Mass cytometry technology enables the simultaneous measurement of over 40 proteins on single cells. This has helped immunologists to increase their understanding of heterogeneity, complexity, and lineage relationships of white blood cells. Current statistical methods often collapse the rich single-cell data into summary statistics before proceeding with downstream analysis, discarding the information in these multivariate datasets. In this article, our aim is to exhibit the use of statistical analyses on the raw, uncompressed data thus improving replicability, and exposing multivariate patterns and their associated uncertainty profiles. We show that multivariate generative models are a valid alternative to univariate hypothesis testing. We propose two models: a multivariate Poisson log-normal mixed model and a logistic linear mixed model. We show that these models are complementary and that either model can account for different confounders. We use Hamiltonian Monte Carlo to provide Bayesian uncertainty quantification. Our models applied to a recent pregnancy study successfully reproduce key findings while quantifying increased overall protein-to-protein correlations between first and third trimester.
Fast and accurate predictions of uncertainties in the computed dose are crucial for the determination of robust treatment plans in radiation therapy. This requires the solution of particle transport problems with uncertain parameters or initial conditions. Monte Carlo methods are often used to solve transport problems especially for applications which require high accuracy. In these cases, common non-intrusive solution strategies that involve repeated simulations of the problem at different points in the parameter space quickly become infeasible due to their long run-times. Intrusive methods h…
Systems subject to uncertain inputs produce uncertain responses. Uncertainty quantification (UQ) deals with the estimation of statistics of the system response, given a computational model of the system and a probabilistic model of its inputs. In engineering applications it is common to assume that the inputs are mutually independent or coupled by a Gaussian or elliptical dependence structure (copula). In this paper we overcome such limitations by modelling the dependence structure of multivariate inputs as vine copulas. Vine copulas are models of multivariate dependence built from simpler pai…
The ocean is filled with microscopic microalgae called phytoplankton, which together are responsible for as much photosynthesis as all plants on land combined. Our ability to predict their response to the warming ocean relies on understanding how the dynamics of phytoplankton populations is influenced by changes in environmental conditions. One powerful technique to study the dynamics of phytoplankton is flow cytometry, which measures the optical properties of thousands of individual cells per second. Today, oceanographers are able to collect flow cytometry data in real-time onboard a moving s…
This paper addresses the problem of quantification and propagation of uncertainties associated with dependence modeling when data for characterizing probability models are limited. Practically, the system inputs are often assumed to be mutually independent or correlated by a multivariate Gaussian distribution. However, this subjective assumption may introduce bias in the response estimate if the real dependence structure deviates from this assumption. In this work, we overcome this limitation by introducing a flexible copula dependence model to capture complex dependencies. A hierarchical Baye…
The analysis of large scale medical claims data has the potential to improve quality of care by generating insights which can be used to create tailored medical programs. In particular, the multivariate probit model can be used to investigate the correlation between multiple binary responses of interest in such data, e.g. the presence of multiple chronic conditions. Bayesian modeling is well suited to such analyses because of the automatic uncertainty quantification provided by the posterior distribution. A complicating factor is that large medical claims datasets often do not fit in memory, w…
How to extract useful insights from data is always a challenge, especially if the data is multidimensional. Often, the data can be organized according to certain hierarchical structure that are stemmed either from data collection process or from the information and phenomena carried by the data itself. The current study attempts to discover and visualize these underlying hierarchies. By regarding each observation in the data as a draw from a (hypothetical) multidimensional joint density, our first goal is to approximate this unknown density with a piecewise constant function via binary partiti…
For modeling multivariate financial time series we propose a single factor copula model together with stochastic volatility margins. This model generalizes single factor models relying on the multivariate normal distribution and allows for symmetric and asymmetric tail dependence. We develop joint Bayesian inference using Hamiltonian Monte Carlo (HMC) within Gibbs sampling. Thus we avoid information loss caused by the two-step approach for margins and dependence in copula models as followed by Schamberger et al(2017). Further, the Bayesian approach allows for high dimensional parameter spaces …
We present a framework to simultaneously align and smooth data in the form of multiple point clouds sampled from unknown densities with support in a d-dimensional Euclidean space. This work is motivated by applications in bioinformatics where researchers aim to automatically homogenize large datasets to compare and analyze characteristics within a same cell population. Inconveniently, the information acquired is most certainly noisy due to mis-alignment caused by technical variations of the environment. To overcome this problem, we propose to register multiple point clouds by using the notion …
Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample size, making it difficult to apply them to massive data. Moreover, resampling is usually necessary to evaluate the statistical significance of the resulting test statistics at finite sample sizes, further worsening the computational burden. We introduce a scalable, resampling-free approach to testing the independence between two random vectors by breaking d…
A Bayesian Framework for Multivariate Differential Analysis
Medical Research Council Biostatistics Unit, University of Cambridge（剑桥大学医学研究委员会生物统计单元）；Université Paris-Saclay, INRAE, AgroParisTech, GABI（巴黎萨克雷大学、法国国家农业食品环境研究院、巴黎综合理工学校GABI）；Université Paris-Saclay, AgroParisTech, INRAE, UMR MIA Paris-Saclay（巴黎萨克雷大学、巴黎综合理工学校、法国国家农业食品环境研究院UMR MIA巴黎萨克雷）
In many fields and applications count data can be subject to delayed reporting. This is where the total count, such as the number of disease cases contracted in a given week, may not be immediately available, instead arriving in parts over time. For short term decision making, the statistical challenge lies in predicting the total count based on any observed partial counts, along with a robust quantification of uncertainty. In this article we discuss previous approaches to modelling delayed reporting and present a multivariate hierarchical framework where the count generating process and delay…
In any other circumstance, it might make sense to define the extent of the terrain (Data Science) first, and then locate and describe the landmarks (Principles). But this data revolution we are experiencing defies a cadastral survey. Areas are continually being annexed into Data Science. For example, biometrics was traditionally statistics for agriculture in all its forms but now, in Data Science, it means the study of characteristics that can be used to identify an individual. Examples of non-intrusive measurements include height, weight, fingerprints, retina scan, voice, photograph/video (fa…
