  We develop a fully Bayesian hierarchical model for trend filtering, itself a
new development in nonparametric, univariate regression. The framework more
broadly applies to the generalized lasso, but focus is on Bayesian trend
filtering. We compare two shrinkage priors, double exponential and generalized
double Pareto. A simulation study, comparing Bayesian trend filtering to the
original formulation and a number of other popular methods shows our method to
improve estimation error while maintaining if not improving coverage
probability. Two time series data sets demonstrate Bayesian trend filtering's
robustness to possible violations of its assumptions.
