Network Bayesian

Castelleti A, Soncini-Sessa R (2007) Bayesian Networks and participatory modelling in water resource management. Environ Modell Softw 22 1075-1088... 

Bayesian networks for multivariate reasoning about cause and effect within R D with a flow bottleneck model (Fig. 11.6) to help combine scientific and economic aspects of decision making. This model can, where research process decisions affect potential candidate value, further incorporate simple estimation of how the candidate value varies based on the target product profile. Factors such as ease of dosing in this profile can then be causally linked to the relevant predictors within the research process (e.g., bioavailability), to model the value of the predictive methods that might be used and to perform sensitivity analysis of how R D process choices affect the expected added... 

One challenge in applying this approach, which relies on prior estimates of method prediction reliability, is how to deal with differences between future compounds to be tested and the universe of all compounds on which the collected experience of R D process effectiveness has been based. If new active compounds fall within the space previously sampled, then knowledge of chemical properties is just another kind of conditioning within a Bayesian network if they fall outside this space, then the initial model of both outcomes and predictions has an unpredictable error. The use of sampling theory and models of diversity [16] are therefore promising extensions of the above approach. 

The Bayesian network technology embedded in the ARBITER tool is also well suited for learning both probability relationships (e.g., method reliability estimates) and the essential structure of cause and effect, from data sets where predictions and outcomes can be compared. Colleagues have already applied this capability on a large scale for risk management (selection of potentially suspect claims for further inspection and examination) in the insurance industry. 

Friedman, N., Linial, M., Nachman, I. and Pe er, D. (2000), Using Bayesian networks to analyze expression data ,/ Comput. Biol, 7, 601-620. 

N.A. Woody and S.D. Brown, Hybrid Bayesian networks making the hybrid Bayesian classifier robust to missing training data, J. Chemom, 17, 266-273 (2003). 

Woody, N.A. and Brown, S.D., Hybrid Bayesian Networks Making the Hybrid Bayesian Classifier Robust to Missing Training Data /. Chemom. 2003, 17, 266-273. 

More complex approaches to this problem involve the use of artificial neural networks [22], Bayesian networks [23] and support vector machines [24], which in turn are based on the same principle of supervised learning [25]. 

Sebastiani, P., Abad, M., and Ramoni, M. R (2005). Bayesian networks for genomic analysis. In Genomic Signal Processing and Statistics, Hindawi Publishing Corporation. 281-320. 

Yao XQ, Zhu H, She ZS. A dynamic Bayesian network approach to protein secondary structure prediction. BMC Bioinformatics. 2008 9 49. 

Sachs K, Gifford D, Jaakkola T, Sorger P, Lauffenburger DA. Bayesian network approach to cell signaling pathway modeling. 

Contrary to pathways inherent association with biological functions, biological networks carry broader definitions in scope. Types of biological networks range from interconnected biological pathways,2728 protein-protein interaction networks,29-31 co-expression networks,32-34 and Bayesian networks.35-37... 

Werhli AV, et al. Comparative evaluation of reverse engineering gene regulatory networks with relevance networks, graphical gaussian models and bayesian networks. Bioinformatics. 2006 22 2523-2531. 

Li Z, Li P, Krishnan A, Liu JD (2011) Large-scale dynamic gene regulatory network inference combining differential equation models with local dynamic Bayesian network analysis. Bioinformatics 27 2686-2691. doi 10.1093/ bioinformatics/btr454... 

Kim S. Y., Imoto S. and Miyano S. (2003). Inferring gene networks from time series microarray data using dynamic Bayesian networks. Briefings in Bioinformatics. 4, pp 228-235. 

Perrin B. E., Ralaivola L., Mazurie A., Bottani S., Mallet J. and dAlche-Buc F. (2003). Gene network inference using dynamic Bayesian networks. Bioinformatics. 19, pp 138-142. 

Zou M. and Conzen S. D. (2004). A new dynamic Bayesian network (DBN) approach for identifying gene regulatory networks from time course microarray data. Bioinformatics. 21, pp. 71-79. 

Bayesian networks are based on Bayes Theorem, which gives a mathematical framework for describing the probability of an event that may have been the result of any of two or more causes [37]. The questions is this What is the probability that the event was the result of a particular cause, and how does it change if the cause is changing ... 

Bayesian networks are statistic models for describing probabilistic dependencies for a set of variables. They trace back to a theorem in the eighteenth century found by Thomas Bayes, who first established a mathematical base for probability inference [38]. Bayes theorem is based on two different states ... 

A Bayesian network can be nsed to model the dependencies between variables that directly inflnence each other, which are nsnally few. The rest of the variables are assumed conditionally independent. A Bayesian network is a directed graph in which each node is annotated with qnantitative probability information. It is constructed by selecting a set of variables that define the nodes of the network. The nodes are connected via directed links that indicate their inheritance, and each node has a conditional probability distribntion that qnantifies the effect of the parents on the node. 

Bayesian Networks are statistic models for describing probabilistic dependencies for a set of variables based on Bayes theorem. 

Jensen, E.V., Bayesian Networks and Decision Graphs, 1st ed.. Springer, New York, 2001. 

Figure 7.1. A causal graph for risk analysis. The model depicted in this figure can be formalized using a Bayesian network (Ricci et al. 2006) A probabilistic framework interprets the model described in this figure as a Bayesian belief network or causal graph model. Each variable with inward-pointing arrows is interpreted as a random variable with a conditional probability distribution that depends only on the values of the variables that point into it. The essence of this approach to modeling and evaluating uncertain risks is to sample successively from the (often conditional) distribution of each variable, given the values of its predecessors. Algorithms exist to identify and validate possible causal structures.

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