03_Estimation_part1

03_Estimation_part1 - Point Estimation What is point...

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Ch8, p.1 Point Estimation • What is point estimation? Example 6.1 (current across muscle cell membrane, TBp. 257-258) Bevan, Kullberg, and Rice (1979) studied random f uctuations of cur- rent across a muscle cell membrane. The cell membrane contained a large number of channels, which opened and closed at random and were assumed to operate independently. The net current resulted from ions f owing through open channels. They obtained 49,152 observations of the net current, x 1 ,...,x 49152 . The net current was the sum of a large number of roughly independent small currents. It seems appropriate to model the net current data, X 1 ,...,X 49152 as i.i.d. N ( μ , σ 2 ), where μ and σ 2 represent the mean and variance of net current. Note that the values of μ and σ 2 are unknown. Question: how to use the observed data, x 1 ,...,x 49152 to gain knowl- edge about the values of μ and σ 2 ? made by Shao-Wei Cheng (NTHU, Taiwan) Ch8, p.2 Example 6.2 (emission of alpha particles, TBp. 255-256) Berkson (1966) conducted an experiment about emission of alpha par- ticles from radioactive sources. The number of emissions per unit of time is not constant but f uctuates in a random fashion. The experimenter recorded 10,220 times between successive emissions. The numbers of emissions, x i , i =1 ,..., 1027 , observed in 1207 time intervals, each of length 10 sec, are summarized in the following table: x i { 0 , 1 , 2 } x i =3 x i =4 ··· 18 28 56 ··· e.g., in 28 of the 1207 intervals, there were 3 counts, etc. Assume (1) the underlying rate of emission is constant over the pe- riod of observation (2) the particles come from a very large number of independent sources It seems appropriate to model the numbers of emissions X 1 ,...,X 1027 as i.i.d. P ( λ ), where λ represents the underlying rate of emission. Note
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03_Estimation_part1 - Point Estimation What is point...

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