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Full-Text Articles in Statistics and Probability
Statistical Approaches Of Gene Set Analysis With Quantitative Trait Loci For High-Throughput Genomic Studies., Samarendra Das
Statistical Approaches Of Gene Set Analysis With Quantitative Trait Loci For High-Throughput Genomic Studies., Samarendra Das
Electronic Theses and Dissertations
Recently, gene set analysis has become the first choice for gaining insights into the underlying complex biology of diseases through high-throughput genomic studies, such as Microarrays, bulk RNA-Sequencing, single cell RNA-Sequencing, etc. It also reduces the complexity of statistical analysis and enhances the explanatory power of the obtained results. Further, the statistical structure and steps common to these approaches have not yet been comprehensively discussed, which limits their utility. Hence, a comprehensive overview of the available gene set analysis approaches used for different high-throughput genomic studies is provided. The analysis of gene sets is usually carried out based on …
Estimation And Testing Of Gene Expression Heterosis, Tieming Ji, Peng Liu, Dan Nettleton
Estimation And Testing Of Gene Expression Heterosis, Tieming Ji, Peng Liu, Dan Nettleton
Dan Nettleton
Heterosis, also known as the hybrid vigor, occurs when the mean phenotype of hybrid offspring is superior to that of its two inbred parents. The heterosis phenomenon is extensively utilized in agriculture though the molecular basis is still unknown. In an effort to understand phenotypic heterosis at the molecular level, researchers have begun to compare expression levels of thousands of genes between parental inbred lines and their hybrid offspring to search for evidence of gene expression heterosis. Standard statistical approaches for separately analyzing expression data for each gene can produce biased and highly variable estimates and unreliable tests of heterosis. …
Nonparametric Methods For Analyzing Replication Origins In Genomewide Data, Debashis Ghosh
Nonparametric Methods For Analyzing Replication Origins In Genomewide Data, Debashis Ghosh
The University of Michigan Department of Biostatistics Working Paper Series
Due to the advent of high-throughput genomic technology, it has become possible to globally monitor cellular activities on a genomewide basis. With these new methods, scientists can begin to address important biological questions. One such question involves the identification of replication origins, which are regions in chromosomes where DNA replication is initiated. In addition, one hypothesis regarding replication origins is that their locations are non-random throughout the genome. In this article, we develop methods for identification of and cluster inference regarding replication origins involving genomewide expression data. We compare several nonparametric regression methods for the identification of replication origin locations. …
The False Discovery Rate: A Variable Selection Perspective, Debashis Ghosh, Wei Chen, Trivellore E. Raghuanthan
The False Discovery Rate: A Variable Selection Perspective, Debashis Ghosh, Wei Chen, Trivellore E. Raghuanthan
The University of Michigan Department of Biostatistics Working Paper Series
In many scientific and medical settings, large-scale experiments are generating large quantities of data that lead to inferential problems involving multiple hypotheses. This has led to recent tremendous interest in statistical methods regarding the false discovery rate (FDR). Several authors have studied the properties involving FDR in a univariate mixture model setting. In this article, we turn the problem on its side; in this manuscript, we show that FDR is a by-product of Bayesian analysis of variable selection problem for a hierarchical linear regression model. This equivalence gives many Bayesian insights as to why FDR is a natural quantity to …
Resampling-Based Multiple Testing: Asymptotic Control Of Type I Error And Applications To Gene Expression Data, Katherine S. Pollard, Mark J. Van Der Laan
Resampling-Based Multiple Testing: Asymptotic Control Of Type I Error And Applications To Gene Expression Data, Katherine S. Pollard, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
We define a general statistical framework for multiple hypothesis testing and show that the correct null distribution for the test statistics is obtained by projecting the true distribution of the test statistics onto the space of mean zero distributions. For common choices of test statistics (based on an asymptotically linear parameter estimator), this distribution is asymptotically multivariate normal with mean zero and the covariance of the vector influence curve for the parameter estimator. This test statistic null distribution can be estimated by applying the non-parametric or parametric bootstrap to correctly centered test statistics. We prove that this bootstrap estimated null …
A Method To Identify Significant Clusters In Gene Expression Data, Katherine S. Pollard, Mark J. Van Der Laan
A Method To Identify Significant Clusters In Gene Expression Data, Katherine S. Pollard, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
Clustering algorithms have been widely applied to gene expression data. For both hierarchical and partitioning clustering algorithms, selecting the number of significant clusters is an important problem and many methods have been proposed. Existing methods for selecting the number of clusters tend to find only the global patterns in the data (e.g.: the over and under expressed genes). We have noted the need for a better method in the gene expression context, where small, biologically meaningful clusters can be difficult to identify. In this paper, we define a new criteria, Mean Split Silhouette (MSS), which is a measure of cluster …
A New Partitioning Around Medoids Algorithm, Mark J. Van Der Laan, Katherine S. Pollard, Jennifer Bryan
A New Partitioning Around Medoids Algorithm, Mark J. Van Der Laan, Katherine S. Pollard, Jennifer Bryan
U.C. Berkeley Division of Biostatistics Working Paper Series
Kaufman & Rousseeuw (1990) proposed a clustering algorithm Partitioning Around Medoids (PAM) which maps a distance matrix into a specified number of clusters. A particularly nice property is that PAM allows clustering with respect to any specified distance metric. In addition, the medoids are robust representations of the cluster centers, which is particularly important in the common context that many elements do not belong well to any cluster. Based on our experience in clustering gene expression data, we have noticed that PAM does have problems recognizing relatively small clusters in situations where good partitions around medoids clearly exist. In this …
Statistical Inference For Simultaneous Clustering Of Gene Expression Data, Katherine S. Pollard, Mark J. Van Der Laan
Statistical Inference For Simultaneous Clustering Of Gene Expression Data, Katherine S. Pollard, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
Current methods for analysis of gene expression data are mostly based on clustering and classification of either genes or samples. We offer support for the idea that more complex patterns can be identified in the data if genes and samples are considered simultaneously. We formalize the approach and propose a statistical framework for two-way clustering. A simultaneous clustering parameter is defined as a function of the true data generating distribution, and an estimate is obtained by applying this function to the empirical distribution. We illustrate that a wide range of clustering procedures, including generalized hierarchical methods, can be defined as …