The microlensing parallax campaign with the $Spitzer$ space telescope aims to measure masses and distances of microlensing planetary events seen towards the Galactic bulge. The hope is to measure how the distribution of planets depends on position within the Galaxy. In this paper, we compare 50 microlens parallax measurements from 2015 $Spitzer$ campaign to three different Galactic models commonly used in microlensing analyses, and we find that $\geq 80\,$\% of these events have microlensing parallax values higher than the medians predicted by Galactic models. We use the Anderson-Darling (AD) and Kolmogorov-Smirnov (KS) tests on the distributions of the prior probability that the each of the $Spitzer$ parallax measurements is at least as large as the observed microlensing parallax values. These tests indicate probabilities of $p_{\rm AD} < 3.0 \times 10^{-8}$ and $p_{\rm KS} < 4.1 \times 10^{-6}$ that the data are consistent with these Galactic models from the AD and KS tests respectively. Given that many $Spitzer$ light curves show evidence of large correlated errors, we conclude that this discrepancy is probably due to systematic errors in the $Spitzer$ photometry. We consider a simple scheme to correct for this problem by multiplying the reported error bars on the $Spitzer$ microlensing parallax measurements by a constant factor, and we find that an error bar renormalization factor of 3.4 provides reasonable agreement with all three Galactic models. We expect, however, that corrections to the uncertainties in the $Spitzer$ photometry itself are likely to be a more effective way to address the systematic errors. We also argue that is important to include the ${\bm \pi_{\rm E}}$ prior distributions when analyzing events with large uncertainties or degeneracies in ${\bm \pi_{\rm E}}$ measurements.

中文翻译：

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斯皮策微透镜视差测量中系统误差的证据

使用 $Spitzer$ 太空望远镜进行的微透镜视差运动旨在测量朝向银河隆起看到的微透镜行星事件的质量和距离。希望是测量行星的分布如何取决于银河系内的位置。在本文中，我们将 2015 年 $Spitzer$ 活动的 50 个微透镜视差测量值与微透镜分析中常用的三种不同的银河模型进行比较，我们发现这些事件中的 $\geq 80\,$\% 的微透镜视差值高于银河模型预测的中位数。我们对先验概率分布使用 Anderson-Darling (AD) 和 Kolmogorov-Smirnov (KS) 检验，即每个 $Spitzer$ 视差测量值至少与观察到的微透镜视差值一样大。这些测试表明 $p_{\rm AD} < 3 的概率。0 \times 10^{-8}$ 和 $p_{\rm KS} < 4.1 \times 10^{-6}$ 数据分别与来自 AD 和 KS 测试的这些银河模型一致。鉴于许多 $Spitzer$ 光度曲线显示存在较大相关误差的证据，我们得出结论，这种差异可能是由于 $Spitzer$ 测光中的系统误差造成的。我们考虑了一个简单的方案来纠正这个问题，通过将 $Spitzer$ 微透镜视差测量报告的误差条乘以一个常数因子，我们发现 3.4 的误差条重整化因子提供了与所有三个银河模型的合理一致性。然而，我们预计，对 $Spitzer$ 光度测量本身的不确定性进行修正可能是解决系统误差的更有效方法。