在流行病學研究上，利用計數資料來估計整個研究區域的疾病地圖是非常重要的議 題。我們在卜瓦松-對數常態模式的架構下，發展一時空模式，將經對數轉換後的條 件期望病例人數表示為數個基底函數的線性組合，將平均數與變異數估計問題視為 迴歸分析，利用傳統的Lasso法與group Lasso法來挑選適合的基底函數及估計平 均數與共變異數。此種方法能描繪平穩或非平穩過程，且在處理龐大的空間資料上， 能迅速有效地被運算。 In epidemiology, disease mapping using count data is a very important issue. Under a Poisson-lognormal model, we develop a spatial-temporal process. The log transformation of the conditional expected number of cases is decomposed as a linear combination of basis functions. The problem of mean and covariance estimations can be considered as a regression. A subset selection method of Lasso and group Lasso are used to choose a suitable subset of the basis functions and estimate the mean and covariances. This method can characterize either non-stationary or nearly stationary spatial processes, and is computationally efficient for large spatial data sets.
