488 research outputs found
Posterior Contraction Rates of the Phylogenetic Indian Buffet Processes
By expressing prior distributions as general stochastic processes,
nonparametric Bayesian methods provide a flexible way to incorporate prior
knowledge and constrain the latent structure in statistical inference. The
Indian buffet process (IBP) is such an example that can be used to define a
prior distribution on infinite binary features, where the exchangeability among
subjects is assumed. The phylogenetic Indian buffet process (pIBP), a
derivative of IBP, enables the modeling of non-exchangeability among subjects
through a stochastic process on a rooted tree, which is similar to that used in
phylogenetics, to describe relationships among the subjects. In this paper, we
study the theoretical properties of IBP and pIBP under a binary factor model.
We establish the posterior contraction rates for both IBP and pIBP and
substantiate the theoretical results through simulation studies. This is the
first work addressing the frequentist property of the posterior behaviors of
IBP and pIBP. We also demonstrated its practical usefulness by applying pIBP
prior to a real data example arising in the field of cancer genomics where the
exchangeability among subjects is violated
VIPER: variability-preserving imputation for accurate gene expression recovery in single-cell RNA sequencing studies
Abstract
We develop a method, VIPER, to impute the zero values in single-cell RNA sequencing studies to facilitate accurate transcriptome quantification at the single-cell level. VIPER is based on nonnegative sparse regression models and is capable of progressively inferring a sparse set of local neighborhood cells that are most predictive of the expression levels of the cell of interest for imputation. A key feature of our method is its ability to preserve gene expression variability across cells after imputation. We illustrate the advantages of our method through several well-designed real data-based analytical experiments.https://deepblue.lib.umich.edu/bitstream/2027.42/146264/1/13059_2018_Article_1575.pd
Change point analysis of histone modifications reveals epigenetic blocks linking to physical domains
Histone modification is a vital epigenetic mechanism for transcriptional control in eukaryotes. High-throughput techniques have enabled whole-genome analysis of histone modifications in recent years. However, most studies assume one combination of histone modification invariantly translates to one transcriptional output regardless of local chromatin environment. In this study we hypothesize that, the genome is organized into local domains that manifest similar enrichment pattern of histone modification, which leads to orchestrated regulation of expression of genes with relevant biological functions. We propose a multivariate Bayesian Change Point (BCP) model to segment the Drosophila melanogaster genome into consecutive blocks on the basis of combinatorial patterns of histone marks. By modeling the sparse distribution of histone marks with a zero-inflated Gaussian mixture, our partitions capture local BLOCKs that manifest relatively homogeneous enrichment pattern of histone marks. We further characterized BLOCKs by their transcription levels, distribution of genes, degree of co-regulation and GO enrichment. Our results demonstrate that these BLOCKs, although inferred merely from histone modifications, reveal strong relevance with physical domains, which suggests their important roles in chromatin organization and coordinated gene regulation
Maxwell quasinormal modes on a global monopole Schwarzschild-anti-de Sitter black hole with Robin boundary conditions
We generalize our previous studies on the Maxwell quasinormal modes around
Schwarzschild-anti-de-Sitter black holes with Robin type vanishing energy flux
boundary conditions, by adding a global monopole on the background. We first
formulate the Maxwell equations both in the Regge-Wheeler-Zerilli and in the
Teukolsky formalisms and derive, based on the vanishing energy flux principle,
two boundary conditions in each formalism. The Maxwell equations are then
solved analytically in pure anti-de Sitter spacetimes with a global monopole,
and two different normal modes are obtained due to the existence of the
monopole parameter. In the small black hole and low frequency approximations,
the Maxwell quasinormal modes are solved perturbatively on top of normal modes
by using an asymptotic matching method, while beyond the aforementioned
approximation, the Maxwell quasinormal modes are obtained numerically. We
analyze the Maxwell quasinormal spectrum by varying the angular momentum
quantum number , the overtone number , and in particular, the monopole
parameter . We show explicitly, through calculating quasinormal
frequencies with both boundary conditions, that the global monopole produces
the repulsive force.Comment: 10 pages, 5 figures, to appear in EPJ
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