arXiv subjects

Xiaodan Fan

Publications and source records attributed to Xiaodan Fan.

18 recordsLinked to original sources

arXiv2026

Projection Is All You Need: Interpreting Polarization Measurements in the Orion Clouds with Sub-Alfv\'enic MHD Simulations

Dust polarization observations are widely used to diagnose the relative importance of magnetic fields and turbulence in star forming molecular clouds, often through summary statistics such as the mean polarization direction $\mu$ and dispersion $\sigma$. Recent multi-scale polarization observations of the Orion Integral-Shaped Filament (ISF) reveal substantial diversity in polarization morphology among its dense cores, raising questions about the underlying Alfv\'enic nature of the cloud. In this work, we develop a statistical framework to compare polarization-based summary statistics from observations with those derived from projected three dimensional MHD simulations, explicitly accounting for projection effects. Using globally sub-Alfv\'enic simulations that naturally produce slightly super-Alfv\'enic dense cores, we show that modest deviations of core-scale magnetic fields from the parent cloud field, when combined with projection, can generate a wide range of plane-of-sky polarization dispersions. Applying hypothesis testing, we find that the observed $(\mu, \sigma)$ values in the Orion ISF are statistically consistent with sub-Alfv\'enic cloud models over a broad range of viewing angles. This broad degeneracy implies that $\mu$ and $\sigma$ alone cannot provide precise information about the three-dimensional magnetic-field distribution, and hence the Alfv\'en Mach number, of an individual cloud. While the observations can provide evidence against certain projection geometries, we demonstrate that polarization statistics based solely on $(\mu, \sigma)$ are insufficient to provide evidence against sub-Alfv\'enic cloud models. Our results highlight the necessity of explicitly incorporating projection effects when interpreting polarization observations of molecular clouds.

astro-ph.GA↗

arXiv2026

Fast Gibbs Sampling on Bayesian Hidden Markov Model with Missing Observations

The Hidden Markov Model (HMM) is a widely-used statistical model for handling sequential data. However, the presence of missing observations in real-world datasets often complicates the application of the model. The EM algorithm and Gibbs samplers can be used to estimate the model, yet suffering from various problems including non-convexity, high computational complexity and slow mixing. In this paper, we propose a collapsed Gibbs sampler that efficiently samples from HMMs' posterior by integrating out both the missing observations and the corresponding latent states. The proposed sampler is fast due to its three advantages. First, it achieves an estimation accuracy that is comparable to existing methods. Second, it can produce a larger Effective Sample Size (ESS) per iteration, which can be justified theoretically and numerically. Third, when the number of missing entries is large, the sampler has a significant smaller computational complexity per iteration compared to other methods, thus is faster computationally. In summary, the proposed sampling algorithm is fast both computationally and theoretically and is particularly advantageous when there are a lot of missing entries. Finally, empirical evaluations based on numerical simulations and real data analysis demonstrate that the proposed algorithm consistently outperforms existing algorithms in terms of time complexity and sampling efficiency (measured in ESS).

stat.ML↗

arXiv2024

Generalized Bayesian nonparametric clustering framework for high-dimensional spatial omics data

The advent of next-generation sequencing-based spatially resolved transcriptomics (SRT) techniques has transformed genomic research by enabling high-throughput gene expression profiling while preserving spatial context. Identifying spatial domains within SRT data is a critical task, with numerous computational approaches currently available. However, most existing methods rely on a multi-stage process that involves ad-hoc dimension reduction techniques to manage the high dimensionality of SRT data. These low-dimensional embeddings are then subjected to model-based or distance-based clustering methods. Additionally, many approaches depend on arbitrarily specifying the number of clusters (i.e., spatial domains), which can result in information loss and suboptimal downstream analysis. To address these limitations, we propose a novel Bayesian nonparametric mixture of factor analysis (BNPMFA) model, which incorporates a Markov random field-constrained Gibbs-type prior for partitioning high-dimensional spatial omics data. This new prior effectively integrates the spatial constraints inherent in SRT data while simultaneously inferring cluster membership and determining the optimal number of spatial domains. We have established the theoretical identifiability of cluster membership within this framework. The efficacy of our proposed approach is demonstrated through realistic simulations and applications to two SRT datasets. Our results show that the BNPMFA model not only surpasses state-of-the-art methods in clustering accuracy and estimating the number of clusters but also offers novel insights for identifying cellular regions within tissue samples.

stat.ME↗

arXiv2024

Polarization Holes as an Indicator of Magnetic Field-Angular Momentum Alignment I. Initial Tests

The formation of protostellar disks is still a mystery, largely due to the difficulties in observations that can constrain theories. For example, the 3D alignment between the rotation of the disk and the magnetic fields (B-fields) in the formation environment is critical in some models, but so far impossible to observe. Here, we study the possibility of probing the alignment between B-field and disk rotation using ``polarization holes'' (PHs). PHs are widely observed and are caused by unresolved B-field structures. With ideal magnetohydrodynamic (MHD) simulations, we demonstrate that different initial alignments between B-field and angular momentum (AM) can result in B-field structures that are distinct enough to produce distinguishable PHs. Thus PHs can potentially serve as probes for alignments between B-field and AM in disk formation.

astro-ph.GA↗

arXiv2024

Decomposition with Monotone B-splines: Fitting and Testing

A univariate continuous function can always be decomposed as the sum of a non-increasing function and a non-decreasing one. Based on this property, we propose a non-parametric regression method that combines two spline-fitted monotone curves. We demonstrate by extensive simulations that, compared to standard spline-fitting methods, the proposed approach is particularly advantageous in high-noise scenarios. Several theoretical guarantees are established for the proposed approach. Additionally, we present statistics to test the monotonicity of a function based on monotone decomposition, which can better control Type I error and achieve comparable (if not always higher) power compared to existing methods. Finally, we apply the proposed fitting and testing approaches to analyze the single-cell pseudotime trajectory datasets, identifying significant biological insights for non-monotonically expressed genes through Gene Ontology enrichment analysis. The source code implementing the methodology and producing all results is accessible at https://github.com/szcf-weiya/MonotoneDecomposition.jl.

stat.ME↗

arXiv2023

Bayesian Nonparametric Clustering with Feature Selection for Spatially Resolved Transcriptomics Data

The advent of next-generation sequencing-based spatially resolved transcriptomics (SRT) techniques has reshaped genomic studies by enabling high-throughput gene expression profiling while preserving spatial and morphological context. Nevertheless, there are inherent challenges associated with these new high-dimensional spatial data, such as zero-inflation, over-dispersion, and heterogeneity. These challenges pose obstacles to effective clustering, which is a fundamental problem in SRT data analysis. Current computational approaches often rely on heuristic data preprocessing and arbitrary cluster number prespecification, leading to considerable information loss and consequently, suboptimal downstream analysis. In response to these challenges, we introduce BNPSpace, a novel Bayesian nonparametric spatial clustering framework that directly models SRT count data. BNPSpace facilitates the partitioning of the whole spatial domain, which is characterized by substantial heterogeneity, into homogeneous spatial domains with similar molecular characteristics while identifying a parsimonious set of discriminating genes among different spatial domains. Moreover, BNPSpace incorporates spatial information through a Markov random field prior model, encouraging a smooth and biologically meaningful partition pattern.

stat.AP↗

arXiv2023

Degrees of Freedom: Search Cost and Self-consistency

Model degrees of freedom ($\df$) is a fundamental concept in statistics because it quantifies the flexibility of a fitting procedure and is indispensable in model selection. To investigate the gap between $\df$ and the number of independent variables in the fitting procedure, \textcite{tibshiraniDegreesFreedomModel2015} introduced the \emph{search degrees of freedom} ($\sdf$) concept to account for the search cost during model selection. However, this definition has two limitations: it does not consider fitting procedures in augmented spaces and does not use the same fitting procedure for $\sdf$ and $\df$. We propose a \emph{modified search degrees of freedom} ($\msdf$) to directly account for the cost of searching in either original or augmented spaces. We check this definition for various fitting procedures, including classical linear regressions, spline methods, adaptive regressions (the best subset and the lasso), regression trees, and multivariate adaptive regression splines (MARS). In many scenarios when $\sdf$ is applicable, $\msdf$ reduces to $\sdf$. However, for certain procedures like the lasso, $\msdf$ offers a fresh perspective on search costs. For some complex procedures like MARS, the $\df$ has been pre-determined during model fitting, but the $\df$ of the final fitted procedure might differ from the pre-determined one. To investigate this discrepancy, we introduce the concepts of \emph{nominal} $\df$ and \emph{actual} $\df$, and define the property of \emph{self-consistency}, which occurs when there is no gap between these two $\df$'s. We propose a correction procedure for MARS to align these two $\df$'s, demonstrating improved fitting performance through extensive simulations and two real data applications.

stat.ME↗

arXiv2023

Monotone Cubic B-Splines with a Neural-Network Generator

We present a method for fitting monotone curves using cubic B-splines, which is equivalent to putting a monotonicity constraint on the coefficients. We explore different ways of enforcing this constraint and analyze their theoretical and empirical properties. We propose two algorithms for solving the spline fitting problem: one that uses standard optimization techniques and one that trains a Multi-Layer Perceptrons (MLP) generator to approximate the solutions under various settings and perturbations. The generator approach can speed up the fitting process when we need to solve the problem repeatedly, such as when constructing confidence bands using bootstrap. We evaluate our method against several existing methods, some of which do not use the monotonicity constraint, on some monotone curves with varying noise levels. We demonstrate that our method outperforms the other methods, especially in high-noise scenarios. We also apply our method to analyze the polarization-hole phenomenon during star formation in astrophysics. The source code is accessible at \texttt{\url{https://github.com/szcf-weiya/MonotoneSplines.jl}}.

stat.ME↗

arXiv2023

Bayesian Inference of Gene Expression Dynamics in Alzheimer Brains

Alzheimer's disease (AD) is a serious neurodegenerative disease consisting of four stages where the illness gets progressively worse. It is of great significance to detect the gene regulatory mechanism as AD progresses and, thus, to help us better understand the causes of AD and find ways to treat or control AD. There are numerous researches to conduct this kind of study. However, the majority of methods are processing region by region of brain, stage by stage of AD, and then compare the results to detect changes. It is unclear how to combine these three dimensions, i.e., gene, region and stage, simultaneously to study gene expression dynamics of AD. This is the motivation of our research. In our study, we propose a statistical model of increments to clarify the relationship between gene expression in adjacent stages, so that we could better estimate the missing data we want and obtain a complete reasonable dynamic regulatory network model. Simulations are conducted to validate the statistical power of our algorithm. Moreover, a real data analysis shows that our method can capture the dynamic gene regulatory relationships among this complex brain data.

stat.ME↗

arXiv2023

A Geometric Statistic for Quantifying Correlation Between Tree-Shaped Datasets

The magnitude of Pearson correlation between two scalar random variables can be visually judged from the two-dimensional scatter plot of an independent and identically distributed sample drawn from the joint distribution of the two variables: the closer the points lie to a straight slanting line, the greater the correlation. To the best of our knowledge, similar graphical representation or geometric quantification of tree correlation does not exist in the literature although tree-shaped datasets are frequently encountered in various fields, such as academic genealogy tree and embryonic development tree. In this paper, we introduce a geometric statistic to both represent tree correlation intuitively and quantify its magnitude precisely. The theoretical properties of the geometric statistic are provided. Large-scale simulations based on various data distributions demonstrate that the geometric statistic is precise in measuring the tree correlation. Its real application on mathematical genealogy trees also demonstrated its usefulness.

stat.ME↗

arXiv2021

Appearance-free Tripartite Matching for Multiple Object Tracking

Multiple Object Tracking (MOT) detects the trajectories of multiple objects given an input video. It has become more and more important for various research and industry areas, such as cell tracking for biomedical research and human tracking in video surveillance. Most existing algorithms depend on the uniqueness of the object's appearance, and the dominating bipartite matching scheme ignores the speed smoothness. Although several methods have incorporated the velocity smoothness for tracking, they either fail to pursue global smooth velocity or are often trapped in local optimums. We focus on the general MOT problem regardless of the appearance and propose an appearance-free tripartite matching to avoid the irregular velocity problem of the bipartite matching. The tripartite matching is formulated as maximizing the likelihood of the state vectors constituted of the position and velocity of objects, which results in a chain-dependent structure. We resort to the dynamic programming algorithm to find such a maximum likelihood estimate. To overcome the high computational cost induced by the vast search space of dynamic programming when many objects are to be tracked, we decompose the space by the number of disappearing objects and propose a reduced-space approach by truncating the decomposition. Extensive simulations have shown the superiority and efficiency of our proposed method, and the comparisons with top methods on Cell Tracking Challenge also demonstrate our competence. We also applied our method to track the motion of natural killer cells around tumor cells in a cancer study.\footnote{The source code is available on \url{https://github.com/szcf-weiya/TriMatchMOT}

cs.CV↗

arXiv2019

Nonparametric Statistical Inference and Imputation for Incomplete Categorical Data

Missingness in categorical data is a common problem in various real applications. Traditional approaches either utilize only the complete observations or impute the missing data by some ad hoc methods rather than the true conditional distribution of the missing data, thus losing or distorting the rich information in the partial observations. In this paper, we propose the Dirichlet Process Mixture of Collapsed Product-Multinomials (DPMCPM) to model the full data jointly and compute the model efficiently. By fitting an infinite mixture of product-multinomial distributions, DPMCPM is applicable for any categorical data regardless of the true distribution, which may contain complex association among variables. Under the framework of latent class analysis, we show that DPMCPM can model general missing mechanisms by creating an extra category to denote missingness, which implicitly integrates out the missing part with regard to their true conditional distribution. Through simulation studies and a real application, we demonstrate that DPMCPM outperforms existing approaches on statistical inference and imputation for incomplete categorical data of various missing mechanisms. DPMCPM is implemented as the R package \texttt{MMDai}, which is available from the Comprehensive R Archive Network at https://cran.r-project.org/web/packages/MMDai/index.html.

stat.ME↗

arXiv2017

A Bayesian Method for Joint Clustering of Vectorial Data and Network Data

We present a new model-based integrative method for clustering objects given both vectorial data, which describes the feature of each object, and network data, which indicates the similarity of connected objects. The proposed general model is able to cluster the two types of data simultaneously within one integrative probabilistic model, while traditional methods can only handle one data type or depend on transforming one data type to another. Bayesian inference of the clustering is conducted based on a Markov chain Monte Carlo algorithm. A special case of the general model combining the Gaussian mixture model and the stochastic block model is extensively studied. We used both synthetic data and real data to evaluate this new method and compare it with alternative methods. The results show that our simultaneous clustering method performs much better. This improvement is due to the power of the model-based probabilistic approach for efficiently integrating information.

stat.ML↗

arXiv2017

The Link between Magnetic-field Orientations and Star Formation Rates

Understanding star formation rates (SFR) is a central goal of modern star-formation models, which mainly involve gravity, turbulence and, in some cases, magnetic fields (B-fields). However, a connection between B-fields and SFR has never been observed. Here, a comparison between the surveys of SFR and a study of cloud-field alignment - which revealed a bimodal (parallel or perpendicular) alignment - shows consistently lower SFR per solar mass for clouds almost perpendicular to the B-fields. This is evidence of B-fields being a primary regulator of SFR. The perpendicular alignment possesses a significantly higher magnetic flux than the parallel alignment and thus a stronger support of the gas against self-gravity. This results in overall lower masses of the fragmented components, which are in agreement with the lower SFR.

astro-ph.GA↗

arXiv2015

Bayesian detection of embryonic gene expression onset in C. elegans

To study how a zygote develops into an embryo with different tissues, large-scale 4D confocal movies of C. elegans embryos have been produced recently by experimental biologists. However, the lack of principled statistical methods for the highly noisy data has hindered the comprehensive analysis of these data sets. We introduced a probabilistic change point model on the cell lineage tree to estimate the embryonic gene expression onset time. A Bayesian approach is used to fit the 4D confocal movies data to the model. Subsequent classification methods are used to decide a model selection threshold and further refine the expression onset time from the branch level to the specific cell time level. Extensive simulations have shown the high accuracy of our method. Its application on real data yields both previously known results and new findings.

stat.AP↗

arXiv2011

The EM Algorithm and the Rise of Computational Biology

In the past decade computational biology has grown from a cottage industry with a handful of researchers to an attractive interdisciplinary field, catching the attention and imagination of many quantitatively-minded scientists. Of interest to us is the key role played by the EM algorithm during this transformation. We survey the use of the EM algorithm in a few important computational biology problems surrounding the "central dogma"; of molecular biology: from DNA to RNA and then to proteins. Topics of this article include sequence motif discovery, protein sequence alignment, population genetics, evolutionary models and mRNA expression microarray data analysis.

stat.ME↗

arXiv2010

Bayesian meta-analysis for identifying periodically expressed genes in fission yeast cell cycle

The effort to identify genes with periodic expression during the cell cycle from genome-wide microarray time series data has been ongoing for a decade. However, the lack of rigorous modeling of periodic expression as well as the lack of a comprehensive model for integrating information across genes and experiments has impaired the effort for the accurate identification of periodically expressed genes. To address the problem, we introduce a Bayesian model to integrate multiple independent microarray data sets from three recent genome-wide cell cycle studies on fission yeast. A hierarchical model was used for data integration. In order to facilitate an efficient Monte Carlo sampling from the joint posterior distribution, we develop a novel Metropolis--Hastings group move. A surprising finding from our integrated analysis is that more than 40% of the genes in fission yeast are significantly periodically expressed, greatly enhancing the reported 10--15% of the genes in the current literature. It calls for a reconsideration of the periodically expressed gene detection problem.

stat.AP↗

arXiv2010

BOOST: A fast approach to detecting gene-gene interactions in genome-wide case-control studies

Gene-gene interactions have long been recognized to be fundamentally important to understand genetic causes of complex disease traits. At present, identifying gene-gene interactions from genome-wide case-control studies is computationally and methodologically challenging. In this paper, we introduce a simple but powerful method, named `BOolean Operation based Screening and Testing'(BOOST). To discover unknown gene-gene interactions that underlie complex diseases, BOOST allows examining all pairwise interactions in genome-wide case-control studies in a remarkably fast manner. We have carried out interaction analyses on seven data sets from the Wellcome Trust Case Control Consortium (WTCCC). Each analysis took less than 60 hours on a standard 3.0 GHz desktop with 4G memory running Windows XP system. The interaction patterns identified from the type 1 diabetes data set display significant difference from those identified from the rheumatoid arthritis data set, while both data sets share a very similar hit region in the WTCCC report. BOOST has also identified many undiscovered interactions between genes in the major histocompatibility complex (MHC) region in the type 1 diabetes data set. In the coming era of large-scale interaction mapping in genome-wide case-control studies, our method can serve as a computationally and statistically useful tool.

q-bio.GN↗