "If an overall random variable is the sum of many random variables, each having its own arbitrary distribution law, but all of them being ...
Are Lock-Free Concurrent Algorithms Practically Wait
... probabilistic scheduler model different from the one considered in this paper. The observation that many lock-free algorithms behave as wait-free in practice was made by Herlihy and Shavit in the context of formalizing minimal and maximal progress conditions [12], and is well-known among practitione ...
... probabilistic scheduler model different from the one considered in this paper. The observation that many lock-free algorithms behave as wait-free in practice was made by Herlihy and Shavit in the context of formalizing minimal and maximal progress conditions [12], and is well-known among practitione ...
ON BERNOULLI DECOMPOSITIONS FOR RANDOM VARIABLES
... The bounds were further improved in a series of works, in particular [Es, K, R2] where use was also made of other methods. One may note here that perhaps quite naturally a general method like the Bernoulli decomposition is not optimized for specific applications. Nevertheless, it has the benefit of ...
... The bounds were further improved in a series of works, in particular [Es, K, R2] where use was also made of other methods. One may note here that perhaps quite naturally a general method like the Bernoulli decomposition is not optimized for specific applications. Nevertheless, it has the benefit of ...
Common Core Lesson Tracker Mathematics Grade 7 Ratios and
... CCSS.Math.Content.7.SP.C.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event tha ...
... CCSS.Math.Content.7.SP.C.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event tha ...
Textbook Chapter 9 File
... (b) If no letter or digit can be repeated, then we can fill in the first blank 26 ways, the second blank 25 ways, the third blank 24 ways, the fourth blank 10 ways, the fifth blank 9 ways, and the sixth blank 8 ways. By the Multiplication Principle, we can fill in all six blanks in 26 25 24 10 ...
... (b) If no letter or digit can be repeated, then we can fill in the first blank 26 ways, the second blank 25 ways, the third blank 24 ways, the fourth blank 10 ways, the fifth blank 9 ways, and the sixth blank 8 ways. By the Multiplication Principle, we can fill in all six blanks in 26 25 24 10 ...
The researcher and the consultant: a dialogue on null hypothesis
... Researcher But how did I decide that ‘‘no association’’ is my null hypothesis and that 5 % is my highest tolerable probability of mistakenly rejecting it if it is true? Consultant In the original formulation of hypothesis testing [20] [21] substantive considerations were used to select the hypothesi ...
... Researcher But how did I decide that ‘‘no association’’ is my null hypothesis and that 5 % is my highest tolerable probability of mistakenly rejecting it if it is true? Consultant In the original formulation of hypothesis testing [20] [21] substantive considerations were used to select the hypothesi ...
Probability interpretations
The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure the real, physical tendency of something to occur or is it a measure of how strongly one believes it will occur, or does it draw on both these elements? In answering such questions, mathematicians interpret the probability values of probability theory.There are two broad categories of probability interpretations which can be called ""physical"" and ""evidential"" probabilities. Physical probabilities, which are also called objective or frequency probabilities, are associated with random physical systems such as roulette wheels, rolling dice and radioactive atoms. In such systems, a given type of event (such as the dice yielding a six) tends to occur at a persistent rate, or ""relative frequency"", in a long run of trials. Physical probabilities either explain, or are invoked to explain, these stable frequencies. Thus talking about physical probability makes sense only when dealing with well defined random experiments. The two main kinds of theory of physical probability are frequentist accounts (such as those of Venn, Reichenbach and von Mises) and propensity accounts (such as those of Popper, Miller, Giere and Fetzer).Evidential probability, also called Bayesian probability (or subjectivist probability), can be assigned to any statement whatsoever, even when no random process is involved, as a way to represent its subjective plausibility, or the degree to which the statement is supported by the available evidence. On most accounts, evidential probabilities are considered to be degrees of belief, defined in terms of dispositions to gamble at certain odds. The four main evidential interpretations are the classical (e.g. Laplace's) interpretation, the subjective interpretation (de Finetti and Savage), the epistemic or inductive interpretation (Ramsey, Cox) and the logical interpretation (Keynes and Carnap).Some interpretations of probability are associated with approaches to statistical inference, including theories of estimation and hypothesis testing. The physical interpretation, for example, is taken by followers of ""frequentist"" statistical methods, such as R. A. Fisher, Jerzy Neyman and Egon Pearson. Statisticians of the opposing Bayesian school typically accept the existence and importance of physical probabilities, but also consider the calculation of evidential probabilities to be both valid and necessary in statistics. This article, however, focuses on the interpretations of probability rather than theories of statistical inference.The terminology of this topic is rather confusing, in part because probabilities are studied within a variety of academic fields. The word ""frequentist"" is especially tricky. To philosophers it refers to a particular theory of physical probability, one that has more or less been abandoned. To scientists, on the other hand, ""frequentist probability"" is just another name for physical (or objective) probability. Those who promote Bayesian inference view ""frequentist statistics"" as an approach to statistical inference that recognises only physical probabilities. Also the word ""objective"", as applied to probability, sometimes means exactly what ""physical"" means here, but is also used of evidential probabilities that are fixed by rational constraints, such as logical and epistemic probabilities.It is unanimously agreed that statistics depends somehow on probability. But, as to what probability is and how it is connected with statistics, there has seldom been such complete disagreement and breakdown of communication since the Tower of Babel. Doubtless, much of the disagreement is merely terminological and would disappear under sufficiently sharp analysis.