Parameter estimation in branching processes with almost sure extinction

Peter Braunsteins; Sophie Hautphenne; Carmen Minuesa

doi:10.3150/21-bej1332

ESTIpop: a computational tool to simulate and estimate parameters for continuous-time Markov branching processes

Bioinformatics ◽

10.1093/bioinformatics/btaa526 ◽

2020 ◽

Vol 36 (15) ◽

pp. 4372-4373

Author(s):

James P Roney ◽

Jeremy Ferlic ◽

Franziska Michor ◽

Thomas O McDonald

Keyword(s):

Parameter Estimation ◽

Continuous Time ◽

Likelihood Function ◽

Branching Processes ◽

R Package ◽

Supplementary Information ◽

Cell Counts ◽

The Central Limit Theorem ◽

Multitype Branching Processes ◽

Analytical Approaches

Abstract Summary ESTIpop is an R package designed to simulate and estimate parameters for continuous-time Markov branching processes with constant or time-dependent rates, a common model for asexually reproducing cell populations. Analytical approaches to parameter estimation quickly become intractable in complex branching processes. In ESTIpop, parameter estimation is based on a likelihood function with respect to a time series of cell counts, approximated by the Central Limit Theorem for multitype branching processes. Additionally, simulation in ESTIpop via approximation can be performed many times faster than exact simulation methods with similar results. Availability and implementation ESTIpop is available as an R package on Github (https://github.com/michorlab/estipop). Supplementary information Supplementary data are available at Bioinformatics online.

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Parameter estimation in two-type continuous-state branching processes with immigration

Statistics & Probability Letters ◽

10.1016/j.spl.2014.04.021 ◽

2014 ◽

Vol 91 ◽

pp. 124-134 ◽

Cited By ~ 5

Author(s):

Wei Xu

Keyword(s):

Parameter Estimation ◽

Branching Processes ◽

Continuous State

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Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

Journal of Applied Probability ◽

10.1017/s0021900200003119 ◽

2007 ◽

Vol 44 (02) ◽

pp. 492-505

Author(s):

M. Molina ◽

M. Mota ◽

A. Ramos

Keyword(s):

Branching Process ◽

Branching Processes ◽

Sufficient Conditions ◽

Positive Probability ◽

Limit Laws ◽

Bisexual Branching Processes ◽

Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

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Ultrastructure of myoepithelial cell in parotid gland

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100103772 ◽

1988 ◽

Vol 46 ◽

pp. 342-343

Author(s):

C. N. Sun

Keyword(s):

Parotid Gland ◽

Osmium Tetroxide ◽

Individual Cell ◽

Branching Processes ◽

Muscle Cells ◽

Myoepithelial Cells ◽

Uranyl Acetate ◽

Thin Sections ◽

Gland Carcinoma ◽

Parotid Gland Carcinoma

Myoepithelial cells have been observed in the prostate, harderian, apocrine, exocrine sweat and mammary glands. Such cells and their numerous branching processes form basket-like structures around the glandular acini. Their shapes are quite different from structures seen either in spindleshaped smooth muscle cells or skeletal muscle cells. These myoepithelial cells lie on the epithelial side of the basement membrane in the glands. This presentation describes the ultrastructure of such myoepithelial cells which have been found also in the parotid gland carcinoma from a 45-year old patient.Specimens were cut into small pieces about 1 mm3 and immediately fixed in 4 percent glutaraldehyde in phosphate buffer for two hours, then post-fixed in 1 percent buffered osmium tetroxide for 1 hour. After dehydration, tissues were embedded in Epon 812. Thin sections were stained with uranyl acetate and lead citrate. Ultrastructurally, the pattern of each individual cell showed wide variations.

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