  The proliferation of mobile devices has led to the collection of large
amounts of population data. This situation has prompted the need to utilize
this rich, multidimensional data in practical applications. In response to this
trend, we have integrated functional data analysis (FDA) and factor analysis to
address the challenge of predicting hourly population changes across various
districts in Tokyo. Specifically, by assuming a Gaussian process, we avoided
the large covariance matrix parameters of the multivariate normal distribution.
In addition, the data were both time and spatially dependent between districts.
To capture these characteristics, a Bayesian factor model was introduced, which
modeled the time series of a small number of common factors and expressed the
spatial structure through factor loading matrices. Furthermore, the factor
loading matrices were made identifiable and sparse to ensure the
interpretability of the model. We also proposed a Bayesian shrinkage method as
a systematic approach for factor selection. Through numerical experiments and
data analysis, we investigated the predictive accuracy and interpretability of
our proposed method. We concluded that the flexibility of the method allows for
the incorporation of additional time series features, thereby improving its
accuracy.
