scholarly journals Accelerated Bayesian inference of gene expression models from snapshots of single-cell transcripts

2018 ◽  
Author(s):  
Yen Ting Lin ◽  
Nicolas E. Buchler
Keyword(s):  
Gene Expression ◽  
Monte Carlo ◽  
Bayesian Inference ◽  
Model Selection ◽  
Single Cell ◽  
Kinetic Parameters ◽  
Information Criterion ◽  
Time Dependent ◽  
Data Sets ◽  
Bayesian Evidence

Understanding how stochastic gene expression is regulated in biological systems using snapshots of single-cell transcripts requires state-of-the-art methods of computational analysis and statistical inference. A Bayesian approach to statistical inference is the most complete method for model selection and uncertainty quantification of kinetic parameters from single-cell data. This approach is impractical because current numerical algorithms are too slow to handle typical models of gene expression. To solve this problem, we first show that time-dependent mRNA distributions of discrete-state models of gene expression are dynamic Poisson mixtures, whose mixing kernels are characterized by a piece-wise deterministic Markov process. We combined this analytical result with a kinetic Monte Carlo algorithm to create a hybrid numerical method that accelerates the calculation of time-dependent mRNA distributions by 1000-fold compared to current methods. We then integrated the hybrid algorithm into an existing Monte Carlo sampler to estimate the Bayesian posterior distribution of many different, competing models in a reasonable amount of time. We validated our method of accelerated Bayesian inference on several synthetic data sets. Our results show that kinetic parameters can be reasonably constrained for modestly sampled data sets, if the model is known a priori. If the model is unknown,the Bayesian evidence can be used to rigorously quantify the likelihood of a model relative to other models from the data. We demonstrate that Bayesian evidence selects the true model and outperforms approximate metrics, e.g., Bayesian Information Criterion (BIC) or Akaike Information Criterion (AIC), often used for model selection.

scholarly journals Enhancing droplet-based single-nucleus RNA-seq resolution using the semi-supervised machine learning classifier DIEM

2019 ◽  
Author(s):  
Marcus Alvarez ◽  
Elior Rahmani ◽  
Brandon Jew ◽  
Kristina M. Garske ◽  
Zong Miao ◽  
...  
Keyword(s):  
Gene Expression ◽  
Single Cell ◽  
Cell Types ◽  
Supervised Machine Learning ◽  
Data Sets ◽  
Rna Seq ◽  
Novel Approach ◽  
Single Nucleus ◽  
Downstream Analysis

AbstractSingle-nucleus RNA sequencing (snRNA-seq) measures gene expression in individual nuclei instead of cells, allowing for unbiased cell type characterization in solid tissues. Contrary to single-cell RNA seq (scRNA-seq), we observe that snRNA-seq is commonly subject to contamination by high amounts of extranuclear background RNA, which can lead to identification of spurious cell types in downstream clustering analyses if overlooked. We present a novel approach to remove debris-contaminated droplets in snRNA-seq experiments, called Debris Identification using Expectation Maximization (DIEM). Our likelihood-based approach models the gene expression distribution of debris and cell types, which are estimated using EM. We evaluated DIEM using three snRNA-seq data sets: 1) human differentiating preadipocytes in vitro, 2) fresh mouse brain tissue, and 3) human frozen adipose tissue (AT) from six individuals. All three data sets showed various degrees of extranuclear RNA contamination. We observed that existing methods fail to account for contaminated droplets and led to spurious cell types. When compared to filtering using these state of the art methods, DIEM better removed droplets containing high levels of extranuclear RNA and led to higher quality clusters. Although DIEM was designed for snRNA-seq data, we also successfully applied DIEM to single-cell data. To conclude, our novel method DIEM removes debris-contaminated droplets from single-cell-based data fast and effectively, leading to cleaner downstream analysis. Our code is freely available for use at https://github.com/marcalva/diem.

scholarly journals M3S: a comprehensive model selection for multi-modal single-cell RNA sequencing data

2019 ◽  
Vol 20 (S24) ◽  
Author(s):  
Yu Zhang ◽  
Changlin Wan ◽  
Pengcheng Wang ◽  
Wennan Chang ◽  
Yan Huo ◽  
...  
Keyword(s):  
Gene Expression ◽  
Model Selection ◽  
Statistical Model ◽  
Single Cell ◽  
Differential Gene Expression ◽  
Large Scale ◽  
Expression Profiles ◽  
Sequencing Data ◽  
Differential Gene ◽  
Selection Of

Abstract Background Various statistical models have been developed to model the single cell RNA-seq expression profiles, capture its multimodality, and conduct differential gene expression test. However, for expression data generated by different experimental design and platforms, there is currently lack of capability to determine the most proper statistical model. Results We developed an R package, namely Multi-Modal Model Selection (M3S), for gene-wise selection of the most proper multi-modality statistical model and downstream analysis, useful in a single-cell or large scale bulk tissue transcriptomic data. M3S is featured with (1) gene-wise selection of the most parsimonious model among 11 most commonly utilized ones, that can best fit the expression distribution of the gene, (2) parameter estimation of a selected model, and (3) differential gene expression test based on the selected model. Conclusion A comprehensive evaluation suggested that M3S can accurately capture the multimodality on simulated and real single cell data. An open source package and is available through GitHub at https://github.com/zy26/M3S.

A STATISTICAL FRAMEWORK FOR HAPLOTYPE BLOCK INFERENCE

2005 ◽  
Vol 03 (05) ◽  
pp. 1021-1038
Author(s):  
AO YUAN ◽  
GUANJIE CHEN ◽  
CHARLES ROTIMI ◽  
GEORGE E. BONNEY
Keyword(s):  
Bayesian Inference ◽  
Model Selection ◽  
Haplotype Block ◽  
Block Structure ◽  
Real Data ◽  
Data Sets ◽  
Block Partitioning ◽  
Haplotype Blocks ◽  
Statistical Framework ◽  
Statistical Model Selection

The existence of haplotype blocks transmitted from parents to offspring has been suggested recently. This has created an interest in the inference of the block structure and length. The motivation is that haplotype blocks that are characterized well will make it relatively easier to quickly map all the genes carrying human diseases. To study the inference of haplotype block systematically, we propose a statistical framework. In this framework, the optimal haplotype block partitioning is formulated as the problem of statistical model selection; missing data can be handled in a standard statistical way; population strata can be implemented; block structure inference/hypothesis testing can be performed; prior knowledge, if present, can be incorporated to perform a Bayesian inference. The algorithm is linear in the number of loci, instead of NP-hard for many such algorithms. We illustrate the applications of our method to both simulated and real data sets.

scholarly journals An introduction to Bayesian inference in gravitational-wave astronomy: Parameter estimation, model selection, and hierarchical models

2019 ◽  
Vol 36 ◽  
Author(s):  
Eric Thrane ◽  
Colm Talbot
Keyword(s):  
Bayesian Inference ◽  
Model Selection ◽  
Gravitational Wave ◽  
Gaussian Noise ◽  
Hierarchical Models ◽  
Selection Effects ◽  
Estimation Model ◽  
Monte Carlo Algorithms ◽  
Bayesian Evidence ◽  
Credible Intervals

AbstractThis is an introduction to Bayesian inference with a focus on hierarchical models and hyper-parameters. We write primarily for an audience of Bayesian novices, but we hope to provide useful insights for seasoned veterans as well. Examples are drawn from gravitational-wave astronomy, though we endeavour for the presentation to be understandable to a broader audience. We begin with a review of the fundamentals: likelihoods, priors, and posteriors. Next, we discuss Bayesian evidence, Bayes factors, odds ratios, and model selection. From there, we describe how posteriors are estimated using samplers such as Markov Chain Monte Carlo algorithms and nested sampling. Finally, we generalise the formalism to discuss hyper-parameters and hierarchical models. We include extensive appendices discussing the creation of credible intervals, Gaussian noise, explicit marginalisation, posterior predictive distributions, and selection effects.

scholarly journals A Novel Hybrid Dimension Reduction Technique for Undersized High Dimensional Gene Expression Data Sets Using Information Complexity Criterion for Cancer Classification

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Esra Pamukçu ◽  
Hamparsum Bozdogan ◽  
Sinan Çalık
Keyword(s):  
Gene Expression ◽  
Dimension Reduction ◽  
Covariance Matrix ◽  
Gene Expression Data ◽  
Information Criterion ◽  
Data Sets ◽  
Expression Data ◽  
Akaike's Information Criterion ◽  
Akaike’S Information Criterion ◽  
Probabilistic Pca

Gene expression data typically are large, complex, and highly noisy. Their dimension is high with several thousand genes (i.e., features) but with only a limited number of observations (i.e., samples). Although the classical principal component analysis (PCA) method is widely used as a first standard step in dimension reduction and in supervised and unsupervised classification, it suffers from several shortcomings in the case of data sets involving undersized samples, since the sample covariance matrix degenerates and becomes singular. In this paper we address these limitations within the context of probabilistic PCA (PPCA) by introducing and developing a new and novel approach using maximum entropy covariance matrix and its hybridized smoothed covariance estimators. To reduce the dimensionality of the data and to choose the number of probabilistic PCs (PPCs) to be retained, we further introduce and develop celebrated Akaike’s information criterion (AIC), consistent Akaike’s information criterion (CAIC), and the information theoretic measure of complexity (ICOMP) criterion of Bozdogan. Six publicly available undersized benchmark data sets were analyzed to show the utility, flexibility, and versatility of our approach with hybridized smoothed covariance matrix estimators, which do not degenerate to perform the PPCA to reduce the dimension and to carry out supervised classification of cancer groups in high dimensions.

Improving data analysis in herpetology: using Akaike's Information Criterion (AIC) to assess the strength of biological hypotheses

2006 ◽  
Vol 27 (2) ◽  
pp. 169-180 ◽  
Author(s):  
Marc Mazerolle
Keyword(s):  
Model Selection ◽  
Observational Studies ◽  
Regression Models ◽  
Model Averaging ◽  
Weighted Average ◽  
Information Criterion ◽  
Data Sets ◽  
Data Set ◽  
Robust Estimates ◽  
Number Of Individuals

AbstractIn ecology, researchers frequently use observational studies to explain a given pattern, such as the number of individuals in a habitat patch, with a large number of explanatory (i.e., independent) variables. To elucidate such relationships, ecologists have long relied on hypothesis testing to include or exclude variables in regression models, although the conclusions often depend on the approach used (e.g., forward, backward, stepwise selection). Though better tools have surfaced in the mid 1970's, they are still underutilized in certain fields, particularly in herpetology. This is the case of the Akaike information criterion (AIC) which is remarkably superior in model selection (i.e., variable selection) than hypothesis-based approaches. It is simple to compute and easy to understand, but more importantly, for a given data set, it provides a measure of the strength of evidence for each model that represents a plausible biological hypothesis relative to the entire set of models considered. Using this approach, one can then compute a weighted average of the estimate and standard error for any given variable of interest across all the models considered. This procedure, termed model-averaging or multimodel inference, yields precise and robust estimates. In this paper, I illustrate the use of the AIC in model selection and inference, as well as the interpretation of results analysed in this framework with two real herpetological data sets. The AIC and measures derived from it is should be routinely adopted by herpetologists.

scholarly journals Bayesian Model Selection in Fisheries Management and Ecology

2019 ◽  
Vol 10 (2) ◽  
pp. 691-707
Author(s):  
Jason C. Doll ◽  
Stephen J. Jacquemin
Keyword(s):  
Bayesian Inference ◽  
Model Selection ◽  
Fisheries Management ◽  
Bayesian Model ◽  
Bayes Factor ◽  
Evaluation Process ◽  
Information Criterion ◽  
Bayesian Model Selection ◽  
Model Parameters ◽  
Inference Methods

Abstract Researchers often test ecological hypotheses relating to a myriad of questions ranging from assemblage structure, population dynamics, demography, abundance, growth rate, and more using mathematical models that explain trends in data. To aid in the evaluation process when faced with competing hypotheses, we employ statistical methods to evaluate the validity of these multiple hypotheses with the goal of deriving the most robust conclusions possible. In fisheries management and ecology, frequentist methodologies have largely dominated this approach. However, in recent years, researchers have increasingly used Bayesian inference methods to estimate model parameters. Our aim with this perspective is to provide the practicing fisheries ecologist with an accessible introduction to Bayesian model selection. Here we discuss Bayesian inference methods for model selection in the context of fisheries management and ecology with empirical examples to guide researchers in the use of these methods. In this perspective we discuss three methods for selecting among competing models. For comparing two models we discuss Bayes factor and for more complex models we discuss Watanabe–Akaike information criterion and leave-one-out cross-validation. We also describe what kinds of information to report when conducting Bayesian inference. We conclude this review with a discussion of final thoughts about these model selection techniques.

scholarly journals LTMG: A novel statistical modeling of transcriptional expression states in single-cell RNA-Seq data

2018 ◽  
Author(s):  
Changlin Wan ◽  
Wennan Chang ◽  
Yu Zhang ◽  
Fenil Shah ◽  
Xiaoyu Lu ◽  
...  
Keyword(s):  
Gene Expression ◽  
Single Cell ◽  
Single Cells ◽  
Cell Types ◽  
R Package ◽  
Data Sets ◽  
Rna Seq ◽  
Cell Functions ◽  
Transcriptional Regulatory ◽  
A Cell

ABSTRACTA key challenge in modeling single-cell RNA-seq (scRNA-seq) data is to capture the diverse gene expression states regulated by different transcriptional regulatory inputs across single cells, which is further complicated by a large number of observed zero and low expressions. We developed a left truncated mixture Gaussian (LTMG) model that stems from the kinetic relationships between the transcriptional regulatory inputs and metabolism of mRNA and gene expression abundance in a cell. LTMG infers the expression multi-modalities across single cell entities, representing a gene’s diverse expression states; meanwhile the dropouts and low expressions are treated as left truncated, specifically representing an expression state that is under suppression. We demonstrated that LTMG has significantly better goodness of fitting on an extensive number of single-cell data sets, comparing to three other state of the art models. In addition, our systems kinetic approach of handling the low and zero expressions and correctness of the identified multimodality are validated on several independent experimental data sets. Application on data of complex tissues demonstrated the capability of LTMG in extracting varied expression states specific to cell types or cell functions. Based on LTMG, a differential gene expression test and a co-regulation module identification method, namely LTMG-DGE and LTMG-GCR, are further developed. We experimentally validated that LTMG-DGE is equipped with higher sensitivity and specificity in detecting differentially expressed genes, compared with other five popular methods, and that LTMG-GCR is capable to retrieve the gene co-regulation modules corresponding to perturbed transcriptional regulations. A user-friendly R package with all the analysis power is available at https://github.com/zy26/LTMGSCA.

scholarly journals bigSCale: An Analytical Framework for Big-Scale Single-Cell Data

2017 ◽  
Author(s):  
Giovanni Iacono ◽  
Elisabetta Mereu ◽  
Amy Guillaumet-Adkins ◽  
Roser Corominas ◽  
Ivon Cuscó ◽  
...  
Keyword(s):  
Gene Expression ◽  
Single Cell ◽  
Single Cells ◽  
A Priori ◽  
Large Data ◽  
Cell Types ◽  
Analytical Framework ◽  
Marker Genes ◽  
Data Sets ◽  
Neuronal Progenitor

AbstractSingle-cell RNA sequencing significantly deepened our insights into complex tissues and latest techniques are capable processing ten-thousands of cells simultaneously. With bigSCale, we provide an analytical framework being scalable to analyze millions of cells, addressing challenges of future large datasets. Unlike previous methods, bigSCale does not constrain data to fit an a priori-defined distribution and instead uses an accurate numerical model of noise. We evaluated the performance of bigSCale using a biological model of aberrant gene expression in patient derived neuronal progenitor cells and simulated datasets, which underlined its speed and accuracy in differential expression analysis. We further applied bigSCale to analyze 1.3 million cells from the mouse developing forebrain. Herein, we identified rare populations, such as Reelin positive Cajal-Retzius neurons, for which we determined a previously not recognized heterogeneity associated to distinct differentiation stages, spatial organization and cellular function. Together, bigSCale presents a perfect solution to address future challenges of large single-cell datasets.Extended AbstractSingle-cell RNA sequencing (scRNAseq) significantly deepened our insights into complex tissues by providing high-resolution phenotypes for individual cells. Recent microfluidic-based methods are scalable to ten-thousands of cells, enabling an unbiased sampling and comprehensive characterization without prior knowledge. Increasing cell numbers, however, generates extremely big datasets, which extends processing time and challenges computing resources. Current scRNAseq analysis tools are not designed to analyze datasets larger than from thousands of cells and often lack sensitivity and specificity to identify marker genes for cell populations or experimental conditions. With bigSCale, we provide an analytical framework for the sensitive detection of population markers and differentially expressed genes, being scalable to analyze millions of single cells. Unlike other methods that use simple or mixture probabilistic models with negative binomial, gamma or Poisson distributions to handle the noise and sparsity of scRNAseq data, bigSCale does not constrain the data to fit an a priori-defined distribution. Instead, bigSCale uses large sample sizes to estimate a highly accurate and comprehensive numerical model of noise and gene expression. The framework further includes modules for differential expression (DE) analysis, cell clustering and population marker identification. Moreover, a directed convolution strategy allows processing of extremely large data sets, while preserving the transcript information from individual cells.We evaluate the performance of bigSCale using a biological model for reduced or elevated gene expression levels. Specifically, we perform scRNAseq of 1,920 patient derived neuronal progenitor cells from Williams-Beuren and 7q11.23 microduplication syndrome patients, harboring a deletion or duplication of 7q11.23, respectively. The affected region contains 28 genes whose transcriptional levels vary in line with their allele frequency. BigSCale detects expression changes with respect to cells from a healthy donor and outperforms other methods for single-cell DE analysis in sensitivity. Simulated data sets, underline the performance of bigSCale in DE analysis as it is faster and more sensitive and specific than other methods. The probabilistic model of cell-distances within bigSCale is further suitable for unsupervised clustering and the identification of cell types and subpopulations. Using bigSCale, we identify all major cell types of the somatosensory cortex and hippocampus analyzing 3,005 cells from adult mouse brains. Remarkably, we increase the number of cell population specific marker genes 4-6-fold compared to the original analysis and, moreover, define markers of higher order cell types. These include CD90 (Thy1), a neuronal surface receptor, potentially suitable for isolating intact neurons from complex brain samples.To test its applicability for large data sets, we apply bigSCale on scRNAseq data from 1.3 million cells derived from the pallium of the mouse developing forebrain (E18, 10x Genomics). Our directed down-sampling strategy accumulates transcript counts from cells with similar transcriptional profiles into index cell transcriptomes, thereby defining cellular clusters with improved resolution. Accordingly, index cell clusters provide a rich resource of marker genes for the main brain cell types and less frequent subpopulations. Our analysis of rare populations includes poorly characterized developmental cell types, such as neuron progenitors from the subventricular zone and neocortical Reelin positive neurons known as Cajal-Retzius (CR) cells. The latter represent a transient population which regulates the laminar formation of the developing neocortex and whose malfunctioning causes major neurodevelopmental disorders like autism or schizophrenia. Most importantly, index cell cluster can be deconvoluted to individual cell level for targeted analysis of populations of interest. Through decomposition of Reelin positive neurons, we determined a previously not recognized heterogeneity among CR cells, which we could associate to distinct differentiation stages as well as spatial and functional differences in the developing mouse brain. Specifically, subtypes of CR cells identified by bigSCale express different compositions of NMDA, AMPA and glycine receptor subunits, pointing to subpopulations with distinct membrane properties. Furthermore, we found Cxcl12, a chemokine secreted by the meninges and regulating the tangential migration of CR cells, to be also expressed in CR cells located in the marginal zone of the neocortex, indicating a self-regulated migration capacity.Together, bigSCale presents a perfect solution for the processing and analysis of scRNAseq data from millions of single cells. Its speed and sensitivity makes it suitable to the address future challenges of large single-cell data sets.

Sign in / Sign up

Export Citation Format

Share Document