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C. J. Oates

Publications and source records attributed to C. J. Oates.

5 recordsLinked to original sources
arXiv2019

A Modern Retrospective on Probabilistic Numerics

This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual development can be related both to applications and to a modern formal treatment. We highlight in particular the parallel contributions of Sul'din and Larkin in the 1960s and how their pioneering early ideas have reached a degree of maturity in the intervening period, mediated by paradigms such as average-case analysis and information-based complexity. We provide a subjective assessment of the state of research in probabilistic numerics and highlight some difficulties to be addressed by future works.

math.NA↗
arXiv2016

Investigation of the widely applicable Bayesian information criterion

The widely applicable Bayesian information criterion (WBIC) is a simple and fast approximation to the model evidence that has received little practical consideration. WBIC uses the fact that the log evidence can be written as an expectation, with respect to a powered posterior proportional to the likelihood raised to a power $t^*\in{(0,1)}$, of the log deviance. Finding this temperature value $t^*$ is generally an intractable problem. We find that for a particular tractable statistical model that the mean squared error of an optimally-tuned version of WBIC with correct temperature $t^*$ is lower than an optimally-tuned version of thermodynamic integration (power posteriors). However in practice WBIC uses the a canonical choice of $t=1/\log(n)$. Here we investigate the performance of WBIC in practice, for a range of statistical models, both regular models and singular models such as latent variable models or those with a hierarchical structure for which BIC cannot provide an adequate solution. Our findings are that, generally WBIC performs adequately when one uses informative priors, but it can systematically overestimate the evidence, particularly for small sample sizes.

stat.ME↗
arXiv2014

Causal network inference using biochemical kinetics

Network models are widely used as structural summaries of biochemical systems. Statistical estimation of networks is usually based on linear or discrete models. However, the dynamics of these systems are generally nonlinear, suggesting that suitable nonlinear formulations may offer gains with respect to network inference and associated prediction problems. We present a general framework for both network inference and dynamical prediction that is rooted in nonlinear biochemical kinetics. This is done by considering a dynamical system based on a chemical reaction graph and associated kinetics parameters. Inference regarding both parameters and the reaction graph itself is carried out within a fully Bayesian framework. Prediction of dynamical behavior is achieved by averaging over both parameters and reaction graphs, allowing prediction even when the underlying reactions themselves are unknown or uncertain. Results, based on (i) data simulated from a mechanistic model of mitogen-activated protein kinase signaling and (ii) phosphoproteomic data from cancer cell lines, demonstrate that nonlinear formulations can yield gains in network inference and permit dynamical prediction in the challenging setting where the reaction graph is unknown.

stat.AP↗
arXiv2005

Direct evidence of the orbital contribution to the magnetic moment in AA'FeReO6 double perovskites

Spin and orbital magnetic moments of Re in AA'FeReO6 double perovskites (A,A' = Ba, Sr, Ca) have been directly probed employing XMCD spectroscopy at the Re L2,3-edges. A considerable orbital magnetic moment is observed in all the studied compounds despite octahedral coordination. Relative orbital to spin contribution per Re atom rises with lattice distortion from mL/mS = -0.28 to -0.34 for AA'=Ba2FeReO6 and Ca2FeReO6, respectively. A preliminary XMCD measurements at the Fe L2,3-edges reveals also a significant orbital moment of iron in Ca2FeReO6. The relation of the results to the magnetic properties of the compounds is discussed.

cond-mat.str-el↗