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We introduce a multiscale test statistic based on local order statistics and spacings that provides simultaneous confidence statements for the existence and location of local increases and decreases of a density or a failure rate. The procedure provides guaranteed finite-sample significance levels, is easy to implement and possesses certain asymptotic optimality and adaptivity properties.
Given a collection of computational models that all estimate values of the same natural process, we compare the performance of the average of the collection to the individual member whose estimates are nearest a given set of observations. Performance
Inspired by sample splitting and the reusable holdout introduced in the field of differential privacy, we consider selective inference with a randomized response. We discuss two major advantages of using a randomized response for model selection. Fir
In many applications it is desirable to infer coarse-grained models from observational data. The observed process often corresponds only to a few selected degrees of freedom of a high-dimensional dynamical system with multiple time scales. In this wo
We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective equation d
Selective inference is a recent research topic that tries to perform valid inference after using the data to select a reasonable statistical model. We propose MAGIC, a new method for selective inference that is general, powerful and tractable. MAGIC