ROBUST KULLBACK-LEIBLER DIVERGENCE AND ITS APPLICATIONS IN UNIVERSAL HYPOTHESIS TESTING AND DEVIATION DETECTION

The Kullback-Leibler (KL) divergence is one of the most fundamental metrics in information theory and statistics and provides various operational interpretations in the context of mathematical communication theory and statistical hypothesis testing. The KL divergence for discrete distributions has the desired continuity property which leads to some fundamental results in universal hypothesis testing. With continuous observations, however, the KL divergence is only lower semi-continuous; difficulties arise when tackling universal hypothesis testing with continuous observations due to the lack of continuity in KL divergence. This dissertation proposes a robust version of the KL divergence for continuous alphabets. Specifically, the KL divergence defined from a distribution to the Levy ball centered at the other distribution is found to be continuous. This robust version of the KL divergence allows one to generalize the result in universal hypothesis testing for discrete alphabets to that for continuous observations. The optimal decision rule is developed whose robust property is provably established for universal hypothesis testing. Another application of the robust KL divergence is in deviation detection: the problem of detecting deviation from a nominal distribution using a sequence of independent and identically distributed observations. An asymptotically -optimal detector is then developed for deviation detection where the Levy metric becomes a very natural distance measure for deviation from the nominal distribution. Lastly, the dissertation considers the following variation of a distributed detection problem: a sensor may overhear other sensors\u27 transmissions and thus may choose to refine its output in the hope of achieving a better detection performance. While this is shown to be possible for the fixed sample size test, asymptotically (in the number of samples) there is no performance gain, as measured by the KL divergence achievable at the fusion center, provided that the observations are conditionally independent. For conditionally dependent observations, however, asymptotic detection performance may indeed be improved when overhearing is utilized

Spike detection using the continuous wavelet transform

This paper combines wavelet transforms with basic detection theory to develop a new unsupervised method for robustly detecting and localizing spikes in noisy neural recordings. The method does not require the construction of templates, or the supervised setting of thresholds. We present extensive Monte Carlo simulations, based on actual extracellular recordings, to show that this technique surpasses other commonly used methods in a wide variety of recording conditions. We further demonstrate that falsely detected spikes corresponding to our method resemble actual spikes more than the false positives of other techniques such as amplitude thresholding. Moreover, the simplicity of the method allows for nearly real-time execution

Forecasting trends with asset prices

In this paper, we consider a stochastic asset price model where the trend is an unobservable Ornstein Uhlenbeck process. We first review some classical results from Kalman filtering. Expectedly, the choice of the parameters is crucial to put it into practice. For this purpose, we obtain the likelihood in closed form, and provide two on-line computations of this function. Then, we investigate the asymptotic behaviour of statistical estimators. Finally, we quantify the effect of a bad calibration with the continuous time mis-specified Kalman filter. Numerical examples illustrate the difficulty of trend forecasting in financial time series.Comment: 26 pages, 11 figure

Online Bivariate Outlier Detection in Final Test Using Kernel Density Estimation

In parametric IC testing, outlier detection is applied to filter out potential unreliable devices. Most outlier detection methods are used in an offline setting and hence are not applicable to Final Test, where immediate pass/fail decisions are required. Therefore, we developed a new bivariate online outlier detection method that is applicable to Final Test without making assumptions about a specific form of relations between two test parameters. An acceptance region is constructed using kernel density estimation. We use a grid discretization in order to enable a fast outlier decision. After each accepted device the grid is updated, hence the method is able to adapt to shifting measurements

Heterogeneous Change Point Inference

We propose HSMUCE (heterogeneous simultaneous multiscale change-point estimator) for the detection of multiple change-points of the signal in a heterogeneous gaussian regression model. A piecewise constant function is estimated by minimizing the number of change-points over the acceptance region of a multiscale test which locally adapts to changes in the variance. The multiscale test is a combination of local likelihood ratio tests which are properly calibrated by scale dependent critical values in order to keep a global nominal level alpha, even for finite samples. We show that HSMUCE controls the error of over- and underestimation of the number of change-points. To this end, new deviation bounds for F-type statistics are derived. Moreover, we obtain confidence sets for the whole signal. All results are non-asymptotic and uniform over a large class of heterogeneous change-point models. HSMUCE is fast to compute, achieves the optimal detection rate and estimates the number of change-points at almost optimal accuracy for vanishing signals, while still being robust. We compare HSMUCE with several state of the art methods in simulations and analyse current recordings of a transmembrane protein in the bacterial outer membrane with pronounced heterogeneity for its states. An R-package is available online

Weak Lensing Mass Reconstruction using Wavelets

This paper presents a new method for the reconstruction of weak lensing mass maps. It uses the multiscale entropy concept, which is based on wavelets, and the False Discovery Rate which allows us to derive robust detection levels in wavelet space. We show that this new restoration approach outperforms several standard techniques currently used for weak shear mass reconstruction. This method can also be used to separate E and B modes in the shear field, and thus test for the presence of residual systematic effects. We concentrate on large blind cosmic shear surveys, and illustrate our results using simulated shear maps derived from N-Body Lambda-CDM simulations with added noise corresponding to both ground-based and space-based observations.Comment: Accepted manuscript with all figures can be downloaded at: http://jstarck.free.fr/aa_wlens05.pdf and software can be downloaded at http://jstarck.free.fr/mrlens.htm

The Galactic Exoplanet Survey Telescope (GEST)

The Galactic Exoplanet Survey Telescope (GEST) will observe a 2 square degree field in the Galactic bulge to search for extra-solar planets using a gravitational lensing technique. This gravitational lensing technique is the only method employing currently available technology that can detect Earth-mass planets at high signal-to-noise, and can measure the frequency of terrestrial planets as a function of Galactic position. GEST's sensitivity extends down to the mass of Mars, and it can detect hundreds of terrestrial planets with semi-major axes ranging from 0.7 AU to infinity. GEST will be the first truly comprehensive survey of the Galaxy for planets like those in our own Solar System.Comment: 17 pages with 13 figures, to be published in Proc. SPIE vol 4854, "Future EUV-UV and Visible Space Astrophysics Missions and Instrumentation

Evaluation and application of multi-source satellite rainfall product CHIRPS to assess spatio-temporal rainfall variability on data-sparse Western margins of Ethiopian Highlands

The spatio-temporal characteristic of rainfall in the Beles Basin of Ethiopia is poorly understood, mainly due to lack of data. With recent advances in remote sensing, satellite derived rainfall products have become alternative sources of rainfall data for such poorly gauged areas. The objectives of this study were: (i) to evaluate a multi-source rainfall product (Climate Hazards Group Infrared Precipitation with Stations: CHIRPS) for the Beles Basin using gauge measurements and (ii) to assess the spatial and temporal variability of rainfall across the basin using validated CHIRPS data for the period 1981-2017. Categorical and continuous validation statistics were used to evaluate the performance, and time-space variability of rainfall was analyzed using GIS operations and statistical methods. Results showed a slight overestimation of rainfall occurrence by CHIRPS for the lowland region and underestimation for the highland region. CHIRPS underestimated the proportion of light daily rainfall events and overestimated the proportion of high intensity daily rainfall events. CHIRPS rainfall amount estimates were better in highland regions than in lowland regions, and became more accurate as the duration of the integration time increases from days to months. The annual spatio-temporal analysis result using CHIRPS revealed: a mean annual rainfall of the basin is 1490 mm (1050-2090 mm), a 50 mm increase of mean annual rainfall per 100 m elevation rise, periodical and persistent drought occurrence every 8 to 10 years, a significant increasing trend of rainfall (similar to 5 mm year(-1)), high rainfall variability observed at the lowland and drier parts of the basin and high coefficient of variation of monthly rainfall in March and April (revealing occurrence of bimodal rainfall characteristics). This study shows that the performance of CHIRPS product can vary spatially within a small basin level, and CHIRPS can help for better decision making in poorly gauged areas by giving an option to understand the space-time variability of rainfall characteristics