Discussion: “Bayesian Optimal Design of Experiments for Inferring the Statistical Expectation of Expensive Black-Box Functions” (Pandita, P., Bilionis, I., and Panchal, J., 2019. ASME. J. Mech. Des. 141(10): 101404)

The authors of the discussed paper simplified the information-based acquisition on estimating statistical expectation and developed analytical computation for each involved quantity under uniform input distribution. In this discussion, we show that (1) the last three terms of the acquisition always add up to zero, leaving a concise form with a much more intuitive interpretation of the acquisition; (2) the analytical computation of the acquisition can be generalized to arbitrary input distribution, greatly broadening the application of the developed framework.

Bivariate Infinite Series Solution of Kepler’s Equations

A class of bivariate infinite series solutions of the elliptic and hyperbolic Kepler equations is described, adding to the handful of 1-D series that have been found throughout the centuries. This result is based on an iterative procedure for the analytical computation of all the higher-order partial derivatives of the eccentric anomaly with respect to the eccentricity e and mean anomaly M in a given base point (ec,Mc) of the (e,M) plane. Explicit examples of such bivariate infinite series are provided, corresponding to different choices of (ec,Mc), and their convergence is studied numerically. In particular, the polynomials that are obtained by truncating the infinite series up to the fifth degree reach high levels of accuracy in significantly large regions of the parameter space (e,M). Besides their theoretical interest, these series can be used for designing 2-D spline numerical algorithms for efficiently solving Kepler’s equations for all values of the eccentricity and mean anomaly.

Bayesian Inference

This chapter evaluates Bayesian inference, which refers to the Bayesian statistical method for estimating the parameters of a model and for testing a hypothesis. It relies on subjective statistics and extensively uses Bayes’s theorem. In the early 1990s, Bayesian statistics boomed with the emergence of sampling techniques. These new tools rely on the computational power to sample from (rather than evaluate) the posterior probability. However, the main drawback of the Bayesian approach lies in the computation of the posterior probability. The analytical computation of the posterior probability is a complex problem for any application, and this has limited Bayesian statistics for years.

Innovative Concepts and Techniques of Data Analytics in Edge Computing Paradigms

Edge analytics is an approach to data collection and analysis in which an automated analytical computation is performed on data at a sensor, network switch, or other device instead of waiting for the data to be sent back to a centralized data store. Cloud computing has revolutionized how people store and use their data; however, there are some areas where cloud is limited; latency, bandwidth, security, and a lack of offline access can be problematic. To solve this problem, users need robust, secure, and intelligent on-premise infrastructure for edge computing. When data is physically located closer to the users who connected to it, information can be shared quickly, securely, and without latency. In financial services, gaming, healthcare, and retail, low levels of latency are vital for a great digital customer experience. To improve reliability and faster response times, combing cloud with edge infrastructure from APC by Schneider electrical is proposed.