Bayesian inference of a negative quantity from positive measurement results

In this paper the Bayesian analysis is applied to assign a probability density to the value of a quantity having a definite sign. This analysis is logically consistent with the results, positive or negative, of repeated measurements. Results are used to estimate the atom density shift in a caesium fountain clock. The comparison with the classical statistical analysis is also reported and the advantages of the Bayesian approach for the realization of the time unit are discussed.Comment: 10 pages, 4 figures, submitted to Metrologi

On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference

Nonparametric methods play a central role in modern empirical work. While they provide inference procedures that are more robust to parametric misspecification bias, they may be quite sensitive to tuning parameter choices. We study the effects of bias correction on confidence interval coverage in the context of kernel density and local polynomial regression estimation, and prove that bias correction can be preferred to undersmoothing for minimizing coverage error and increasing robustness to tuning parameter choice. This is achieved using a novel, yet simple, Studentization, which leads to a new way of constructing kernel-based bias-corrected confidence intervals. In addition, for practical cases, we derive coverage error optimal bandwidths and discuss easy-to-implement bandwidth selectors. For interior points, we show that the MSE-optimal bandwidth for the original point estimator (before bias correction) delivers the fastest coverage error decay rate after bias correction when second-order (equivalent) kernels are employed, but is otherwise suboptimal because it is too "large". Finally, for odd-degree local polynomial regression, we show that, as with point estimation, coverage error adapts to boundary points automatically when appropriate Studentization is used; however, the MSE-optimal bandwidth for the original point estimator is suboptimal. All the results are established using valid Edgeworth expansions and illustrated with simulated data. Our findings have important consequences for empirical work as they indicate that bias-corrected confidence intervals, coupled with appropriate standard errors, have smaller coverage error and are less sensitive to tuning parameter choices in practically relevant cases where additional smoothness is available

Optimal Bandwidth Choice for Robust Bias Corrected Inference in Regression Discontinuity Designs

Modern empirical work in Regression Discontinuity (RD) designs often employs local polynomial estimation and inference with a mean square error (MSE) optimal bandwidth choice. This bandwidth yields an MSE-optimal RD treatment effect estimator, but is by construction invalid for inference. Robust bias corrected (RBC) inference methods are valid when using the MSE-optimal bandwidth, but we show they yield suboptimal confidence intervals in terms of coverage error. We establish valid coverage error expansions for RBC confidence interval estimators and use these results to propose new inference-optimal bandwidth choices for forming these intervals. We find that the standard MSE-optimal bandwidth for the RD point estimator is too large when the goal is to construct RBC confidence intervals with the smallest coverage error. We further optimize the constant terms behind the coverage error to derive new optimal choices for the auxiliary bandwidth required for RBC inference. Our expansions also establish that RBC inference yields higher-order refinements (relative to traditional undersmoothing) in the context of RD designs. Our main results cover sharp and sharp kink RD designs under conditional heteroskedasticity, and we discuss extensions to fuzzy and other RD designs, clustered sampling, and pre-intervention covariates adjustments. The theoretical findings are illustrated with a Monte Carlo experiment and an empirical application, and the main methodological results are available in \texttt{R} and \texttt{Stata} packages

Regression Discontinuity Designs Using Covariates

We study regression discontinuity designs when covariates are included in the estimation. We examine local polynomial estimators that include discrete or continuous covariates in an additive separable way, but without imposing any parametric restrictions on the underlying population regression functions. We recommend a covariate-adjustment approach that retains consistency under intuitive conditions, and characterize the potential for estimation and inference improvements. We also present new covariate-adjusted mean squared error expansions and robust bias-corrected inference procedures, with heteroskedasticity-consistent and cluster-robust standard errors. An empirical illustration and an extensive simulation study is presented. All methods are implemented in \texttt{R} and \texttt{Stata} software packages

Realization of a twin beam source based on four-wave mixing in Cesium

Four-wave mixing (4WM) is a known source of intense non-classical twin beams. It can be generated when an intense laser beam (the pump) and a weak laser beam (the seed) overlap in a $\chi^{(3)}$ medium (here cesium vapor), with frequencies close to resonance with atomic transitions. The twin beams generated by 4WM have frequencies naturally close to atomic transitions, and can be intense (gain $\gg 1$) even in the CW pump regime, which is not the case for PDC $\chi^{(2)}$ phenomenon in non-linear crystals. So, 4WM is well suited for atom-light interaction and atom-based quantum protocols. Here we present the first realization of a source of 4-wave mixing exploiting $D_2$ line of Cesium atoms.Comment: 10 pages, 10 figure

Generation of an ultrastable 578 nm laser for Yb lattice clock

In this paper we described the development and the characterization of a 578 nm laser source to be the clock laser for an Ytterbium Lattice Optical clock. Two independent laser sources have been realized and the characterization of the stability with a beat note technique is presente

Measurement of the Blackbody Radiation Shift of the 133Cs Hyperfine Transition in an Atomic Fountain

We used a Cs atomic fountain frequency standard to measure the Stark shift on the ground state hyperfine transiton frequency in cesium (9.2 GHz) due to the electric field generated by the blackbody radiation. The measures relative shift at 300 K is -1.43(11)e-14 and agrees with our theoretical evaluation -1.49(07)e-14. This value differs from the currently accepted one -1.69(04)e-14. The difference has a significant implication on the accuracy of frequency standards, in clocks comparison, and in a variety of high precision physics tests such as the time stability of fundamental constants.Comment: 4 pages, 2 figures, 2 table

A Large Area Fiber Optic Gyroscope on multiplexed fiber network

We describe a fiber optical gyroscope based on the Sagnac effect realized on a multiplexed telecom fiber network. Our loop encloses an area of 20 km2 and coexists with Internet data traffic. This Sagnac interferometer achieves a sensitivity of about (10-8 rad/s)/sqrt(Hz), thus approaching ring laser gyroscopes without using narrow linewidth laser nor sophisticated optics. The proposed gyroscope is sensitive enough for seismic applications, opening new possibilities for this kind of optical fiber sensors

Realization of an Ultrastable 578-nm Laser for an Yb Lattice Clock

In this paper, we describe the development of an ultrastable laser source at 578 nm, realized using frequency sum generation. This source will be used to excite the clock transition 1S0-3P0 in an ytterbium optical lattice clock experiment. Two independent ultrastable lasers have been realized, and the laser frequency noise and stability have been characterize

Beyond the fundamental noise limit in coherent optical fiber links

It is well known that temperature variations and acoustic noise affect ultrastable frequency dissemination along optical fiber. Active stabilization techniques are in general adopted to compensate for the fiber-induced phase noise. However, despite this compensation, the ultimate link performances remain limited by the so called delay-unsuppressed fiber noise that is related to the propagation delay of the light in the fiber. In this paper, we demonstrate a data post-processing approach which enables us to overcome this limit. We implement a subtraction algorithm between the optical signal delivered at the remote link end and the round-trip signal. In this way, a 6 dB improvement beyond the fundamental limit imposed by delay-unsuppressed noise is obtained. This result enhances the resolution of possible comparisons between remote optical clocks by a factor of 2. We confirm the theoretical prediction with experimental data obtained on a 47 km metropolitan fiber link, and propose how to extend this method for frequency dissemination purposes as well