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Likelihood‐based inference for discretely observed birth–death‐shift processes, with applications to evolution of mobile genetic elements
Author(s) -
Xu Jason,
Guttorp Peter,
KatoMaeda Midori,
Minin Vladimir N.
Publication year - 2015
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.12352
Subject(s) - inference , branching process , covariate , computer science , birth–death process , expectation–maximization algorithm , econometrics , statistics , mathematical optimization , mathematics , artificial intelligence , machine learning , maximum likelihood , population , demography , sociology
Summary Continuous‐time birth–death‐shift (BDS) processes are frequently used in stochastic modeling, with many applications in ecology and epidemiology. In particular, such processes can model evolutionary dynamics of transposable elements—important genetic markers in molecular epidemiology. Estimation of the effects of individual covariates on the birth, death, and shift rates of the process can be accomplished by analyzing patient data, but inferring these rates in a discretely and unevenly observed setting presents computational challenges. We propose a multi‐type branching process approximation to BDS processes and develop a corresponding expectation maximization algorithm, where we use spectral techniques to reduce calculation of expected sufficient statistics to low‐dimensional integration. These techniques yield an efficient and robust optimization routine for inferring the rates of the BDS process, and apply broadly to multi‐type branching processes whose rates can depend on many covariates. After rigorously testing our methodology in simulation studies, we apply our method to study intrapatient time evolution of IS 6110 transposable element, a genetic marker frequently used during estimation of epidemiological clusters of Mycobacterium tuberculosis infections.