  We develop a flexible spline-based Bayesian hidden Markov model stochastic
weather generator to statistically model daily precipitation over time by
season at individual locations. The model naturally accounts for missing data
(considered missing at random), avoiding potential sensitivity from systematic
missingness patterns or from using arbitrary cutoffs to deal with missingness
when computing metrics on daily precipitation data. The fitted model can then
be used for inference about trends in arbitrary measures of precipitation
behavior, either by multiple imputation of the missing data followed by
frequentist analysis or by simulation from the Bayesian posterior predictive
distribution. We show that the model fits the data well, including a variety of
multi-day characteristics, indicating fidelity to the autocorrelation structure
of the data. Using three stations from the western United States, we develop
case studies in which we assess trends in various aspects of precipitation
(such as dry spell length and precipitation intensity), finding only limited
evidence of trends in certain seasons based on the use of Sen's slope as a
nonparametric measure of trend. In future work, we plan to apply the method to
the complete set of GHCN stations in selected regions to systematically assess
the evidence for trends.
