Page 104 - Statistics and Data Analysis in Geology

Statistics and Data Analysis in Geology - Chapter 4

Step 1. Initial estimate of transition frequency matrix, with 1000 inserted in
each diagonal position.

A- 1000 13 36 19 52 1120
B 29 1000 5 4 0 1038
from c 35 2 1000 45 12 1094
D 29 1 44 1000 3 1077
E- 26 23 9 9 1000 1067
5397 Grand Total

Step 2. Estimate of transition probabilities of diagonal elements, found by
dividing row totals by grand total.

to
Row
A B C D E - Totals
A 0.208 0.208
B 0.192 0.192
from C 0.203 0.203
D 0.200 0.200
E 0.198 - 0.198

Step 3. Square the probabilities along the diagonal.
Step 4. Second estimate of transition frequency matrix using new diagonal
elements calculated by multiplying probabilities on the diagonal by the grand total
of 5397. Off-diagonal terms are the original observed frequencies. New row totals
and grand total are then found
to
Row
A B C D E Totals
A 232 13 36 19 52 352
B 29 199 5 4 0 237
from C 35 2 222 45 12 316
D 29 1 44 215 3 292
E - 26 23 9 9 211 278
1475 Grand Total

The process is repeated again and again, until the estimated transition frequen-
cies along the diagonal do not change from time to time. This generally requires
about 10 to 20 iterations, depending upon how closely the initial guesses were to
the final, stable estimates. In this example, the estimates do not change after 10
iterations.
The final form of the transition frequency matrix with estimated diagonal fre-
quencies is given below.

176