Haber, GregoryMalinovsky, Yaakov2018-05-292018-05-292019-08-14Gregory Haber. Yaakov Malinovsky. "Efficient methods for the estimation of the multinomial parameter for the two-trait group testing model." Electron. J. Statist. 13, no. 2 (14 August 2019): 2624 - 2657. https://doi.org/10.1214/19-EJS1583https://doi.org/10.1214/19-EJS1583http://hdl.handle.net/11603/10869Project Directors Dan Bailey, Imaging Research Center, UMBC Burt Kummerow, Maryland Historical Society Production and Research Tamara Peters – primary researcher and project lead Ryan Zuber – technical director Lindsay Previtt and Joshua Cole – geographic information systems specialists Mark Jarzynski and Shawn Squire – programmers Christina Jeresano – senior modeler Ganna Vikhlyayeva – texture artist Kristen Schenning and Debbie Harner – text content, Maryland Historical Society Scholars Mary Ellen Hayward Lance Humphries 2D and 3D Content Creation Assistants Rachael Birky, Katherine Bobby, Bianca Bouknight, Wilfred Brownell, Timothy Bubb, Natalie Cheeto, Timothy Connell, Rachael Devore, Nathan Frankoff, Drake Gao, Thomas Harvey, Oliver Hill, Alison Holloway, Annette Horan, Calvin Kumagai, Yan Lin, Robyn Lott, Megan Masciana, Gloria Okafor, Brianna Paige, Nicolette Riggin, Joseph Rigoroso, Shelly Ryan, Ben Schaffer, Jonathan Schubbe, Cameron Smith, Carly Sullivan, Paul Tschirgi, Andrea WozniakEstimation of a single Bernoulli parameter using pooled sampling is among the oldest problems in the group testing literature. To carry out such estimation, an array of efficient estimators have been introduced covering a wide range of situations routinely encountered in applications. More recently, there has been growing interest in using group testing to simultaneously estimate the joint probabilities of two correlated traits using a multinomial model. Unfortunately, basic estimation results, such as the maximum likelihood estimator (MLE), have not been adequately addressed in the literature for such cases. In this paper, we show that finding the MLE for this problem is equivalent to maximizing a multinomial likelihood with a restricted parameter space. A solution using the EM algorithm is presented which is guaranteed to converge to the global maximizer, even on the boundary of the parameter space. Two additional closed form estimators are presented with the goal of minimizing the bias and/or mean square error. The methods are illustrated by considering an application to the joint estimation of transmission prevalence for two strains of the Potato virus Y by the aphid myzus persicae.34 pagesen-USThis work was written as part of one of the author's official duties as an Employee of the United States Government and is therefore a work of the United States Government. In accordance with 17 U.S.C. 105, no copyright protection is available for such works under U.S. Law.Public Domainhttps://creativecommons.org/publicdomain/mark/1.0/Bernoulli parameterpooled samplinggroup testingmaximum likelihood estimatorestimationText