Natural inflation after Planck 2018

We calculate high-precision constraints on Natural Inflation relative to current observational constraints from Planck 2018 + BICEP/Keck(BK15) Polarization + BAO on r and n S, including post-inflationary history of the universe. We find that, for conventional post-inflationary dynamics, Natural Inflation with a cosine potential is disfavored at greater than 95% confidence out by current data. If we assume protracted reheating characterized by w̅>1/3, Natural Inflation can be brought into agreement with current observational constraints. However, bringing unmodified Natural Inflation into the 68% confidence region requires values of T re below the scale of electroweak symmetry breaking. The addition of a SHOES prior on the Hubble Constant H 0 only worsens the fit.

Estimation of the Tapered Gutenberg-Richter Distribution Parameters for Catalogs with Variable Completeness: An Application to the Atlantic Ridge Seismicity

The use of the tapered Gutenberg-Richter distribution in earthquake source models is rapidly increasing, allowing overcoming the definition of a hard threshold for the maximum magnitude. Here, we expand the classical maximum likelihood estimation method for estimating the parameters of the tapered Gutenberg-Richter distribution, allowing the use of a variable through-time magnitude of completeness. Adopting a well-established technique based on asymptotic theory, we also estimate the uncertainties relative to the parameters. Differently from other estimation methods for catalogs with a variable completeness, available for example for the classical truncated Gutenberg-Richter distribution, our approach does not need the assumption on the distribution of the number of events (usually the Poisson distribution). We test the methodology checking the consistency of parameter estimations with synthetic catalogs generated with multiple completeness levels. Then, we analyze the Atlantic ridge seismicity, using the global centroid moment tensor catalog, finding that our method allows better constraining distribution parameters, allowing the use more data than estimations based on a single completeness level. This leads to a sharp decrease in the uncertainties associated with the parameter estimation, when compared with existing methods based on a single time-independent magnitude of completeness. This also allows analyzing subsets of events, to deepen data analysis. For example, separating normal and strike-slip events, we found that they have significantly different but well-constrained corner magnitudes. Instead, without distinguishing for focal mechanism and considering all the events in the catalog, we obtain an intermediate value that is relatively less constrained from data, with an open confidence region.

Inferences for Generalized Pareto Distribution Based on Progressive First-Failure Censoring Scheme

In this article, we consider estimation of the parameters of a generalized Pareto distribution and some lifetime indices such as those relating to reliability and hazard rate functions when the failure data are progressive first-failure censored. Both classical and Bayesian techniques are obtained. In the Bayesian framework, the point estimations of unknown parameters under both symmetric and asymmetric loss functions are discussed, after having been estimated using the conjugate gamma and discrete priors for the shape and scale parameters, respectively. In addition, both exact and approximate confidence intervals as well as the exact confidence region for the estimators are constructed. A practical example using a simulated data set is analyzed. Finally, the performance of Bayes estimates is compared with that of maximum likelihood estimates through a Monte Carlo simulation study.

Ways to identify bearings in two-position goniometric airborne radiomonitoring systems.

For aeronautical goniometric systems for radio monitoring of radio emission sources (RES), one of the primary tasks is the identification of bearings. It is especially difficult to solve the problem of identifying bearings if there are several RESs in the observation area in the case when they are located in the same plane with the direction finders. In this case, the problem of identifying bearings in goniometric two-position systems is solved in the process of performing a two-stage procedure. At the first stage, the primary identification of single measurements of bearings is carried out separately at each receiving position (RP) when receiving radio signals from the RES, and at the second stage, the secondary (inter-positional) identification of bearings arriving from both RPs is carried out. In the initial identification, strobe and strobeless identification algorithms are used. In the secondary identification for selection of true and false points of intersection of bearings on the plane, it is proposed to use the kinematic parameters of the relative RES. However, this type of selection does not provide interposition identification with an arbitrary nature of the movement of the RES relative to the RP, and also assumes a constant angular position of the RP base on the plane. More practical are ways of identifying bearings with RES, in which the procedure for constructing a confidence region (CR) in the form of a circle with a certain radius is used. However, a more correct form of CR is an elliptical CR, since the errors in determining the position of the RES are characterized by an error ellipse, a particular case of which is a circle. Therefore, methods for identifying coordinate information have been developed, in which elliptical CRs are used. In this case, not only the bearings of the RES, but also other measured parameters, for example, estimates of the rectangular coordinates of the RES, calculated on the basis of the triangulation method, can be used as coordinate information. The purpose of the article is to systematize and analyze the developed methods for identifying bearings, which allow one to get a fairly general idea of how to solve the problem of identifying bearings and indirect measurements of the coordinates of radio emission sources in aviation goniometric two-position radio monitoring systems. As a result, a classification of identification methods is given. The existing possibilities and limitations of using various identification methods in solving radio monitoring problems are analyzed. The necessary information on the methods and algorithms for interpositional identification of coordinate information about the position of the RES, using ellipsoidal CRs in solving the identification problem, is given. The practical significance of the presented methods is to increase the likelihood of correct identification of coordinate information, as well as the accuracy of the positioning of RES due to the use of elliptical CRs, which more accurately reflect the regularity of the distribution of errors in determining the position of RES.

Confidence polytopes for quantum process tomography

In the present work, we propose a generalization of the confidence polytopes approach for quantum state tomography (QST) to the case of quantum process tomography (QPT). Our approach allows obtaining a confidence region in the polytope form for a Choi matrix of an unknown quantum channel based on the measurement results of the corresponding QPT experiment. The method uses the improved version of the expression for confidence levels for the case of several positive operator-valued measures (POVMs). We then show how confidence polytopes can be employed for calculating confidence intervals for affine functions of quantum states (Choi matrices), such as fidelities and observables mean values, which are used both in QST and QPT settings. As we discuss this problem can be efficiently solved using linear programming tools. We also demonstrate the performance and scalability of the developed approach on the basis of simulation and experimental data collected using IBM cloud quantum processor.

Asymptotic Analysis for a Stochastic Second-Order Cone Programming and Applications

Stochastic second-order cone programming (SSOCP) is an extension of deterministic second-order cone programming, which demonstrates underlying uncertainties in practical problems arising in economics engineering and operations management. In this paper, asymptotic analysis of sample average approximation estimator for SSOCP is established. Conditions ensuring the asymptotic normality of sample average approximation estimators for SSOCP are obtained and the corresponding covariance matrix is described in a closed form. Based on the analysis, the method to estimate the confidence region of a stationary point of SSOCP is provided and three examples are illustrated to show the applications of the method.

Distributional Robustness of K-class Estimators and the PULSE

While causal models are robust in that they are prediction optimal under arbitrarily strong interventions, they may not be optimal when the interventions are bounded. We prove that the classical K-class estimator satisfies such optimality by establishing a connection between K-class estimators and anchor regression. This connection further motivates a novel estimator in instrumental variable settings that minimizes the mean squared prediction error subject to the constraint that the estimator lies in an asymptotically valid confidence region of the causal coefficient. We call this estimator PULSE (p-uncorrelated least squares estimator), relate it to work on invariance, show that it can be computed efficiently as a data-driven K-class estimator, even though the underlying optimization problem is non-convex, and prove consistency. We evaluate the estimators on real data and perform simulation experiments illustrating that PULSE suffers from less variability. There are several settings including weak instrument settings, where it outperforms other estimators.

Investigating support by minimal detectable displacement in confidence region determination and significance test of displacements

The Minimal Detectable Displacement (MDD) is an important measure of monitoring networks sensitivity to displacements. In addition to the accuracy criteria, it is used as a detectability criterion in the optimal design of such networks. The paper examines whether the MDD provides grounds for verifying the correctness of the confidence, and the significance thresholds applied in the analyses of the determined displacements. According to our knowledge, the task so formulated has not yet been the subject of research presented in the literature in the field of geodetic determination of displacements. Hence, the approach presented here can be regarded as a new proposal extending the application area of the MDD. The investigations are focused on a probabilistic aspect of combining confidence and detectability as well as significance and detectability by the superimposition of the corresponding ellipsoids and their joint analysis. An initial research result is the diagrams showing a significance index and a non-centrality parameter as functions of the rank of the covariance matrix for displacements and also of system redundancy for specified values of Type I and Type II error probabilities. The diagrams, together with the theoretical basis created within the research, made it possible to analyse and evaluate the support by Minimal Detectable Displacement in confidence region determination and significance test of displacements. Based on the analysis of MDD support, two options of modifying the confidence and significance thresholds related to single point displacements are proposed for practical use.