Bayesian Photometric Redshift Estimation
Bayesian Photometric Redshift Estimation
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DOI：
10.1086/308947
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发表时间：
1998-11
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影响因子：
--
通讯作者：
N. Benı́tez
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作者：
N. Benı́tez
测光红移正迅速成为观测宇宙学的一个重要工具，尽管现有方法的某些缺点在某种程度上阻碍了它们的利用，例如，最大似然技术的不可靠性或“训练集”方法的应用范围有限。贝叶斯推理的应用光度红移估计的问题，有效地克服了大多数这些问题。先验概率和贝叶斯边缘化的使用有助于纳入相关知识，如红移分布的预期形状和星系类型分数，这些知识可以很容易地从现有的调查中获得，但通常被其他方法忽略。如果先前的信息是缺乏或不必要的，例如，由于前所未有的深度观测，相应的先验分布可以校准使用甚至是正在获得的光度红移的数据样本。贝叶斯统计的一个重要优点是，红移估计的准确性可以用其他统计方法无法比拟的方式来表征，从而能够选择具有非常可靠的光度红移的星系样本。通过这种方式，可以更准确地确定单个星系的属性，同时以最佳方式估计样本的统计属性。此外，这里描述的贝叶斯形式主义可以很容易地推广到处理广泛的问题，利用光度红移。哈勃深场北（HDF-N）光谱红移与该方法的预测之间有很好的一致性，在z < 6之前，均方根误差Δz ≤ 0.06（1 + zspec），没有异常值或系统偏差。应该注意的是，由于这些结果在训练集程序之后尚未达到，因此上述Δz值应该是任何类似样本的预期准确度的合理估计。通过估计HDF-N中的红移但将颜色信息限制在UBVI滤波器中来进一步测试该方法;结果显示出比用最大似然技术获得的结果更可靠。
Photometric redshifts are quickly becoming an essential tool of observational cosmology, although their utilization is somewhat hindered by certain shortcomings of the existing methods, e.g., the unreliability of maximum-likelihood techniques or the limited application range of the "training-set" approach. The application of Bayesian inference to the problem of photometric redshift estimation effectively overcomes most of these problems. The use of prior probabilities and Bayesian marginalization facilitates the inclusion of relevant knowledge, such as the expected shape of the redshift distributions and the galaxy type fractions, which can be readily obtained from existing surveys but are often ignored by other methods. If this previous information is lacking or insufficient—for instance, because of the unprecedented depth of the observations—the corresponding prior distributions can be calibrated using even the data sample for which the photometric redshifts are being obtained. An important advantage of Bayesian statistics is that the accuracy of the redshift estimation can be characterized in a way that has no equivalents in other statistical approaches, enabling the selection of galaxy samples with extremely reliable photometric redshifts. In this way, it is possible to determine the properties of individual galaxies more accurately, and simultaneously estimate the statistical properties of a sample in an optimal fashion. Moreover, the Bayesian formalism described here can be easily generalized to deal with a wide range of problems that make use of photometric redshifts. There is excellent agreement between the ≈130 Hubble Deep Field North (HDF-N) spectroscopic redshifts and the predictions of the method, with a rms error of Δz ≈ 0.06(1 + zspec) up to z < 6 and no outliers nor systematic biases. It should be remarked that since these results have not been reached following a training-set procedure, the above value of Δz should be a fair estimate of the expected accuracy for any similar sample. The method is further tested by estimating redshifts in the HDF-N but restricting the color information to the UBVI filters; the results are shown to be significantly more reliable than those obtained with maximum-likelihood techniques.