Ch8, p.1
Point Estimation
• What is point estimation?
Example
6.1
(current across muscle cell membrane, TBp. 257258)
•
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 ShaoWei Cheng (NTHU, Taiwan)
Ch8, p.2
Example 6.2
(emission of alpha particles, TBp. 255256)
•
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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 Spring '11
 lisa
 Normal Distribution, Standard Deviation, Probability distribution, Probability theory, ShaoWei Cheng

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