S231 Lecture 4 Cyntha

S231 Lecture 4 Cyntha

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Unformatted text preview: infected. Statistics and Actuarial Science () Model Fitting, Estimation and Checking Jan 2013 19 / 45 HIV example. Suppose Y represents the number of persons infected with the human immunode...ciency virus (HIV) in a randomly selected group of n persons. Modelled by Binomial P (Y = y ; ) = f (y ; ) = n y (1 y )n y for y = 0, 1, . . . , n where is the fraction of the population that are infected. In a random sample of n persons tested for HIV, y = y is the observed number infected. n L( ) = (y ) y (1 ^ = y /n. )n y for 0 < < 1 is maximized by the value Statistics and Actuarial Science () Model Fitting, Estimation and Checking Jan 2013 19 / 45 HIV example. Suppose Y represents the number of persons infected with the human immunode...ciency virus (HIV) in a randomly selected group of n persons. Modelled by Binomial P (Y = y ; ) = f (y ; ) = n y (1 y )n y for y = 0, 1, . . . , n where is the fraction of the population that are infected. In a random sample of n persons tested for HIV, y = y is the observed number infected. n L( ) = (y ) y (1 ^ = y /n. )n y for 0 < < 1 is maximized by the value If n is large and is very small, we might prefer to model Y using the Poisson() distribution with = n. Why is this reasonable? Statistics and Actuarial Science () Model Fitting, Estimation and Checking Jan 2013 19 / 45 If you' a likelihood value, (relative) size matters: re The shape of L( ) and its maximum value are not aected if we multiply L( ) by a constant. Relative value at two dierent values of the parameter, e.g. L( 1 )/L( 2 ) is important. It determines how much more or less consistent the data is with the parameter 1 versus 2 . Statistics and Actuarial Science () Model Fitting, Estimation and Checking Jan 2013 20 / 45 If you' a likelihood value, (relative) size matters: re The shape of L( ) and its maximum value are not aected if we multiply L( ) by a constant. Relative value at two dierent values of the parameter, e.g. L( 1 )/L( 2 ) is important. It determines how much more or...
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This note was uploaded on 04/17/2013 for the course STAT 231 taught by Professor Cantremember during the Winter '08 term at Waterloo.

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