Topic

# Event (probability theory)

About: Event (probability theory) is a research topic. Over the lifetime, 7151 publications have been published within this topic receiving 120866 citations.

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TL;DR: A mathematical model is developed to provide a theoretical framework for a computer-oriented solution to the problem of recognizing those records in two files which represent identical persons, objects or events.

Abstract: A mathematical model is developed to provide a theoretical framework for a computer-oriented solution to the problem of recognizing those records in two files which represent identical persons, objects or events (said to be matched). A comparison is to be made between the recorded characteristics and values in two records (one from each file) and a decision made as to whether or not the members of the comparison-pair represent the same person or event, or whether there is insufficient evidence to justify either of these decisions at stipulated levels of error. These three decisions are referred to as link (A 1), a non-link (A 3), and a possible link (A 2). The first two decisions are called positive dispositions. The two types of error are defined as the error of the decision A 1 when the members of the comparison pair are in fact unmatched, and the error of the decision A 3 when the members of the comparison pair are, in fact matched. The probabilities of these errors are defined as and respecti...

2,306 citations

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TL;DR: It is demonstrated that a simple adjustment to the cross-sectional techniques produces appropriate rejection rates when the null is true and equally powerful tests when it is false.

1,743 citations

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TL;DR: A recursive approach based on Kalman's work in linear dynamic filtering and prediction is applied, derivable also from the work of Swerling (1959), which provides an example of many other possible uses of recursive techniques in nonlinear estimation and in related areas.

Abstract: SUMMARY A method for estimating the probability of occurrence of an event from dichotomous or polychotomous data is developed, using a recursive approach. The method in the dichotomous case is applied to the data of a 10-year prospective study of coronary disease. Other areas of application are briefly indicated. The purpose of this paper is to develop a method for estimating from dichotomous (quantal) or polychotomous data, the probability of occurrence of an event as a function of a relatively large number of independent variables. A key feature of the method is a recursive approach based on Kalman's work (Kalman, 1960 and unpublished report) in linear dynamic filtering and prediction, derivable also from the work of Swerling (1959), which provides an example of many other possible uses of recursive techniques in nonlinear estimation and in related areas. The problem that motivated the investigation is a central one in the epidemiology of coronary heart disease, and it will be used to fix ideas and illustrate the method. Some indication of the range of applications will be given in the conclusion.

1,662 citations

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04 Dec 2017

TL;DR: Probability theory as mentioned in this paper is a framework and tools to quantify and predict the chance of occurrence of an event in the presence of uncertainties, and also provides a logical way to make decisions in situations where the outcomes are uncertain.

Abstract: This chapter focuses on the basic results and illustrate the theory with several numerical examples. Probability theory essentially provides a framework and tools to quantify and predict the chance of occurrence of an event in the presence of uncertainties. Probability theory also provides a logical way to make decisions in situations where the outcomes are uncertain. Probability theory has widespread applications in a plethora of different fields such as financial modeling, weather prediction, and engineering. The literature on probability theory is rich and extensive. The proofs of the major results are not provided and relegated to the references. While there are many different philosophical approaches to define and derive probability theory, Kolmogorov's axiomatic approach is the most widely used. This axiomatic approach begins by defining a small number of precise axioms or postulates and then deriving the rest of the theory from these postulates.

1,563 citations

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TL;DR: This book proposes a unified mathematical treatment of a class of 'linear' discrete event systems, which contains important subclasses of Petri nets and queuing networks with synchronization constraints, which is shown to parallel the classical linear system theory in several ways.

Abstract: This book proposes a unified mathematical treatment of a class of 'linear' discrete event systems, which contains important subclasses of Petri nets and queuing networks with synchronization constraints. The linearity has to be understood with respect to nonstandard algebraic structures, e.g. the 'max-plus algebra'. A calculus is developed based on such structures, which is followed by tools for computing the time behaviour to such systems. This algebraic vision lays the foundation of a bona fide 'discrete event system theory', which is shown to parallel the classical linear system theory in several ways.

1,424 citations