Estimation for General Birth-Death Processes

DOI10.1080/01621459.2013.866565zbMath1367.62245arXiv1111.4954OpenAlexW2096272023WikidataQ42058110 ScholiaQ42058110MaRDI QIDQ4975412

Forrest W. Crawford, Vladimir N. Minin, Marc A. Suchard

Publication date: 4 August 2017

Published in: Journal of the American Statistical Association (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.4954

zbMATH Keywords

EM algorithmmaximum likelihood estimationcontinuous-time Markov chainMM algorithmmicrosatellite evolution

Mathematics Subject Classification ID

Applications of statistics to biology and medical sciences; meta analysis (62P10) Markov processes: estimation; hidden Markov models (62M05) Continuous-time Markov processes on discrete state spaces (60J27)

Related Items (17)

Towards a statistical physics of dating apps ⋮ Gain-loss-duplication models for copy number evolution on a phylogeny: exact algorithms for computing the likelihood and its gradient ⋮ A numerical approach for evaluating the time-dependent distribution of a quasi birth-death process ⋮ Probabilistic predictions of SIS epidemics on networks based on population-level observations ⋮ Parameter estimation for discretely observed linear birth‐and‐death processes ⋮ Coupling bounds for approximating birth-death processes by truncation ⋮ Inferring density-dependent population dynamics mechanisms through rate disambiguation for logistic birth-death processes ⋮ INAR approximation of bivariate linear birth and death process ⋮ Some mechanisms leading to underdispersion: Old and new proposals ⋮ Birth/birth-death processes and their computable transition probabilities with biological applications ⋮ The probability distribution of the ancestral population size conditioned on the reconstructed phylogenetic tree with occurrence data ⋮ A three-term recurrence relation for accurate evaluation of transition probabilities of the simple birth-and-death process ⋮ Likelihood-based inference for discretely observed birth-death-shift processes, with applications to evolution of mobile genetic elements ⋮ The linear birth‒death process: an inferential retrospective ⋮ Sex, lies and self-reported counts: Bayesian mixture models for heaping in longitudinal count data via birth-death processes ⋮ On a reward rate estimation for the finite irreducible continuous-time Markov chain ⋮ Parameter estimation for multivariate population processes: a saddlepoint approach

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution
• Estimating change rates of genetic markers using serial samples: applications to the transposon IS6110 in Mycobacterium tuberculosis
• Graphics processing units and high-dimensional optimization
• Counting labeled transitions in continuous-time Markov models of evolution
• Simulation from endpoint-conditioned, continuous-time Markov chains on a finite state space, with applications to molecular evolution
• The Fourier-series method for inverting transforms of probability distributions
• Continued fractions with applications
• Numerical inversion of probability generating functions
• Maximum likelihood estimation in the birth-and-death process
• A survey of truncation error analysis for Padé and continued fraction approximants
• Ancestral processes with selection
• Bayesian inference for linear growth birth and death processes.
• Stochastic epidemic models and their statistical analysis
• Mathematical biology. Vol. 1: An introduction.
• Fitting birth-death processes to panel data with applications to bacterial DNA fingerprinting
• Generator estimation of Markov jump processes
• Exact transient solution of a state-dependent birth-death process
• Stochastic Population Processes
• Summary Statistics for Endpoint-Conditioned Continuous-Time Markov Chains
• THE BEHAVIOUR OF AN ESTIMATOR FOR A SIMPLE BIRTH AND DEATH PROCESS
• Numerical Analysis for Statisticians
• Some Properties of Continued Fractions with Applications in Markov Processes
• Miscellanea. Information matrix computation from conditional information via normal approximation
• Direct Calculation of the Information Matrix via the EM Algorithm
• The ECME algorithm: A simple extension of EM and ECM with faster monotone convergence
• Continued Fraction Analysis of the Duration of an Excursion in an M/M/∞ System
• Computing Laplace Transforms for Numerical Inversion Via Continued Fractions
• The formal theory of birth-and-death processes, lattice path combinatorics and continued fractions
• Application of Stieltjes theory for S-fractions to birth and death processes
• Numerical Inversion of Laplace Transforms of Probability Distributions
• Excursions of birth and death processes, orthogonal polynomials, and continued fractions
• Development of non-linear transformations for improving convergence of sequences
• Estimation in the birth process
• Statistical Inference for Discretely Observed Markov Jump Processes
• Numerical Evaluation of Continued Fractions
• Density estimation in high and ultra high dimensions, regularization, and the L 1 asymptotics
• Problems of Statistical Inference for Birth and Death Queuing Models
• Numerical Continued Fractions

This page was built for publication: Estimation for General Birth-Death Processes