  In a bag-of-words model, the senses of a word with multiple meanings, e.g.
"bank" (used either in a river-bank or an institution sense), are represented
as probability distributions over context words, and sense prevalence is
represented as a probability distribution over senses. Both of these may change
with time. Modelling and measuring this kind of sense change is challenging due
to the typically high-dimensional parameter space and sparse datasets. A
recently published corpus of ancient Greek texts contains expert-annotated
sense labels for selected target words. Automatic sense-annotation for the word
"kosmos" (meaning decoration, order or world) has been used as a test case in
recent work with related generative models and Monte Carlo methods. We adapt an
existing generative sense change model to develop a simpler model for the main
effects of sense and time, and give MCMC methods for Bayesian inference on all
these models that are more efficient than existing methods. We carry out
automatic sense-annotation of snippets containing "kosmos" using our model, and
measure the time-evolution of its three senses and their prevalence. As far as
we are aware, ours is the first analysis of this data, within the class of
generative models we consider, that quantifies uncertainty and returns credible
sets for evolving sense prevalence in good agreement with those given by expert
annotation.
