Empirical Bayes estimation: When does gg-modeling beat ff-modeling in theory (and in practice)?

Empirical Bayes (EB) is a popular framework for large-scale inference that aims to find data-driven estimators to compete with the Bayesian oracle that knows the true prior. Two principled approaches to EB estimation have emerged over the years: $f$-modeling, which constructs an approximate Bayes rule by estimating the marginal distribution of the data, and $g$-modeling, which estimates the prior from data and then applies the learned Bayes rule. For the Poisson model, the prototypical examples are the celebrated Robbins estimator and the nonparametric MLE (NPMLE), respectively. It has long been recognized in practice that the Robbins estimator, while being conceptually appealing and computationally simple, lacks robustness and can be easily derailed by "outliers" (data points that were rarely observed before), unlike the NPMLE which provides more stable and interpretable fit thanks to its Bayes form. On the other hand, not only do the existing theories shed little light on this phenomenon, but they all point to the opposite, as both methods have recently been shown optimal in terms of the \emph{regret} (excess over the Bayes risk) for compactly supported and subexponential priors with exact logarithmic factors. In this paper we provide a theoretical justification for the superiority of NPMLE over Robbins for heavy-tailed data by considering priors with bounded $p$th moment previously studied for the Gaussian model. For the Poisson model with sample size $n$, assuming $p>1$ (for otherwise triviality arises), we show that the NPMLE with appropriate regularization and truncation achieves a total regret $\tilde \Theta(n^{\frac{3}{2p+1}})$, which is minimax optimal within logarithmic factors. In contrast, the total regret of Robbins estimator (with similar truncation) is $\tilde{\Theta}(n^{\frac{3}{p+2}})$ and hence suboptimal by a polynomial factor

All-condition pulse detection using a magnetic sensor

A plethora of wearable devices have been developed or commercialized for continuous non-invasive monitoring of physiological signals that are crucial for preventive care and management of chronic conditions. However, most of these devices are either sensitive to skin conditions or its interface with the skin due to the requirement that the external stimuli such as light or electrical excitation must penetrate the skin to detect the pulse. This often results in large motion artefacts and unsuitability for certain skin conditions. Here, we demonstrate a simple fingertip-type device which can detect clear pulse signals under all conditions, including fingers covered by opaque substances such as a plaster or nail polish, or fingers immersed in liquid. The device has a very simple structure, consisting of only a pair of magnets and a magnetic sensor. We show through both experiments and simulations that the detected pulsation signals correspond directly to the magnet vibrations caused by blood circulation, and therefore, in addition to heartrate detection, the proposed device can also be potentially used for blood pressure measurement

A throughput Fast Measurement Method for Two-Antenna Equipped Wireless MIMO Terminals

According to the Third Generation Partnership Project Specification, a Period of 8-12.8 H is Required to Evaluate the Multiple-Input-Multiple-Output (MIMO) Performance of a Wireless Terminal for a Single Frequency Point and Channel Model Combination. the Following Article Proposes a Semi-Simulation, Semi-Measurement-Based MIMO throughput Modeling Scheme Which Can Reduce the 8-12.8-H Measurement Time to 40-60 Min, Corresponding to More Than a Ten Times Improvement of the Test Efficiency, Without Loss of the Test Accuracy

Interference enhancement of Raman signal of graphene

Raman spectroscopic studies of graphene have attracted much interest. The G-band Raman intensity of a single layer graphene on Si substrate with 300 nm SiO2 capping layer is surprisingly strong and is comparable to that of bulk graphite. To explain this Raman intensity anomaly, we show that in addition to the interference due to multiple reflection of the incident laser, the multiple reflection of the Raman signal inside the graphene layer must be also accounted for. Further studies of the role of SiO2 layer in the enhancement Raman signal of graphene are carried out and an enhancement factor of ~30 is achievable, which is very significant for the Raman studies. Finally, we discuss the potential application of this enhancement effect on other ultra-thin films and nanoflakes and a general selection criterion of capping layer and substrate is given.Comment: 13 pages, 3 figures to be published in Applied Physics Letter