Transcription of Chapter 8 The exponential family: Basics
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Chapter 8 The exponential family: Basics
Chapter 8 The exponential family: BasicsIn this Chapter we extend the scope of our modeling toolbox to accommodate a variety ofadditional data types, including counts, time intervals and rates. We introduce the expo-nential family of distributions, a family that includes the Gaussian, binomial, multinomial,Poisson, gamma, von Mises and beta distributions, as well as many others. In this chapterwe focus on unconditional models and in the following Chapter we show how these ideas canbe carried over to the setting of conditional first blush this Chapter may appear to involve a large dose of mathematical detail, butappearances shouldn t deceive most of the detail involves working out examples that showhow the exponential family formalism relates to more familiar material.
Lebesgue integration that standard calculus will suffice for an understanding of this chapter. In particular, in all of the examples that we will treat, ν will either be Lebesgue measure, in which case “ν(dx)” reduces to “dx” and the integral in Eq. (??) can be handled using standard multivariable calculus, or counting measure,
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