Electronic Journal of Statistics

A preferential attachment model for the stellar initial mass function

Jessi Cisewski-Kehe, Grant Weller, and Chad Schafer

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Accurate specification of a likelihood function is becoming increasingly difficult in many inference problems in astronomy. As sample sizes resulting from astronomical surveys continue to grow, deficiencies in the likelihood function lead to larger biases in key parameter estimates. These deficiencies result from the oversimplification of the physical processes that generated the data, and from the failure to account for observational limitations. Unfortunately, realistic models often do not yield an analytical form for the likelihood. The estimation of a stellar initial mass function (IMF) is an important example. The stellar IMF is the mass distribution of stars initially formed in a given cluster of stars, a population which is not directly observable due to stellar evolution and other disruptions and observational limitations of the cluster. There are several difficulties with specifying a likelihood in this setting since the physical processes and observational challenges result in measurable masses that cannot legitimately be considered independent draws from an IMF. This work improves inference of the IMF by using an approximate Bayesian computation approach that both accounts for observational and astrophysical effects and incorporates a physically-motivated model for star cluster formation. The methodology is illustrated via a simulation study, demonstrating that the proposed approach can recover the true posterior in realistic situations, and applied to observations from astrophysical simulation data.

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Electron. J. Statist., Volume 13, Number 1 (2019), 1580-1607.

Received: July 2018
First available in Project Euclid: 16 April 2019

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Approximate Bayesian computation astrostatistics computational statistics dependent data

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Cisewski-Kehe, Jessi; Weller, Grant; Schafer, Chad. A preferential attachment model for the stellar initial mass function. Electron. J. Statist. 13 (2019), no. 1, 1580--1607. doi:10.1214/19-EJS1556. https://projecteuclid.org/euclid.ejs/1555380051

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