Adjustment in several stages

Now suppose that we intend to adjust B sequentially by the collections of quantities . We define the cumulative collection

and denote the cumulative adjustment

We may `partial out' any stage of the adjustment, defining for any the partial adjustment of B by given as

Corresponding to the adjustment is the bearing . The bearing for the partial adjustment is

As before, we have

The bearing for the partial adjustment expresses the change in both magnitude and direction in beliefs between stages [j] and [i]. The stepwise partial adjustment, is

with bearing . We refer to the full sequence of stepwise adjusted bearings as the data trajectory. For each j we may write

We have therefore have that

where

So to examine the ways in which the individual terms combine to determine the revision we must consider

• the prior expectation for each change to assess which subcollections of data are expected to be informative;
• the individual adjusted bearings to identify the stages at which larger than expected changes in belief occur;
• the path correlations to see whether the evidence is internally supportive or contradictory.