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• W2096272023 abstract "Birth-death processes (BDPs) are continuous-time Markov chains that track the number of particles in a system over time. While widely used in population biology, genetics and ecology, statistical inference of the instantaneous particle birth and death rates remains largely limited to restrictive linear BDPs in which per-particle birth and death rates are constant. Researchers often observe the number of particles at discrete times, necessitating data augmentation procedures such as expectation-maximization (EM) to find maximum likelihood estimates. For BDPs on finite state-spaces, there are powerful matrix methods for computing the conditional expectations needed for the E-step of the EM algorithm. For BDPs on infinite state-spaces, closed-form solutions for the E-step are available for some linear models, but most previous work has resorted to time-consuming simulation. Remarkably, we show that the E-step conditional expectations can be expressed as convolutions of computable transition probabilities for any general BDP with arbitrary rates. This important observation, along with a convenient continued fraction representation of the Laplace transforms of the transition probabilities, allows for novel and efficient computation of the conditional expectations for all BDPs, eliminating the need for truncation of the state-space or costly simulation. We use this insight to derive EM algorithms that yield maximum likelihood estimation for general BDPs characterized by various rate models, including generalized linear models. We show that our Laplace convolution technique outperforms competing methods when they are available and demonstrate a technique to accelerate EM algorithm convergence. We validate our approach using synthetic data and then apply our methods to cancer cell growth and estimation of mutation parameters in microsatellite evolution." @default.
• W2096272023 created "2016-06-24" @default.
• W2096272023 creator A5039905606 @default.
• W2096272023 creator A5080170176 @default.
• W2096272023 creator A5089671301 @default.
• W2096272023 date "2014-04-03" @default.
• W2096272023 modified "2023-09-23" @default.
• W2096272023 title "Estimation for General Birth-Death Processes" @default.
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• W2096272023 doi "https://doi.org/10.1080/01621459.2013.866565" @default.
• W2096272023 hasPubMedCentralId "https://www.ncbi.nlm.nih.gov/pmc/articles/4196218" @default.
• W2096272023 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/25328261" @default.
• W2096272023 hasPublicationYear "2014" @default.
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