Nonparametric maximum likelihood approach to multiple change-point problems

In multiple change-point problems, different data segments often follow different distributions, for which the changes may occur in the mean, scale or the entire distribution from one segment to another. Without the need to know the number of change-points in advance, we propose a nonparametric maximum likelihood approach to detecting multiple change-points. Our method does not impose any parametric assumption on the underlying distributions of the data sequence, which is thus suitable for detection of any changes in the distributions. The number of change-points is determined by the Bayesian information criterion and the locations of the change-points can be estimated via the dynamic programming algorithm and the use of the intrinsic order structure of the likelihood function. Under some mild conditions, we show that the new method provides consistent estimation with an optimal rate. We also suggest a prescreening procedure to exclude most of the irrelevant points prior to the implementation of the nonparametric likelihood method. Simulation studies show that the proposed method has satisfactory performance of identifying multiple change-points in terms of estimation accuracy and computation time.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1210 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Zipper: Addressing degeneracy in algorithm-agnostic inference

The widespread use of black box prediction methods has sparked an increasing interest in algorithm/model-agnostic approaches for quantifying goodness-of-fit, with direct ties to specification testing, model selection and variable importance assessment. A commonly used framework involves defining a predictiveness criterion, applying a cross-fitting procedure to estimate the predictiveness, and utilizing the difference in estimated predictiveness between two models as the test statistic. However, even after standardization, the test statistic typically fails to converge to a non-degenerate distribution under the null hypothesis of equal goodness, leading to what is known as the degeneracy issue. To addresses this degeneracy issue, we present a simple yet effective device, Zipper. It draws inspiration from the strategy of additional splitting of testing data, but encourages an overlap between two testing data splits in predictiveness evaluation. Zipper binds together the two overlapping splits using a slider parameter that controls the proportion of overlap. Our proposed test statistic follows an asymptotically normal distribution under the null hypothesis for any fixed slider value, guaranteeing valid size control while enhancing power by effective data reuse. Finite-sample experiments demonstrate that our procedure, with a simple choice of the slider, works well across a wide range of settings

Selective Conformal Inference with FCR Control

Conformal inference is a popular tool for constructing prediction intervals (PI). We consider here the scenario of post-selection/selective conformal inference, that is PIs are reported only for individuals selected from an unlabeled test data. To account for multiplicity, we develop a general split conformal framework to construct selective PIs with the false coverage-statement rate (FCR) control. We first investigate the Benjamini and Yekutieli (2005)'s FCR-adjusted method in the present setting, and show that it is able to achieve FCR control but yields uniformly inflated PIs. We then propose a novel solution to the problem, named as Selective COnditional conformal Predictions (SCOP), which entails performing selection procedures on both calibration set and test set and construct marginal conformal PIs on the selected sets by the aid of conditional empirical distribution obtained by the calibration set. Under a unified framework and exchangeable assumptions, we show that the SCOP can exactly control the FCR. More importantly, we provide non-asymptotic miscoverage bounds for a general class of selection procedures beyond exchangeablity and discuss the conditions under which the SCOP is able to control the FCR. As special cases, the SCOP with quantile-based selection or conformal p-values-based multiple testing procedures enjoys valid coverage guarantee under mild conditions. Numerical results confirm the effectiveness and robustness of SCOP in FCR control and show that it achieves more narrowed PIs over existing methods in many settings

Evaluation of Analgesic and Anti-Inflammatory Activities of Water Extract of Galla Chinensis In Vivo

Aim. Pain and inflammation are associated with many diseases in humans and animals. Galla Chinensis, a traditional Chinese medicine, has a variety of pharmacological properties. The purpose of this study was to evaluate analgesic and anti-inflammatory activities of Galla Chinensis through different animal models. Method. The analgesic activities were evaluated by hot-plate and writhing tests. The anti-inflammatory effects were assessed by ear edema, capillary permeability, and paw edema tests. The contents of cytokines (NO, iNOS, PGE2, and IL-10) in serum of rats in paw edema test were inspected by ELISA assays. Results. In the hot-plate test, Galla Chinensis could significantly extend pain threshold when compared to control group. The inhibitory rates of writhes ranged from 36.62% to 68.57% in Galla Chinensis-treated mice. Treatment with Galla Chinensis (1 and 0.5 g/kg) could significantly inhibit ear edema (47.45 and 36.91%, resp.; P < 0.01). Galla Chinensis (1 g/kg) had significant (P < 0.05) anti-inflammatory activity in capillary permeability test (29.04%). In carrageenan-induced edema test, the inhibitory rates were 43.71% and 44.07% (P < 0.01) at 1 h and 2 h after administration of Galla Chinensis (1 g/kg), respectively, and the levels of proinflammatory cytokines were significantly reduced. Conclusion. These results suggest that Galla Chinensis has analgesic and anti-inflammatory effects, which may be a candidate drug for the treatment of inflammation and pain

In Vivo

Aim. Dermatophytosis is one of the main fungal diseases in humans and animals all over the world. Galla chinensis, a traditional medicine, has various pharmacological effects. The goal of this study was to evaluate the treatment effect of Galla chinensis solution (GCS) on dermatophytosis-infected dogs (Microsporum canis, Microsporum gypseum, and Trichophyton mentagrophytes, resp.). Methods. The treatment effects of GCS were evaluated by mycological cure rates and clinical score comprised of three indices, including inflammation, hair loss, and lesion scale. Results. The results showed that, in the three models of dermatophytosis, GCS significantly (P<0.05) improved skin lesions and fungal eradication. GCS (10% and 5%) had higher efficacy compared to the positive control (Tujingpi Tincture). The fungal eradication efficacy exceeds 85% after treatment with GCS (10%, 5%, and 2.5%) on day 14. Conclusion. The GCS has antidermatophytosis effect in dogs, which may be a candidate drug for the treatment of dermatophytosis