Bayesian Algorithms for One-Dimensional Global Optimization

In this paper Bayesian analysis and Wiener process are used in orderto build an algorithm to solve the problem of globaloptimization.The paper is divided in two main parts.In the first part an already known algorithm is considered: a new (Bayesian)stopping ruleis added to it and some results are given, such asan upper bound for the number of iterations under the new stopping rule.In the second part a new algorithm is introduced in which the Bayesianapproach is exploited not onlyin the choice of the Wiener model but also in the estimationof the parameter ² of the Wiener process, whose value appears to bequite crucial.Some results about this algorithm are also given.     

Surrogate docking: structure-based virtual screening at high throughput speed

Summary Structure-based screening using fully flexible docking is still too slow for large molecular libraries. High quality docking of a million molecule library can take days even on a cluster with hundreds of CPUs. This performance issue prohibits the use of fully flexible docking in the design of large combinatorial libraries. We have developed a fast structure-based screening method, which utilizes docking of a limited number of compounds to build a 2D QSAR model used to rapidly score the rest of the database. We compare here a model based on radial basis functions and a Bayesian categorization model. The number of compounds that need to be actually docked depends on the number of docking hits found. In our case studies reasonable quality models are built after docking of the number of molecules containing 50 docking hits. The rest of the library is screened by the QSAR model. Optionally a fraction of the QSAR-prioritized library can be docked in order to find the true docking hits. The quality of the model only depends on the training set size – not on the size of the library to be screened. Therefore, for larger libraries the method yields higher gain in speed no change in performance. Prioritizing a large library with these models provides a significant enrichment with docking hits: it attains the values of 13 and 35 at the beginning of the score-sorted libraries in our two case studies: screening of the NCI collection and a combinatorial libraries on CDK2 kinase structure. With such enrichments, only a fraction of the database must actually be docked to find many of the true hits. The throughput of the method allows its use in screening of large compound collections and in the design of large combinatorial libraries. The strategy proposed has an important effect on efficiency but does not affect retrieval of actives, the latter being determined by the quality of the docking method itself. Electronic supplementary material is available at http://dx.doi.org/10.1007/s10822-005-9002-6.     

Optimal selection of R&D projects

A model for the selection process of research and development (R&D) projects belonging to some common area and submitted to a funding agency is presented. Every project is evaluated, the result of this procedure providing the agency with some useful information about the distribution of the project's payoff. The uncertainty due to the unknown perspectives of the whole area of R&D is incorporated in a Bayesian way, so that the agency learns about the area value from the projects already handled. After specifying the model assumptions, adaptive dynamic programming techniques are applied to develop an optimal funding strategy for a given number of submitted projects. Some qualitative properties of the optimal strategy are derived, and the asymptotical behavior of the maximum expected reward is determined.     

Application of a Bayesian Approach to the Tomographic Analysis of Hopper Flow

This paper presents a new approach to the analysis of data on powder flow from electrical capacitance tomography (ECT) using probability modelling and Bayesian statistics. The methodology is illustrated for powder flow in a hopper. The purpose, and special features, of this approach is that ‘high‐level’ statistical Bayesian modelling combined with a Markov chain Monte Carlo (MCMC) sampling algorithm allows direct estimation of control parameters of industrial processes in contrast to usually applied ‘low‐level’, pixel‐based methods of data analysis. This enables reliable recognition of key process features in a quantitative manner. The main difficulty when investigating hopper flow with ECT is due to the need to measure small differences in particle packing density. The MCMC protocol enables more robust identification of the responses of such complex systems. This paper demonstrates the feasibility of the approach for a simple case of particulate material flow during discharging of a hopper. It is concluded that these approaches can offer significant advantages for the analysis and control of some industrial powder and other multi‐phase flow processes.     

Blind estimation of number of motion multi-human targets in wireless pyroelectric infrared sensor networks

Due to the features of low energy consumption and flexible networking, nowadays the pyroelectric sensor has been applied widely in areas such as network instruction detection or human body target tracking recognition. Moreover, accurate estimation and judgment about the number of human targets moving in the networks is the foundation of tracking and recognition. This paper, under the condition of being lack of relevant prior knowledge, presents a novel method which selects the maximum likelihood function of the Bayesian network models as the independent criterion. In addition, the objective function is optimally solved by the Laplace estimation. The results of numerous experiments on both simulation and hardware experimental platforms are shown that this method has capability to blindly estimate the number of motion multiple human targets in wireless pyroelectric infrared sensor networks.     

Quantum Graphical Models and Belief Propagation

Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences amongst large numbers of random variables. This paper presents a generalization of these concepts and methods to the quantum case, based on the idea that quantum theory can be thought of as a noncommutative, operator-valued, generalization of classical probability theory. Some novel characterizations of quantum conditional independence are derived, and definitions of Quantum n-Bifactor Networks, Markov Networks, Factor Graphs and Bayesian Networks are proposed. The structure of Quantum Markov Networks is investigated and some partial characterization results are obtained, along the lines of the Hammersley–Clifford theorem. A Quantum Belief Propagation algorithm is presented and is shown to converge on 1-Bifactor Networks and Markov Networks when the underlying graph is a tree. The use of Quantum Belief Propagation as a heuristic algorithm in cases where it is not known to converge is discussed. Applications to decoding quantum error correcting codes and to the simulation of many-body quantum systems are described.     

Bayesian credible interval construction for Poisson statistics

The construction of the Bayesian credible (confidence) interval for a Poisson observable including both the signal and background with and without systematic uncertainties is presented.Introducing the conditional probability satisfying the requirement of the background not larger than the observed events to construct the Bayesian credible interval is also discussed.A Fortran routine,BPOCI,has been developed to implement the calculation.     

Bayesian Networks for enterprise risk assessment

According to different typologies of activity and priority, risks can assume diverse meanings and it can be assessed in different ways.Risk, in general, is measured in terms of a probability combination of an event (frequency) and its consequence (impact). To estimate the frequency and the impact (severity) historical data or expert opinions (either qualitative or quantitative data) are used. Moreover, qualitative data must be converted in numerical values or bounds to be used in the model.In the case of enterprise risk assessment the considered risks are, for instance, strategic, operational, legal and of image, which many times are difficult to be quantified. So in most cases only expert data, gathered by scorecard approaches, are available for risk analysis.The Bayesian Networks (BNs) are a useful tool to integrate different information and in particular to study the risk's joint distribution by using data collected from experts.In this paper we want to show a possible approach for building a BN in the particular case in which only prior probabilities of node states and marginal correlations between nodes are available, and when the variables have only two states.     

不完全信息动态二维价格博弈模型及其分析

单位生产成本为不完全信息条件下,本文首先讨论了两个企业关于具有一定替代性的两种产品价格的动态二维博弈模型,并求得其精练Bayes均衡.然后分析了当两种产品不存在替代关系时,企业对这两种产品价格进行动态博弈的精练Bayes均衡相当于对这两种产品单独进行博弈的精练Bayes均衡的简单组合.