ISSN 1932-6157 (print) ISSN 1941-7330 (online) THE ANNALS of APPLIED STATISTICS AN OFFICIAL JOURNAL OF THE INSTITUTE OF MATHEMATICAL STATISTICS Articles Estimating the rate constant from biosensor data via an adaptive variational Bayesian approach....................YE ZHANG,ZHIGANG YAO,PATRIK FORSSÉN AND TORGNY FORNSTEDT 2011 Estimating abundance from multiple sampling capture-recapture data via a multi-state multi-period stopover model . .... HANNAH WORTHINGTON,RACHEL MCCREA, RUTH KING AND RICHARD GRIFFITHS 2043 Robust elastic net estimators for variable selection and identification of proteomic biomarkers..................GABRIELA V. C OHEN FREUE,DAV I D KEPPLINGER, MATÍAS SALIBIÁN-BARRERA AND EZEQUIEL SMUCLER 2065 Statistical inference for partially observed branching processes with application to cell lineage tracking of in vivo hematopoiesis JASON XU,SAMSON KOELLE,PETER GUTTORP,CHUANFENG WU, CYNTHIA DUNBAR,JANIS L. ABKOWITZ AND VLADIMIR N. 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REICH 2341 Vol. 13, No. 4—December 2019 ISSN 1932-6157 (print) ISSN 1941-7330 (online) THE ANNALS of APPLIED STATISTICS AN OFFICIAL JOURNAL OF THE INSTITUTE OF MATHEMATICAL STATISTICS Articles—Continued from front cover Predicting paleoclimate from compositional data using multivariate Gaussian process inverse prediction . JOHN R. TIPTON,MEVIN B. HOOTEN,CONNOR NOLAN, ROBERT K. BOOTH AND JASON MCLACHLAN 2363 Propensity score weighting for causal inference with multiple treatments FAN LI AND FAN LI 2389 Outline analyses of the called strike zone in Major League Baseball DALE L. 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Editor: Vlada Limic, UMR 7501 de l’Université de Strasbourg et du CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France The Annals of Applied Statistics [ISSN 1932-6157 (print); ISSN 1941-7330 (online)], Volume 13, Number 4, December 2019. Published quarterly by the Institute of Mathematical Statistics, 3163 Somerset Drive, Cleveland, Ohio 44122, USA. Periodicals postage pending at Cleveland, Ohio, and at additional mailing offices. POSTMASTER: Send address changes to The Annals of Applied Statistics, Institute of Mathematical Statistics, Dues and Subscriptions Office, 9650 Rockville Pike, Suite L 2310, Bethesda, Maryland 20814-3998, USA. Copyright © 2019 by the Institute of Mathematical Statistics Printed in the United States of America The Annals of Applied Statistics 2019, Vol. 13, No. 4, 2011–2042 https://doi.org/10.1214/19-AOAS1263 © Institute of Mathematical Statistics, 2019 ESTIMATING THE RATE CONSTANT FROM BIOSENSOR DATA VIA AN ADAPTIVE VARIATIONAL BAYESIAN APPROACH ∗ BY YE ZHANG ,1,ZHIGANG YAO†,2,4,PATRIK FORSSÉN‡,3 AND TORGNY FORNSTEDT‡,3 Chemnitz University of Technology∗, National University of Singapore† and Karlstad University‡ The means to obtain the rate constants of a chemical reaction is a funda- mental open problem in both science and the industry. Traditional techniques for finding rate constants require either chemical modifications of the reac- tants or indirect measurements. The rate constant map method is a modern technique to study binding equilibrium and kinetics in chemical reactions. Finding a rate constant map from biosensor data is an ill-posed inverse prob- lem that is usually solved by regularization. In this work, rather than finding a deterministic regularized rate constant map that does not provide uncertainty quantification of the solution, we develop an adaptive variational Bayesian approach to estimate the distribution of the rate constant map, from which some intrinsic properties of a chemical reaction can be explored, including information about rate constants. Our new approach is more realistic than the existing approaches used for biosensors and allows us to estimate the dynam- ics of the interactions, which are usually hidden in a deterministic approx- imate solution. We verify the performance of the new proposed method by numerical simulations, and compare it with the Markov chain Monte Carlo algorithm. The results illustrate that the variational method can reliably cap- ture the posterior distribution in a computationally efficient way. Finally, the developed method is also tested on the real biosensor data (parathyroid hor- mone), where we provide two novel analysis tools—the thresholding contour map and the high order moment map—to estimate the number of interactions as well as their rate constants. REFERENCES ALTSCHUH,D.,BJÖKELUND,H.,STRANDGÅRD,J.,CHOULIER,L.,MALMQVIST,M.andAN-