Using Complexity for the Estimation of Bayesian Networks
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Peter Salzman
Statistical inference of graphical models has become an important tool in the reconstruction of biological networks of the type which model, for example, gene regulatory interactions. In particular, the construction of a score-based Bayesian posterior density over the space of models provides an intuitive and computationally feasible method of assessing model uncertainty and of assigning statistical confidence to structural features. One problem which frequently occurs with this approach is the tendency to overestimate the degree of model complexity. Spurious graphical features obtained in this way may affect the inference in unpredictable ways, even when using scoring techniques, such as the Bayesian Information Criterion (BIC), that are specifically designed to compensate for overfitting.In this article we propose a simple adjustment to a BIC-based scoring procedure. The method proceeds in two steps. In the first step we derive an independent estimate of the parametric complexity of the model. In the second we modify the BIC score so that the mean parametric complexity of the posterior density is equal to the estimated value. The method is applied to a set of test networks, and to a collection of genes from the yeast genome known to possess regulatory relationships. A Bayesian network model with binary responses is employed. In the examples considered, we find that the number of spurious graph edges inferred is reduced, while the effect on the identification of true edges is minimal.
©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
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- Letter to the Editor
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- Reader's Reaction
- Reader's Reaction to "Dimension Reduction for Classification with Gene Expression Microarray Data" by Dai et al (2006)
Articles in the same Issue
- Article
- Low-Order Conditional Independence Graphs for Inferring Genetic Networks
- A Generalized Clustering Problem, with Application to DNA Microarrays
- A Bayes Regression Approach to Array-CGH Data
- Statistical Selection of Maintenance Genes for Normalization of Gene Expressions
- Predicting the Strongest Domain-Domain Contact in Interacting Protein Pairs
- Dimension Reduction for Classification with Gene Expression Microarray Data
- A New Type of Stochastic Dependence Revealed in Gene Expression Data
- A New Order Estimator for Fixed and Variable Length Markov Models with Applications to DNA Sequence Similarity
- Quality Optimised Analysis of General Paired Microarray Experiments
- Issues of Processing and Multiple Testing of SELDI-TOF MS Proteomic Data
- Cross-Validated Bagged Prediction of Survival
- Treatment of Uninformative Families in Mean Allele Sharing Tests for Linkage
- Quantile-Function Based Null Distribution in Resampling Based Multiple Testing
- Combining Results of Microarray Experiments: A Rank Aggregation Approach
- Model Selection for Mixtures of Mutagenetic Trees
- Pseudo-likelihood for Non-reversible Nucleotide Substitution Models with Neighbour Dependent Rates
- A Method to Increase the Power of Multiple Testing Procedures Through Sample Splitting
- Bayesian Hierarchical Model for Correcting Signal Saturation in Microarrays Using Pixel Intensities
- Using Complexity for the Estimation of Bayesian Networks
- Detecting Local High-Scoring Segments: a First-Stage Approach for Genome-Wide Association Studies
- Examining Protein Structure and Similarities by Spectral Analysis Technique
- Parameter Estimation for the Exponential-Normal Convolution Model for Background Correction of Affymetrix GeneChip Data
- Approximate Sample Size Calculations with Microarray Data: An Illustration
- Numerical Solutions for Patterns Statistics on Markov Chains
- A Heuristic Bayesian Method for Segmenting DNA Sequence Alignments and Detecting Evidence for Recombination and Gene Conversion
- A Two-Step Multiple Comparison Procedure for a Large Number of Tests and Multiple Treatments
- Validation in Genomics: CpG Island Methylation Revisited
- An Improved Nonparametric Approach for Detecting Differentially Expressed Genes with Replicated Microarray Data
- Letter to the Editor
- Treating Expression Levels of Different Genes as a Sample in Microarray Data Analysis: Is it Worth a Risk?
- Reader's Reaction
- Reader's Reaction to "Dimension Reduction for Classification with Gene Expression Microarray Data" by Dai et al (2006)
