Discrete outcomes

Lecture "Advanced Econometrics (Part II)  Chapter 3: Discrete choice analysis  Binary outcome models" presentation of content: Discrete choice model, basic types of discrete values, the probability models, estimation and inference in binary choice model, binary choice models for panel data.
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Probability and statistics are concerned with events which occur by chance. Examples include occurrence of accidents, errors of measurements, production of defective and nondefective items from a production line, and various games of chance, such as drawing a card from a wellmixed deck, flipping a coin, or throwing a symmetrical sixsided die. In each case we may have some knowledge of the likelihood of various possible results, but we cannot predict with any certainty the outcome of any particular trial....
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With the ever increasing amounts of data in electronic form, the need for automated methods for data analysis continues to grow. The goal of machine learning is to develop methods that can automatically detect patterns in data, and then to use the uncovered patterns to predict future data or other outcomes of interest. Machine learning is thus closely related to the fields of statistics and data mining, but differs slightly in terms of its emphasis and terminology.
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The original motivation for writing this book was rather personal. The first author, in the course of his teaching career in the Department of Pure Mathematics and Mathematical Statistics (DPMMS), University of Cambridge, and St John’s College, Cambridge, had many painful experiences when good (or even brilliant) students, who were interested in the subject of mathematics and its applications and who performed well during their first academic year, stumbled or nearly failed in the exams. This led to great frustration, which was very hard to overcome in subsequent undergraduate years.
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The size of banks’ balance sheets and the maturity structure of assets and liabilities is key to the generation of liquidity. Taking the view that banks manage their assets and liabilities independently of each other overlooks the structural interdependence between the asset side and the liability side of the balance sheet.
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Responding to the challenge of [NAR], the National Council of Teachers of Mathematics (NCTM) convened its ﬁrst meeting in 1986 for the purpose of drafting a reform document. The NCTM Standards ([N1]) is the outcome. Such an abbreviated account of the genesis of the current reform is of course oversimpliﬁed. A Nation at Risk may have spawned the idea of reform, but what ultimately brought it to reality was the business commu nity.
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Chapter 1 Discrete Probability Distributions 1.1 Simulation of Discrete Probabilities Probability In this chapter, we shall ﬁrst consider chance experiments with a ﬁnite number of possible outcomes ω1 , ω2 , . . . , ωn . For example, we roll a die and the possible outcomes are 1, 2, 3, 4, 5, 6 corresponding to the side that turns up. We toss a coin with possible outcomes H (heads) and T (tails). It is frequently useful to be able to refer to an outcome of an experiment. For example, we might want to write the mathematical expression which gives the sum of...
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5 Contaminant Transport Modeling A useful approximation of realty or an intellectual toy? 5.1 INTRODUCTION A contaminant transport model is a workinprogress hypothesis. Contaminant transport models are useful because they simplify reality for the purpose of predicting outcomes. In environmental litigation, contaminant transport models are used to confirm or challenge the allegation that a contaminant release occurred at a discrete point in time based on the observed presence of a contaminant some distance from the source.
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Chapter 8 Law of Large Numbers 8.1 Law of Large Numbers for Discrete Random Variables We are now in a position to prove our ﬁrst fundamental theorem of probability. We have seen that an intuitive way to view the probability of a certain outcome is as the frequency with which that outcome occurs in the long run
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The outcomes are expressed as a twolevel model, with 1 major ‘Level 1’ outcomes, each being further defined by a set of more detailed ‘Level ’ outcomes. A further set of outcomes has been defined under the heading “Medical professionalism” – many of which are common to graduates of other disciplines in Higher Education. The Level 1 outcomes and ‘Medical professionalism’ are suitable for implementation as “curriculum themes”, and applications such as blueprinting of assessment programmes.
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