Banburismus revisited: depths and Bayes

Abstract

Chapter 13 covered all aspects of Banburismus, but without much of the mathematical and other detail. This chapter seeks to explain depth, Bayes’ theorem, logarithmic scoring (and its application to the Banburies discovered in the roof of Hut 6), decibanning, chains and depth cribbing, comic strips, and twiddling. This seems to be the first publication of much of this explanation. In Chapter 13 I promised a simple illustrative example of depth and some of the terms associated with it. In Table 38.1 QVAJX . . . and the others are three enciphered messages as transmitted. This table does not relate to any particular real-life cipher, and its three enciphered messages are unrealistically short. It illustrates an imaginary system which enciphers letter by letter (as Enigma did), using an enciphering table which would provide hundreds, or more probably thousands, of individual enciphering units, whatever the nature of the imaginary enciphering system. The numbers 180, 181, . . . indicate the positions of the units in the table. The encipherer could choose where in the table to begin enciphering (say, at position 183) and, once started, continued to use the enciphering units in sequence (183, 184, 185, . . .). The legitimate receiver of the message had to be told where to start in the table. This was done by an ‘indicator’, which was itself enciphered, usually by a different system, and formed part of a preamble to the message as transmitted. The three enciphered messages in this example, which may have come from different sources, start at different positions in the enciphering table. They have significant overlaps, and it is where they overlap that they are said to be ‘in depth’. Here the depths are of two messages (as in column 182) or of three (column 183). In real life they could be of ten or twenty. All the letters in a particular column (as QDF in column 183) have been enciphered in exactly the same way.

Inferring the differences in incubation-period and generation-interval distributions of the Delta and Omicron variants of SARS-CoV-2

“…We calculate time-varying growth rates from each parameter set and use equi-tailed quantiles to generate 95% confidence limits. We note that this method of calculating confidence intervals gives point-wise confidence intervals, meaning that the confidence intervals give 95% coverage for the set of estimates at each time point; these intervals are narrower than simultaneous confidence intervals, which give 95% coverage for the set of estimated time series across the whole time period [7].…”