In this paper we study statistical inference for certain inverse problems. We go beyond mere estimation purposes and review and develop the construction of confidence intervals and confidence bands in some inverse problems, including deconvolution and the backward heat equation. Further, we...

An increasing trend in functional MRI experiments involves discriminating between experimental conditions on the basis of fine-grained spatial patterns extending across many voxels. Typically, these approaches have used randomized resampling to derive inferences. Here, we introduce an analytical...