# Accession Number:

## AD0425901

# Title:

## ESTIMATING THE CURRENT MEAN OF A NORMAL DISTRIBUTION WHICH IS SUBJECTED TO CHANGES IN TIME,

# Descriptive Note:

# Corporate Author:

## STANFORD UNIV CALIF

# Personal Author(s):

# Report Date:

## 1963-10-31

# Pagination or Media Count:

## 42.0

# Abstract:

A tracking problem is considered. Observations are taken on the successive positions of an object traveling on a path, and it is desired to estimate its current position. The objective is to arrive at a simple formula which implicitly accounts for possible changes in direction and discounts observations taken before the latest change. To develop a reasonable procedure, a simpler problem is studied. Successive observations are taken on n independently and normally distributed random variables X sub 1, X sub 2, ..., X sub n with means mu sub 1, mu sub 2, ..., mu sub n and variance 1. Each mean mu sub i is equal to the preceding mean mu sub i-1 except when an occasional change takes place. The object is to estimate the current mean mu sub n. This problem is studied from a Bayesian point of view. An ad hoc estimator is described, which applies a combination of the A.M.O.C. Bayes estimator and a sequence of tests designed to locate the last time point of change. The various estimators are then compared by a Monte Carlo study of samples of size 9. This Bayesian approach seems to be more appropriate for the related problem of testing whether a change in mean has occurred. This test procedure is simpler than that used by Page. The power functions of the two procedures are compared. Author