Titlebook: Probability; Methods and measurem Anthony O’Hagan Book 1988 A. O’Hagan 1988 Parameter.probability.probability theory.Random variable.standa

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Book 1988, the per­ sonal (or subjective) view of probability is adopted throughout. Second, emphasis is placed on how values are assigned to probabilities in practice, i.e. the measurement of probabilities. The personal approach to probability is in many ways more natural than other current formulations, an

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Probability measurements,may not in practice obey the probability laws. Section 2.1 discusses true probabilities and measured probabilities, and considers the significance of the failure of measured probabilities to follow the probability laws. A new form of measurement, elaborative measurement, is introduced in Section 2.2

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,Bayes’ theorem,whenever You feel that a target probability would be easier to measure if You had some extra information. Bayes’ theorem, which we derive in Section 3.2, can be considered as having the opposite effect. It is useful when You feel You could measure probabilities accurately if some specific informatio

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Trials and deals,m a bag. If each ball is replaced in the bag before the next is drawn, then the draws are essentially identical and independent. Partitions of this kind are known as trials and are the subject of the first half of this chapter. Notions of independence are important here, and so we begin by extending

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Random variables,ber. It is convenient to be able to deal with the numbers themselves. A device which allows us to do this is the random variable. We can then operate easily with ideas such as the square of the number of tails in ten tosses, notions of an ‘average’ or ‘expected’ number of tails, and so on.

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Distribution theory,ons, their summaries and relationships between them. The first two sections develop theory concerning the families of standard distributions introduced in Section 5.8. Section 6.1 is concerned with ways of deriving the standard distributions as objective distributions in appropriate problems, and Se

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Continuous distributions,ndom variables of this type. However, it is more usual in many problem areas for random variables to vary continuously. The lifetime of a light-bulb, for instance, will not be an exact number of hours. The space between one possible value and the next is not one hour, one minute, one second or even