BACKGROUND Mixtures of beta distributions are a flexible tool for modeling data with values on the unit interval, such as methylation levels. However, maximum likelihood parameter estimation with beta distributions suffers from problems because of singularities in the log-likelihood function if some observations take the values 0 or 1. METHODS While ad-hoc corrections have been proposed to mitigate this problem, we propose a different approach to parameter estimation for beta mixtures where such problems do not arise in the first place. Our algorithm combines latent variables with the method of moments instead of maximum likelihood, which has computational advantages over the popular EM algorithm. RESULTS As an application, we demonstrate that methylation state classification is more accurate when using adaptive thresholds from beta mixtures than non-adaptive thresholds on observed methylation levels. We also demonstrate that we can accurately infer the number of mixture components. CONCLUSIONS The hybrid algorithm between likelihood-based component un-mixing and moment-based parameter estimation is a robust and efficient method for beta mixture estimation. We provide an implementation of the method ("betamix") as open source software under the MIT license.

中文翻译：

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用于β混合物的混合参数估计算法及其在甲基化状态分类中的应用。

背景技术β分布的混合物是用于对数据进行建模的灵活工具，该数据具有单位间隔上的值，例如甲基化水平。但是，如果某些观测值取值为0或1，则由于对数似然函数的奇异性，具有beta分布的最大似然参数估计会遇到问题。方法尽管已提出临时校正来缓解此问题，但我们提出了另一种方法首先不会出现此类问题的β混合物的参数估计。我们的算法将隐变量与矩量法相结合而不是最大似然法，与流行的EM算法相比具有计算优势。结果作为一个应用程序，我们证明，当使用来自β混合物的适应性阈值时，甲基化状态分类比观察到的甲基化水平的非适应性阈值更准确。我们还证明了我们可以准确地推断出混合物成分的数量。结论基于似然性的分量解混合与基于矩的参数估计之间的混合算法是一种可靠且有效的Beta混合估计方法。我们提供此方法（“ betamix”）的实现作为MIT许可下的开源软件。结论基于似然性的分量解混合与基于矩的参数估计之间的混合算法是一种可靠且有效的Beta混合估计方法。我们提供此方法（“ betamix”）的实现作为MIT许可下的开源软件。结论基于似然性的分量解混合与基于矩的参数估计之间的混合算法是一种可靠且有效的β混合估计方法。我们提供此方法（“ betamix”）的实现作为MIT许可下的开源软件。