The synoptic problem is concerned with hypotheses about the relationships between the synoptic gospels of Matthew, Mark and Luke. The use of statistics in the study of the synoptic problem goes back to the end of the nineteenth century, but the study of the statistics of verbal agreements between Matthew, Mark and Luke began with the work of Honoré (1968). Apart from the well-known two-source model, where Matthew and Luke have Mark and a hypothetical Q as sources, there are many models of the relationships between the synoptic gospels that do not require the existence of a Q source.
In the work presented here, under the assumption of Markan priority, the text of Mark is examined word by word to record if the word is retained unchanged by Matthew and Luke, respectively. This results in a pair of binary series, series of 0s and 1s, where a 1 is recorded if the word has been retained and a 0 if not.
The main focus here is on the question of whether Matthew and Luke were independent in their use of Mark, as is assumed in the standard two-source model. The statistical technique that uses hidden Markov models is outlined and some of its results presented. One of the products of the analysis is the identification of passages where the evidence for dependence between Matthew and Luke in their use of Mark appears to be strongest. These passages may then be examined to see precisely how the apparent dependence manifests itself in the text and to draw conclusions.