We propose a fully Bayesian methodology for estimation of functions that have jump discontinuities. The proposed model is an extension of the LARK model, which enables functions to be represented by the small number of elements from an overcomplete system. In the proposed model, multiple kernels are used as the elements of an overcomplete system. Since these elements are composed of different types of functions such as Haar, Laplacian, and Gaussian kernel, the proposed model can estimate discontinuous as well as smooth functions without model selection. The location of jumps, the number of basis functions, and even the smoothness of the target function are automatically determined by the Levy random measure. A simulation study and a real data analysis illustrate that the proposed model performs better than the standard nonparametric methods for the estimation of discontinuous functions. Finally, we prove prior positivity of the model and show that the prior has sufficiently large support including discontinuous functions with a finite number of jumps.

中文翻译：

---

使用具有多个内核的超完备系统进行不连续函数的贝叶斯曲线拟合

我们提出了一种完全贝叶斯方法来估计具有跳跃间断的函数。所提出的模型是LARK模型的扩展，该模型使功能能够由过完备的系统中的少量元素表示。在提出的模型中，多个内核被用作超完备系统的元素。由于这些元素由不同类型的函数组成，例如Haar，Laplacian和Gaussian核，因此所提出的模型无需模型选择即可估算不连续函数和平滑函数。跳跃的位置，基函数的数量，甚至目标函数的平滑度都是由Levy随机度量自动确定的。仿真研究和实际数据分析表明，对于不连续函数的估计，该模型的性能优于标准非参数方法。最后，我们证明了该模型的先验正性，并表明该先验具有足够大的支持，包括具有有限跳数的不连续函数。