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An introduction to probability theory and its applications

01 Jan 1950-
About: The article was published on 1950-01-01 and is currently open access. It has received 31532 citations till now. The article focuses on the topics: Probability and statistics & Imprecise probability.
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Proceedings ArticleDOI
23 May 1998
TL;DR: In this paper, the authors present two algorithms for the approximate nearest neighbor problem in high-dimensional spaces, for data sets of size n living in R d, which require space that is only polynomial in n and d.
Abstract: We present two algorithms for the approximate nearest neighbor problem in high-dimensional spaces. For data sets of size n living in R d , the algorithms require space that is only polynomial in n and d, while achieving query times that are sub-linear in n and polynomial in d. We also show applications to other high-dimensional geometric problems, such as the approximate minimum spanning tree. The article is based on the material from the authors' STOC'98 and FOCS'01 papers. It unifies, generalizes and simplifies the results from those papers.

4,478 citations

Journal ArticleDOI
TL;DR: In this paper, the subjective probability of an event, or a sample, is determined by the degree to which it is similar in essential characteristics to its parent population and reflects the salient features of the process by which it was generated.

4,231 citations

Journal ArticleDOI
TL;DR: In this article, the adequacy of a mixing specification can be tested simply as an omitted variable test with appropriately definedartificial variables, and a practicalestimation of aarametricmixingfamily can be run by MaximumSimulated Likelihood EstimationorMethod ofSimulatedMoments, andeasilycomputedinstruments are provided that make the latter procedure fairly eAcient.
Abstract: SUMMARY Thispaperconsidersmixed,orrandomcoeAcients,multinomiallogit (MMNL)modelsfordiscreteresponse, andestablishesthefollowingresults.Undermildregularityconditions,anydiscretechoicemodelderivedfrom random utility maximization has choice probabilities that can be approximated as closely as one pleases by a MMNLmodel.PracticalestimationofaparametricmixingfamilycanbecarriedoutbyMaximumSimulated LikelihoodEstimationorMethodofSimulatedMoments,andeasilycomputedinstrumentsareprovidedthat make the latter procedure fairly eAcient. The adequacy of a mixing specification can be tested simply as an omittedvariabletestwithappropriatelydefinedartificialvariables.Anapplicationtoaproblemofdemandfor alternativevehiclesshowsthatMMNL provides aflexible and computationally practical approach todiscrete response analysis. Copyright # 2000 John Wiley & Sons, Ltd.

3,967 citations

Book ChapterDOI
TL;DR: This chapter reproduces the English translation by B. Seckler of the paper by Vapnik and Chervonenkis in which they gave proofs for the innovative results they had obtained in a draft form in July 1966 and announced in 1968 in their note in Soviet Mathematics Doklady.
Abstract: This chapter reproduces the English translation by B. Seckler of the paper by Vapnik and Chervonenkis in which they gave proofs for the innovative results they had obtained in a draft form in July 1966 and announced in 1968 in their note in Soviet Mathematics Doklady. The paper was first published in Russian as Вапник В. Н. and Червоненкис А. Я. О равномерноЙ сходимости частот появления событиЙ к их вероятностям. Теория вероятностеЙ и ее применения 16(2), 264–279 (1971).

3,939 citations

Journal ArticleDOI
TL;DR: It is found that user-initiated TCP session arrivals, such as remote-login and file-transfer, are well-modeled as Poisson processes with fixed hourly rates, but that other connection arrivals deviate considerably from Poisson.
Abstract: Network arrivals are often modeled as Poisson processes for analytic simplicity, even though a number of traffic studies have shown that packet interarrivals are not exponentially distributed. We evaluate 24 wide area traces, investigating a number of wide area TCP arrival processes (session and connection arrivals, FTP data connection arrivals within FTP sessions, and TELNET packet arrivals) to determine the error introduced by modeling them using Poisson processes. We find that user-initiated TCP session arrivals, such as remote-login and file-transfer, are well-modeled as Poisson processes with fixed hourly rates, but that other connection arrivals deviate considerably from Poisson; that modeling TELNET packet interarrivals as exponential grievously underestimates the burstiness of TELNET traffic, but using the empirical Tcplib interarrivals preserves burstiness over many time scales; and that FTP data connection arrivals within FTP sessions come bunched into "connection bursts", the largest of which are so large that they completely dominate FTP data traffic. Finally, we offer some results regarding how our findings relate to the possible self-similarity of wide area traffic. >

3,915 citations