Multiscale Poisson Data Smoothing
提出一个针对泊松数据的非线性多尺度分解框架，通过条件化观测总和，使经典小波阈值方法可应用于泊松数据，并引入贝叶斯收缩方法，相比现有技术显著降低均方误差。
Summary The paper introduces a framework for non-linear multiscale decompositions of Poisson data that have piecewise smooth intensity curves. The key concept is conditioning on the sum of the observations that are involved in the computation of a given multiscale coefficient. Within this framework, most classical wavelet thresholding schemes for data with additive homoscedastic noise can be used. Any family of wavelet transforms (orthogonal, biorthogonal or second generation) can be incorporated in this framework. Our second contribution is to propose a Bayesian shrinkage approach with an original prior for coefficients of this decomposition. As such, the method combines the advantages of the Haar–Fisz transform with wavelet smoothing and (Bayesian) multiscale likelihood models, with additional benefits, such as extendability towards arbitrary wavelet families. Simulations show an important reduction in average squared error of the output, compared with the present techniques of Anscombe or Fisz variance stabilization or multiscale likelihood modelling.