An Empirical Bayesian Method for Estimating Biological Networks from Temporal Microarray Data

Rau, Andrea; Jaffrézic, Florence; Foulley, Jean Louis; Doerge, R. W.

doi:10.2202/1544-6115.1513

Cited by 53 publications

(52 citation statements)

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“…In addition, a hierarchical Bayesian framework may be defined on the SSM of Equation 1 (Beal et al, 2005;Rau et al, 2010). That is, let a (j) , b (j) , c (j) , and θ (j) denote vectors made up of the jth rows of matrices A, B, C, and Θ, respectively.…”

Section: Empirical Bayes Methodsmentioning

confidence: 99%

“…To do, first the dimension of the hidden state (i.e., K) is chosen using a time series method for model selection, based on the autocovariances between observations (see Bremer, 2006;Bremer and Doerge, 2009;Rau et al, 2010;Rau, 2010, for more details). Second, a set of recursive calculations known as the Kalman filter and smoother (Kalman, 1960) is used to estimate the values of the hidden states (Bremer and Doerge, 2009;Rau et al, 2010), given the current values of the model parameters. Third, posterior distributions for the model parameters A, B, C, and Θ are calculated based on a two-step Expectation-Maximization (EM) estimation (Dempster et al, 1977) of model hyperparameters ψ.…”

Section: Empirical Bayes Methodsmentioning

confidence: 99%

“…Third, posterior distributions for the model parameters A, B, C, and Θ are calculated based on a two-step Expectation-Maximization (EM) estimation (Dempster et al, 1977) of model hyperparameters ψ. See Rau et al (2010) for additional details on the EBDBN algorithm.…”

Section: Empirical Bayes Methodsmentioning

confidence: 99%

See 2 more Smart Citations

Approximate Bayesian Approaches for Reverse Engineering Biological Networks

Rau¹,

Jaffrézic²,

Foulley³

et al. 2010

Conference on Applied Statistics in Agriculture

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Genes are known to interact with one another through proteins by regulating the rate at which gene transcription takes place. As such, identifying these gene-to-gene interactions is essential to improving our knowledge of how complex biological systems work. In recent years, a growing body of work has focused on methods for reverse-engineering these so-called gene regulatory networks from time-course gene expression data. However, reconstruction of these networks is often complicated by the large number of genes potentially involved in a given network and the limited number of time points and biological replicates typically measured. Bayesian methods are particularly well-suited for dealing with problems of this nature, as they provide a systematic way to deal with different sources of variation and allow for a measure of uncertainty in parameter estimates through posterior distributions, rather than point estimates. Our current work examines the application of approximate Bayesian methodology for the purpose of reverse engineering regulatory networks from time-course gene expression data. We demonstrate the advantages of our proposed approximate Bayesian approaches by comparing their performance on a well-characterized pathway in Escherichia coli.

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Section: Empirical Bayes Methodsmentioning

confidence: 99%

Section: Empirical Bayes Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Approximate Bayesian Approaches for Reverse Engineering Biological Networks

Rau¹,

Jaffrézic²,

Foulley³

et al. 2010

Conference on Applied Statistics in Agriculture

Self Cite

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show abstract

“…At the same time differentially expressed transcripts are linked to transcription factors and pathways. In a consensus step all results are combined either via simple overlap analysis, via a shortest-path based approximate Steiner tree algorithm [77,78] or via a dynamic Bayesian Network structure learning algorithm [79].…”

Section: Using Molecular Network For Data Integrationmentioning

confidence: 99%

Integrating Heterogeneous omics Data via Statistical Inference and Learning Techniques

Ahmad

Fröhlich

2016

Genomics Comput Biol

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Multi-omics studies are believed to provide a more comprehensive picture of a complex biological system than traditional studies with one omics data source. However, from a statistical point of view data integration implies non-trivial challenges. In this review, we highlight recent statistical inference and learning techniques that have been devised in this context. In the first part of our article, we focus on techniques to identify a relevant biological sub-system based on combined omics data. In the second part of our article we ask, in which way integrated omics data could be used for better personalized patient treatment in a supervised as well as unsupervised learning setting. Different classes of algorithms are discussed for both application tasks. Existing and future challenges for data integration methods are pointed out.

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“…A general state-space framework that allows to model non-stationary time course data is given in Grzegorczyk and Husmeier (2009). Rau et al (2010) present an empirical Bayes approach to learning dynamical Bayesian networks and apply it to gene expression data.…”

Section: Dynamic Bayesian Networkmentioning

confidence: 99%

Introduction to Graphical Modelling

Scutari

Strimmer²

2011

Handbook of Statistical Systems Biology

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The aim of this chapter is twofold. In the first part (Sections 12.1, 12.2 and 12.3) we will provide a brief overview of the mathematical and statistical foundations of graphical models, along with their fundamental properties, estimation and basic inference procedures. In particular we will develop Markov networks (also known as Markov random fields) and Bayesian networks, which are the subjects of most past and current literature on graphical models. In the second part (Section 12.4) we will review some applications of graphical models in systems biology. Graphical Structures and Random VariablesGraphical models are a class of statistical models which combine the rigour of a probabilistic approach with the intuitive representation of relationships given by graphs. They are composed by two parts:1. a set X = {X 1 , X 2 , . . . , X p } of random variables describing the quantities of interest. The statistical distribution of X is called the global distribution of the data, while the components it factorises into are called local distributions.2. a graph G = (V, E) in which each vertex v ∈ V, also called a node, is associated with one of the random variables in X (they are usually referred to interchangeably). Edges e ∈ E, also called links, are used to express the dependence structure of the data (the set of dependence relationships among Graph representations meet our earlier requirements of explicitness, saliency, and stability. The links in the graph permit us to express directly and quantitatively the dependence relationships, and the graph topology displays these relationships explicitly and preserves them, under any assignment of numerical parameters.The nature of the link outlined above between the dependence structure of the data and its graphical representation is given again by Pearl (1988) in terms of conditional independence (denoted with ⊥ ⊥ P ) and graphical separation (denoted with ⊥ ⊥ G ).Definition 12.1.1 A graph G is a dependency map (or D-map) of the probabilistic dependence structure P of X if there is a one-to-one correspondence between the random variables in X and the nodes V of G, such that for all disjoint subsets A, B, C of X we have Similarly, G is an independency map (or I-map) of P ifG is said to be a perfect map of P if it is both a D-map and an I-map, that is (12.3) and in this case P is said to be isomorphic to G.Note that this definition does not depend on a particular characterisation of graphical separation, and therefore on the type of graph used in the graphical model. In fact both Markov networks (Whittaker 1990) and Bayesian networks (Pearl 1988), which are by far the two most common classes of graphical models treated in literature, are defined as minimal I-maps even though the former use undirected graphs an the latter use directed acyclic graphs. Minimality requires that, if the dependence structure P of X can be expressed by multiple graphs, we must use the one with the minimum number of edges; if any further edge is removed then the graph is no longer an I-map of P...

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An Empirical Bayesian Method for Estimating Biological Networks from Temporal Microarray Data

Cited by 53 publications

References 0 publications

Approximate Bayesian Approaches for Reverse Engineering Biological Networks

Approximate Bayesian Approaches for Reverse Engineering Biological Networks

Integrating Heterogeneous omics Data via Statistical Inference and Learning Techniques

Introduction to Graphical Modelling

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