  The histogram method is a powerful non-parametric approach for estimating the
probability density function of a continuous variable. But the construction of
a histogram, compared to the parametric approaches, demands a large number of
observations to capture the underlying density function. Thus it is not
suitable for analyzing a sparse data set, a collection of units with a small
size of data. In this paper, by employing the probabilistic topic model, we
develop a novel Bayesian approach to alleviating the sparsity problem in the
conventional histogram estimation. Our method estimates a unit's density
function as a mixture of basis histograms, in which the number of bins for each
basis, as well as their heights, is determined automatically. The estimation
procedure is performed by using the fast and easy-to-implement collapsed Gibbs
sampling. We apply the proposed method to synthetic data, showing that it
performs well.
