On the Estimation of Random Uncertainties of Star Formation Histories

TL;DR

This paper compares bootstrap and MCMC methods for estimating uncertainties in star formation histories, showing MCMC, especially Hybrid Monte Carlo, provides more accurate confidence intervals.

Contribution

It introduces an MCMC-based approach, particularly Hybrid Monte Carlo, to improve uncertainty estimation in SFHs over traditional bootstrap methods.

Findings

Bootstrap underestimates uncertainties at low or zero star formation rates.

Hybrid Monte Carlo efficiently samples high-dimensional, correlated parameter spaces.

MCMC provides more reliable confidence intervals for SFH measurements.

Abstract

The standard technique for measurement of random uncertainties of star formation histories (SFHs) is the bootstrap Monte Carlo, in which the color-magnitude diagram (CMD) is repeatedly resampled. The variation in SFHs measured from the resampled CMDs is assumed to represent the random uncertainty in the SFH measured from the original data. However, this technique systematically and significantly underestimates the uncertainties for times in which the measured star formation rate is low or zero, leading to overly (and incorrectly) high confidence in that measurement. This study proposes an alternative technique, the Markov Chain Monte Carlo (MCMC), which samples the probability distribution of the parameters used in the original solution to directly estimate confidence intervals. While the most commonly used MCMC algorithms are incapable of adequately sampling a probability distribution that can involve thousands of highly correlated dimensions, the Hybrid Monte Carlo algorithm is shown to be extremely effective and efficient for this particular task. Several implementation details, such as the handling of implicit priors created by parameterization of the SFH, are discussed in detail.