Statistical Methods for Particle Physics
... In particle physics there are various elements of uncertainty: final theory not known, that’s why we search further theory is not deterministic, quantum mechanics random measurement errors, present even without quantum effects things we could know in principle but don’t, e.g. from limitations of cos ...
... In particle physics there are various elements of uncertainty: final theory not known, that’s why we search further theory is not deterministic, quantum mechanics random measurement errors, present even without quantum effects things we could know in principle but don’t, e.g. from limitations of cos ...
Probability, Markov Chains, Queues, and Simulation
... Example 1.5 The sample space derived from an experiment that consists of observing the number of email messages received at a government office in one day may be taken to be denumerable. The sample space is denumerable since we may tag each arriving email message with a unique integer n that denotes ...
... Example 1.5 The sample space derived from an experiment that consists of observing the number of email messages received at a government office in one day may be taken to be denumerable. The sample space is denumerable since we may tag each arriving email message with a unique integer n that denotes ...
The Fallacy of Placing Confidence in Confidence Intervals
... notes that there are a wide range of locations that are possible for the location of the hatch. Because the craft is 10 meters long, no bubble can originate more than 5 meters from hatch. Given two bubbles, the only possible locations for the hatch are within 5 meters of both bubbles. These values a ...
... notes that there are a wide range of locations that are possible for the location of the hatch. Because the craft is 10 meters long, no bubble can originate more than 5 meters from hatch. Given two bubbles, the only possible locations for the hatch are within 5 meters of both bubbles. These values a ...
Proceedings Version
... meaningful forecast testing may actually be possible. However, observe that an efficient forecaster that knows the algorithm for Nature cannot even pass the test of Fortnow and Vohra. This is because their algorithm for Nature keeps hidden state in the sense that after generating p and q, the algori ...
... meaningful forecast testing may actually be possible. However, observe that an efficient forecaster that knows the algorithm for Nature cannot even pass the test of Fortnow and Vohra. This is because their algorithm for Nature keeps hidden state in the sense that after generating p and q, the algori ...
On the round complexity of black-box constructions of
... and therefore does not apply when considering schemes that might use random oracles. In contrast, Theorem 1.2 does hold relative to any oracle, and in the case of Item 3 of Theorem 1.2, is black-box. This is important for two reasons: first, Proposition 1.6 does not say whether such constructions a ...
... and therefore does not apply when considering schemes that might use random oracles. In contrast, Theorem 1.2 does hold relative to any oracle, and in the case of Item 3 of Theorem 1.2, is black-box. This is important for two reasons: first, Proposition 1.6 does not say whether such constructions a ...
TRACTABLE AND CONSISTENT RANDOM GRAPH MODELS
... larger cliques, stars, etc., layered upon each other, all of which can depend on characteristics of the nodes involved. We show if such models are sufficiently sparse, parameter estimates are consistent and asymptotically normally distributed. Such sparse networks appear in many if not most applicat ...
... larger cliques, stars, etc., layered upon each other, all of which can depend on characteristics of the nodes involved. We show if such models are sufficiently sparse, parameter estimates are consistent and asymptotically normally distributed. Such sparse networks appear in many if not most applicat ...
What has been will be again : A Machine Learning Approach to the Analysis of Natural Language
... prede ned rules for each possible input sequence that represent one of the possible forms of human communication. This approach is also referred to as the knowledge-based or knowledge-engineering approach. There are situations where a xed prescribed set of rules suce to perform a limited task. For ...
... prede ned rules for each possible input sequence that represent one of the possible forms of human communication. This approach is also referred to as the knowledge-based or knowledge-engineering approach. There are situations where a xed prescribed set of rules suce to perform a limited task. For ...
local pdf - University of Oxford
... diversification between two risky positions should always reduce risk. Artzner et al. [1] pointed out that VaR does not, in general, satisfy the subadditivity property, especially when the portfolio contains derivative instruments. Föllmer and Schied [22] and Frittelli and Rosazza Gianin [24] argue ...
... diversification between two risky positions should always reduce risk. Artzner et al. [1] pointed out that VaR does not, in general, satisfy the subadditivity property, especially when the portfolio contains derivative instruments. Föllmer and Schied [22] and Frittelli and Rosazza Gianin [24] argue ...
Probabilistic Networks — An Introduction to Bayesian Networks and
... known as arcs and edges) between the nodes. Any pair of unconnected/nonadjacent nodes of such a graph indicates (conditional) independence between the variables represented by these nodes under particular circumstances that can easily be read from the graph. Hence, probabilistic networks capture a s ...
... known as arcs and edges) between the nodes. Any pair of unconnected/nonadjacent nodes of such a graph indicates (conditional) independence between the variables represented by these nodes under particular circumstances that can easily be read from the graph. Hence, probabilistic networks capture a s ...
How to Delegate Computations: The Power of No
... The problem of delegating computation considers a setting where one party, the delegator (or verifier), wishes to delegate the computation of a function f to another party, the worker (or prover). The challenge is that the delegator may not trust the worker, and thus it is desirable to have the work ...
... The problem of delegating computation considers a setting where one party, the delegator (or verifier), wishes to delegate the computation of a function f to another party, the worker (or prover). The challenge is that the delegator may not trust the worker, and thus it is desirable to have the work ...
Lecture Notes CH. 2 - Electrical and Computer Engineering
... of non-negative integers {0, 1, 2, ...}. Then the indexed family of r.v’s {Xt (ω)}t∈T is said to be a stochastic process. This means that for each fixed t ∈ T , Xt (ω) defines a random variable. If T is an interval of < then Xt (ω) is said to be a continuous one-parameter stochastic process. Usually ...
... of non-negative integers {0, 1, 2, ...}. Then the indexed family of r.v’s {Xt (ω)}t∈T is said to be a stochastic process. This means that for each fixed t ∈ T , Xt (ω) defines a random variable. If T is an interval of < then Xt (ω) is said to be a continuous one-parameter stochastic process. Usually ...
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.