Robust Online Hamiltonian Learning

In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer-Rao lower bound, certifying its own performance.Comment: 24 pages, 12 figures; to appear in New Journal of Physic

Mathematical statistics: with applications

In their bestselling MATHEMATICAL STATISTICS WITH APPLICATIONS, premiere authors Dennis Wackerly, William Mendenhall, and Richard L. Scheaffer present a solid foundation in statistical theory while conveying the relevance and importance of the theory in solving practical problems in the real world. The authors' use of practical applications and excellent exercises helps you discover the nature of statistics and understand its essential role in scientific research

A Critique of Statistical Modelling in Management Science from a Critical Realist Perspective: Its Role Within Multimethodology

Management science was historically dominated by an empiricist philosophy that saw quantitative modelling and statistical analysis as the only legitimate research method. More recently interpretive or constructivist philosophies have also developed employing a range of non-quantitative methods. This has sometimes led to divisive debates. “Critical realism” has been proposed as a philosophy of science that can potentially provide a synthesis in recognizing both the value and limitations of these approaches. This paper explores the critical realist critique of quantitative modelling, as exemplified by multivariate statistics, and argues that its grounds must be re-conceptualised within a multimethodological framework