The overlooked potential of generalized linear models in astronomy - III. Bayesian negative binomial regression and globular cluster populations
The overlooked potential of generalized linear models in astronomy - III. Bayesian negative binomial regression and globular cluster populations
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DOI：
10.1093/mnras/stv1825
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发表时间：
2015-10-21
影响因子：
4.8
通讯作者：
Killedar, M.
中科院分区：
文献类型：
--
作者：
de Souza, R. S.;Hilbe, J. M.;Killedar, M.
在本文中，第三个系列说明了广义线性模型（GLM）的天文社区的权力，我们阐明了潜在的GLM类处理计数数据。一个星系的球状星团（GC）人口（NGC）的大小是天文学文献中一个长期的难题。它福尔斯计数数据分析的范畴，但它通常被建模为连续响应变量。我们建立了一个贝叶斯负二项回归模型来研究NGC与以下星系性质之间的联系：中心黑洞质量，动力学球质量，球速度色散和绝对视星等。本文介绍的方法自然占异方差，内在的分散，误差测量两个轴（离散或连续），并允许建模的人口GC在其自然规模作为一个非负整数变量。NGC预测趋势的99%的预测区间轻松地涵盖了数据，特别是包括银河系，迄今为止一直被认为是一个有问题的离群值。最后，我们演示了如何随机拦截模型可以将每个特定的星系形态类型的信息。贝叶斯变量选择方法允许自动识别具有不同GC产物的星系类型，这表明平均S0星系的GC人口比具有类似亮度的其他类型小35%。
In this paper, the third in a series illustrating the power of generalized linear models (GLMs) for the astronomical community, we elucidate the potential of the class of GLMs which handles count data. The size of a galaxy's globular cluster (GC) population (NGC) is a prolonged puzzle in the astronomical literature. It falls in the category of count data analysis, yet it is usually modelled as if it were a continuous response variable. We have developed a Bayesian negative binomial regression model to study the connection between NGC and the following galaxy properties: central black hole mass, dynamical bulge mass, bulge velocity dispersion and absolute visual magnitude. The methodology introduced herein naturally accounts for heteroscedasticity, intrinsic scatter, errors in measurements in both axes (either discrete or continuous) and allows modelling the population of GCs on their natural scale as a non-negative integer variable. Prediction intervals of 99 per cent around the trend for expected NGC comfortably envelope the data, notably including the Milky Way, which has hitherto been considered a problematic outlier. Finally, we demonstrate how random intercept models can incorporate information of each particular galaxy morphological type. Bayesian variable selection methodology allows for automatically identifying galaxy types with different productions of GCs, suggesting that on average S0 galaxies have a GC population 35 per cent smaller than other types with similar brightness.