Page 91 - Classification Parameter Estimation & State Estimation An Engg Approach Using MATLAB

80 PARAMETER ESTIMATION

9. If, without having observed z, the parameter x in exercise 8 is uniformly distributed
between 0 and 1, what will be the posterior density p(xjz)of x? Develop the MMSE
estimator and the MAP estimator for this case. What will be the bias and the variance
of these estimators? ( )
10. A Geiger counter is an instrument that measures radioactivity. Essentially, it counts
the number of events (arrival of nuclear particles) within a given period of time.
These numbers are Poisson distributed with expectation , i.e. the mean number of
events within the period. z is the counted number of events within a period. We
assume that is uniform distributed between 0 and L.
. Develop the ML estimator for . (0)
. Develop the MAP estimator for . What is the bias and the variance of the ML
estimator? ( )
. Show that the ML estimator is absolutely unbiased, and that the MAP estimator is
biased. ( )
. Give an expression for the (overall) variance of the ML estimator. (0)