### Citation:

barnett, B. N. 91962) 'Problems in probability theory : properties of decision boundaries of some Bayesian sequential sampling procedures obtained by dynamic programming. PhD thesis, Institute of mathematics and Physics (Statistics), Aberystwyth University

### Abstract:

Some sequential sampling problems where there in one
unknown parameter in a generating stochastic process are
considered by Bayesian concepts with the aid of Dynamic
Programming equations. Some properties of the boundaries
between the sets of points in the observation sample space
corrosponding to each terminal decision and the continuation
decision are found. The economics of the problems are considered by using
the Bayesian idea of a prior distribution with accompanying
utilities for the possible decisions and a cost of sampling.
Problems whose sample space consist of an enumerable
number of points are considered first. The last part considers
some problems with a non-enumerable sample space and the
properties of the boundaries are much more difficult to obtain.