In optical and infrared long-baseline interferometry, data often display significant correlated errors because of uncertain multiplicative factors such as the instrumental transfer function or the pixel-to-visibility matrix. In the context of model fitting, this situation often leads to a significant bias in the model parameters. In the most severe cases, this can can result in a fit lying outside of the range of measurement values. This is known in nuclear physics as Peelle’s Pertinent Puzzle. I show how this arises in the context of interferometry and determine that the relative bias is of the order of the square root of the correlated component of the relative uncertainty times the number of measurements. It impacts preferentially large datasets, such as those obtained in medium to high spectral resolution. I then give a conceptually simple and computationally cheap way to avoid the issue: model the data without covariances, estimate the covariance matrix by error propagation using the modelled data instead of the actual data, and perform the model fitting using the covariance matrix. I also show that a more imprecise but also unbiased result can be obtained from ignoring correlations in the model fitting.

中文翻译：

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干涉测量中相关数据的无偏差模型拟合

在光学和红外长基线干涉测量中，由于不确定的乘法因素（例如仪器传递函数或像素到能见度矩阵），数据通常会显示出显着的相关误差。在模型拟合的情况下，这种情况通常会导致模型参数出现显着偏差。在最严重的情况下，这可能会导致拟合超出测量值的范围。这在核物理学中被称为 Peelle 的相关谜题。我展示了这是如何在干涉测量的背景下出现的，并确定相对偏差是相对不确定性的相关分量的平方根乘以测量次数的数量级。它优先影响大型数据集，例如以中到高光谱分辨率获得的数据集。然后，我给出了一种概念上简单且计算成本低廉的方法来避免该问题：对没有协方差的数据进行建模，使用建模数据而不是实际数据通过误差传播来估计协方差矩阵，并使用协方差矩阵执行模型拟合。我还表明，忽略模型拟合中的相关性可以获得更不精确但更无偏的结果。