Abstract Data increasingly take the form of a multi-way array, or tensor, in several biomedical domains. Such tensors are often incompletely observed. For example, we are motivated by longitudinal microbiome studies in which several timepoints are missing for several subjects. There is a growing literature on missing data imputation for tensors. However, existing methods give a point estimate for missing values without capturing uncertainty. We propose a multiple imputation approach for tensors in a flexible Bayesian framework, that yields realistic simulated values for missing entries and can propagate uncertainty through subsequent analyses. Our model uses efficient and widely applicable conjugate priors for a CANDECOMP/PARAFAC (CP) factorization, with a separable residual covariance structure. This approach is shown to perform well with respect to both imputation accuracy and uncertainty calibration, for scenarios in which either single entries or entire fibers of the tensor are missing. For two microbiome applications, it is shown to accurately capture uncertainty in the full microbiome profile at missing timepoints and used to infer trends in species diversity for the population. Documented R code to perform our multiple imputation approach is available at https://github.com/lockEF/MultiwayImputation.

Ziren Jiang

Gen Li

Eric F Lock

Biostatistics

20 世纪重要的科学发展之一是统计推理和应用于人类健康研究的方法的爆炸式增长。例子包括推理的可能性方法、流行病学统计、临床试验、生存分析和统计遗传学的发展。公共卫生和生物医学研究中的实质性问题推动了统计方法的发展，这反过来又提高了我们从数据中得出有效推论的能力。生物统计学的目标是推进统计科学及其在人类健康和疾病问题上的应用，最终目标是促进公众健康。

One of the significant scientific developments of the 20th century is the rapid growth of statistical inference and its application methods in public health research. This includes advancements in likelihood methods, epidemiological statistics, clinical trials, survival analysis, and statistical genetics. Substantial issues in public health and biomedical research drive the development of statistical methods, which in turn enhance our ability to draw valid inferences from data. The goal of Biostatistics is to advance statistical science and its application to human health and disease issues, ultimately aiming to promote public health.

20 世纪重要的科学发展之一是统计推理及其在公共卫生研究中的应用方法的迅猛增长。这包括推理的可能性方法、流行病学统计、临床试验、生存分析和统计遗传学等领域的发展。公共卫生和生物医学研究中的重要问题推动了统计方法的进步，而这些进步又增强了我们从数据中得出有效推论的能力。生物统计学的目标是推动统计科学的发展及其在人类健康和疾病问题上的应用，最终旨在促进公众健康。

Category	Quartile
数学	3
数学, 数学与计算生物学	2
数学, 统计学与概率论	3

BAMITA: Bayesian multiple imputation for tensor arrays

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Category	Quartile
STATISTICS & PROBABILITY	1