Bayesian neural networks statistics

A common use of statistics in structural biology is as a tool for deriving predictive distributions of strucmral parameters based on sequence. The simplest of these are predictions of secondary structure and side-chain surface accessibility. Various algorithms that can learn from data and then make predictions have been used to predict secondary structure and surface accessibility, including ordinary statistics [79], infonnation theory [80], neural networks [81-86], and Bayesian methods [87-89]. A disadvantage of some neural network methods is that the parameters of the network sometimes have no physical meaning and are difficult to interpret. 

Thus, multilinear models were introduced, and then a wide series of tools, such as nonlinear models, including artificial neural networks, fuzzy logic, Bayesian models, and expert systems. A number of reviews deal with the different techniques [4-6]. Mathematical techniques have also been used to keep into account the high number (up to several thousands) of chemical descriptors and fragments that can be used for modeling purposes, with the problem of increase in noise and lack of statistical robustness. Also in this case, linear and nonlinear methods have been used, such as principal component analysis (PCA) and genetic algorithms (GA) [6]. 

A whole spectrum of statistical techniques have been applied to the analysis of DNA microarray data [26-28]. These include clustering analysis (hierarchical, K-means, self-organizing maps), dimension reduction (singular value decomposition, principal component analysis, multidimensional scaling, or correspondence analysis), and supervised classification (support vector machines, artificial neural networks, discriminant methods, or between-group analysis) methods. More recently, a number of Bayesian and other probabilistic approaches have been employed in the analysis of DNA microarray data [11], Generally, the first phase of microarray data analysis is exploratory data analysis. 

A later chapter will discuss these methods in more detail. For example, support vector machines and traditional neural networks are analogs of multiple regression or discriminant analysis that provide more flexibility in the form of the relationship between molecular properties and bioactivity.Kohonen neural nets are a more flexible analog to principal component analysis. Various Bayesian approaches are alternatives to the statistical methods described earlier. A freely available program oflcrs many of these capabilities. ... 

Training a neural network model essentially means selecting one model from the set of allowed models (or, in a Bayesian framework, determining a distribution over the set of allowed models) that minimizes the cost criterion. There are numerous algorithms available for training neural network models most of them can be viewed as a straightforward application of optimization theory and statistical estimation. Recent developments in this field use particle swarm optimization and other swarm intelligence techniques. 

Artifical Neural Networks Computer Algorithms Databases Fourier Series Functional Analysis Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems Statistics, Bayesian Wavelets... 

Billard and Diday Symbolic Data Analysis Conceptual Statistics and Data Mining Dunne A Statistical Approach to Neural Networks for Pattern Recognition Ntzoufras Bayesian Modeling Using WinBUGS Bolstad Understanding Computational Bayesian Statistics... 

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