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The proliferation of mobile devices has led to the collection of largeamounts of population data. This situation has prompted the need to utilizethis rich, multidimensional data in practical applications. In response to thistrend, we have integrated functional data analysis (FDA) and factor analysis toaddress the challenge of predicting hourly population changes across variousdistricts in Tokyo. Specifically, by assuming a Gaussian process, we avoidedthe 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, whichmodeled the time series of a small number of common factors and expressed thespatial structure through factor loading matrices. Furthermore, the factorloading matrices were made identifiable and sparse to ensure theinterpretability of the model. We also proposed a Bayesian shrinkage method asa systematic approach for factor selection. Through numerical experiments anddata analysis, we investigated the predictive accuracy and interpretability ofour proposed method. We concluded that the flexibility of the method allows forthe incorporation of additional time series features, thereby improving itsaccuracy.

Spatiotemporal factor models for functional data with application to population map forecast