Bayes' rule

We propose and discuss improved Bayes rules to discriminate between two populations using ordered predictors. To address the problem we propose an alternative formulation using a latent space that allows to introduce the information about the order in the theoretical rules. The rules are first defined when the marginal densities are fully known and then under normality when the parameters are unknown and training samples are available. Several numerical examples and simulations in the paper illustrate the methodology and show that the new rules handle the information appropriately. We compare the new rules with the classical Bayes and Fisher rules in these examples and we show that the misclassification probability is smaller for the new rules. The method is also applied to data from a diabetes study where we again show that the new rules improve over the usual Fisher rule.

Simultaneous localization and map-building (SLAM) continues to draw considerable attention in the robotics community due to the advantages it can offer in building autonomous robots. It examines the ability of an autonomous robot starting in an unknown environment to incrementally build an environment map and simultaneously localize itself within this map. Recent advances in computer vision have contributed a whole class of solutions for the challenge of SLAM. This paper surveys contemporary progress in SLAM algorithms, especially those using computer vision as main sensing means, i.e., visual SLAM. We categorize and introduce these visual SLAM techniques with four main frameworks: Kalman filter (KF)-based, particle filter (PF)-based, expectation-maximization (EM)-based and set membership-based schemes. Important topics of SLAM involving different frameworks are also presented. This article complements other surveys in this field by being current as well as reviewing a large body of research in the area of vision-based SLAM, which has not been covered. It clearly identifies the inherent relationship between the state estimation via the KF versus PF and EM techniques, all of which are derivations of Bayes rule. In addition to the probabilistic methods in other surveys, non-probabilistic approaches are also covered.

How should the Fermi paradox affect an estimate of humankind's likelihood and best means of long-term survival? A significant probability that many other civilizations have been in our situation but failed to become spacefaring increases the probability that our optimal existential risk strategies are costly, likely to fail, likely to leave traces if they do fail, and might require talents that mankind has but that other scientifically advanced species lack. The Fermi paradox implies that we should seek scientific data based on astronomical observations not accessible to civilizations that lived in the distant past, and that we should create machines to flood our galaxy with radio signals conditional on our civilization's collapse. Our ability to use Bayesian updating on the Fermi paradox reduces the chance that aliens exist but are hiding from us because of their desire to not interfere in our development: giving us a false understanding of the fate of intelligent life in the universe would cloud our understanding of existential risks. The paradox also provides clues as to types of trap that might destroy us. The possibility that our universe is fine-tuned not only for life but also for the Fermi paradox magnifies these results.

Incorporation of expert information in inference or decision settings is often important, especially in cases where data are unavailable, costly or unreliable. One approach is to elicit prior quantiles from an expert and then to fit these to a statistical distribution and proceed according to Bayes rule. An incentive-compatible elicitation method using an external randomization is available.

In Part I of this paper , an equivalence between the concepts of fuzzy clustering and soft competitive learning in clustering algorithms is proposed on the basis of the existing literature. Moreover, a set of functional attributes is selected for use as dictionary entries in the comparison of clustering algorithms.

Simultaneous localization and map-building (SLAM) continues to draw considerable attention in the robotics community due to the advantages it can offer in building autonomous robots. It examines the ability of an autonomous robot starting in an unknown environment to incrementally build an environment map and simultaneously localize itself within this map. Recent advances in computer vision have contributed a whole class of solutions for the challenge of SLAM. This paper surveys contemporary progress in SLAM algorithms, especially those using computer vision as main sensing means, i.e., visual SLAM. We categorize and introduce these visual SLAM techniques with four main frameworks: Kalman filter (KF)-based, particle filter (PF)-based, expectation-maximization (EM)-based and set membership-based schemes. Important topics of SLAM involving different frameworks are also presented. This article complements other surveys in this field by being current as well as reviewing a large body of research in the area of vision-based SLAM, which has not been covered. It clearly identifies the inherent relationship between the state estimation via the KF versus PF and EM techniques, all of which are derivations of Bayes rule. In addition to the probabilistic methods in other surveys, non-probabilistic approaches are also covered.

This paper aims to make explicit the methodological conditions that should be satisfied for the Bayesian model to be used as a normative model of human probability judgment. After noticing the lack of a clear definition of Bayesianism in the psychological literature and the lack of justification for using it, a classic definition of subjective Bayesianism is recalled, based on the following three criteria: an epistemic criterion, a static coherence criterion and a dynamic coherence criterion. Then it is shown that the adoption of this framework has two kinds of implications. The first one regards the methodology of the experimental study of probability judgment. The Bayesian framework creates pragmatic constraints on the methodology that are linked to the interpretation of, and the belief in, the information presented, or referred to, by an experimenter in order for it to be the basis of a probability judgment by individual participants. It is shown that these constraints have not been satisfied in the past, and the question of whether they can be satisfied in principle is raised and answered negatively. The second kind of implications consists of two limitations in the scope of the Bayesian model. They regard (1) the background of revision (the Bayesian model considers only revising situations but not updating situations), and (2) the notorious case of the null priors. In both cases Lewis' rule is an appropriate alternative to Bayes' rule, but its use faces the same operational difficulties.

Resumen: Cada vez son más numerosas las investigaciones que trabajan con un amplio número de variables donde existen relaciones complejas entre ellas. Las redes bayesianas son herramientas estadísticas surgidas en el campo de la Inteligencia Artificial que nos permiten afrontar situaciones de investigación de estas características. Una red bayesiana es un grafo dirigido acíclico que codifica relaciones probabilísticas de dependencia e independencia condicional y que actualiza el modelo con base en las evidencias muestrales mediante la regla de Bayes. Este artículo describirá los principios matemático-estadísticos esenciales de las redes bayesianas y las ventajas que tienen frente a otras herramientas multivariantes. Finalmente, revisaremos las aplicaciones, que desde la Psicología, se han aportado, así como se describen sus usos potenciales. Palabras clave: Redes bayesianas; sistemas expertos; estadística bayesiana y modelado estadístico.

This paper describes a hybrid fuzzy weights-of-evidence (WofE) model for mineral potential mapping that generates fuzzy predictor patterns based on (a) knowledge-based fuzzy membership values and (b) data-based conditional probabilities. The fuzzy membership values are calculated using a knowledge-driven logistic membership function, which provides a framework for treating systemic uncertainty and also facilitates the use of multiclass predictor maps in the modeling procedure. The fuzzy predictor patterns are combined using Bayes’ rule in a log-linear form (under an assumption of conditional independence) to update the prior probability of target deposit-type occurrence in every unique combination of predictor patterns. The hybrid fuzzy WofE model is applied to a regional-scale mapping of base-metal deposit potential in the south-central part of the Aravalli metallogenic province (western India). The output map of fuzzy posterior probabilities of base-metal deposit occurrence is classified subsequently to delineate zones with high-favorability, moderate favorability, and low-favorability for occurrence of base-metal deposits. An analysis of the favorability map indicates (a) significant improvement of probability of base-metal deposit occurrence in the high-favorability and moderate-favorability zones and (b) significant deterioration of probability of base-metal deposit occurrence in the low-favorability zones. The results demonstrate usefulness of the hybrid fuzzy WofE model in representation and in integration of evidential features to map relative potential for mineral deposit occurrence.

Clustering algorithms aim at modeling fuzzy (i.e., ambiguous) unlabeled patterns efficiently. Our goal is to propose a theoretical framework where the expressive power of clustering systems can be compared on the basis of a meaningful set of common functional features. Part I of this paper reviews the following issues related to clustering approaches found in the literature: relative (probabilistic) and absolute (possibilistic) fuzzy membership functions and their relationships to the Bayes rule, batch and on-line learning, prototype editing schemes, growing and pruning networks, modular network architectures, topologically perfect mapping, ecological nets and neuro-fuzziness. From this discussion an equivalence between the concepts of fuzzy clustering and soft competitive learning in clustering algorithms is proposed as a unifying framework in the comparison of clustering systems. Moreover, a set of functional attributes is selected for use as dictionary entries in the comparison of clustering algorithms, which is the subject of Part II of this paper [1].

Bayes’ rule shows how one might rationally change one’s beliefs in the light of evidence. It is the foundation of a statistical method called Bayesianism. In health care research, Bayesianism has its advocates but the dominant statistical method is frequentism.

There are at least two important philosophical differences between these methods. First, Bayesianism takes a subjectivist view of probability (i.e. that probability scores are statements of subjective belief, not objective fact) whilst frequentism takes an objectivist view. Second, Bayesianism is explicitly inductive (i.e. it shows how we may induce views about the world based on partial data from it) whereas frequentism is at least compatible with non-inductive views of scientific method, particularly the critical realism of Popper.

Popper and others detail significant problems with induction. Frequentism’s apparent ability to avoid these, plus its ability to give a seemingly more scientific and objective take on probability, lies behind its philosophical appeal to health care researchers.

However, there are also significant problems with frequentism, particularly its inability to assign probability scores to single events. Popper thus proposed an alternative objectivist view of probability, called propensity theory, which he allies to a theory of corroboration; but this too has significant problems, in particular, it may not successfully avoid induction. If this is so then Bayesianism might be philosophically the strongest of the statistical approaches. The article sets out a number of its philosophical and methodological attractions. Finally, it outlines a way in which critical realism and Bayesianism might work together.

While gait recognition is the mapping of a gait sequence to an identity known to the system, gait authentication refers to the problem of identifying whether a given gait sequence belongs to the claimed identity. A typical gait authentication system starts with a feature representation such as a gait template, then proceeds to extract its features, and a transformation is ultimately applied to obtain a discriminant feature set. Almost every authentication approach in literature favours the use of Euclidean distance as a threshold to mark the boundary between a legitimate subject and an impostor. This article proposes a method that uses the posterior probability of a Bayes' classifier in place of the Euclidean distance. The proposed framework is applied to template-based gait feature representations and is evaluated using the standard CASIA-B gait database. Our study experimentally demonstrates that the Bayesian posterior probability performs significantly better than the de facto Euclidean distance approach and the cosine distance which is established in research to be the current state of the art.

We discuss a Bayesian discovery procedure for multiple comparison problems. We show that under a coherent decision theoretic framework, a loss function combining true positive and false positive counts leads to a decision rule based on a threshold of the posterior probability of the alternative. Under a semi-parametric model for the data, we show that the Bayes rule can be approximated by the optimal discovery procedure (ODP), recently introduced by Storey . Improving the approximation leads us to a Bayesian discovery procedure (BDP), which exploits the multiple shrinkage in clusters implied by the assumed nonparametric model. We compare the BDP and the ODP estimates in a simple simulation study and in an assessment of differential gene expression based on microarray data from tumor samples. We extend the setting of the ODP by discussing modifications of the loss function that lead to different single thresholding statistics. Finally, we provide an application of the previous arguments to dependent (spatial) data.

This paper presents a novel unsupervised methodology for automatic disam- biguation of nouns found in unrestricted corpora. The proposed method is based on extending the context of a target word by querying the web, and then measuring the overlap of the extended context with the topic signatures of the different senses by using Bayes rule. The algorithm is evaluated on

A concern has been expressed that "the Jaynes principle can produce fake entanglement" [R. Horodecki et al., Phys. Rev. A 59, 1799]. In this paper we discuss the general problem of distilling maximally entangled states from N copies of a bipartite quantum system about which only partial information is known, for instance in the form of a given expectation value. We point out that there is indeed a problem with applying the Jaynes principle of maximum entropy to more than one copy of a system, but the nature of this problem is classical and was discussed extensively by Jaynes. Under the additional assumption that the state ρ (N ) of the N copies of the quantum system is exchangeable, one can write down a simple general expression for ρ (N ) . We show how to modify two standard entanglement purification protocols, one-way hashing and recurrence, so that they can be applied to exchangeable states. We thus give an explicit algorithm for distilling entanglement from an unknown or partially known quantum state.

Dental age estimation methods based on the radiologically detected third molar developmental stages are implemented in forensic age assessments to discriminate between juveniles and adults considering the judgment of young unaccompanied asylum seekers. Accurate and unbiased age estimates combined with appropriate quantified uncertainties are the required properties for accurate forensic reporting. In this study, a subset of 910 individuals uniformly distributed in age between 16 and 22 years was selected from an existing dataset collected by Gunst et al. containing 2,513 panoramic radiographs with known third molar developmental stages of Belgian Caucasian men and women. This subset was randomly split in a training set to develop a classical regression analysis and a Bayesian model for the multivariate distribution of the third molar developmental stages conditional on age and in a test set to assess the performance of both models. The aim of this study was to verify if the Bayesian approach differentiates the age of maturity more precisely and removes the bias, which disadvantages the systematically overestimated young individuals. The Bayesian model offers the discrimination of subjects being older than 18 years more appropriate and produces more meaningful prediction intervals but does not strongly outperform the classical approaches.

This paper describes a method to estimate the position of a mobile robot in an indoor scenario using the odometric calculus and the WiFi energy received from the wireless infrastructure. This energy will be measured by wireless network card on-board a mobile ...

Learning and memory operations in neural circuits are believed to involve molecular cascades of synaptic and nonsynaptic changes that lead to a diverse repertoire of dynamical phenomena at higher levels of processing. Hebbian and homeostatic plasticity, neuromodulation, and intrinsic excitability all conspire to form and maintain memories. But it is still unclear how these seemingly redundant mechanisms could jointly orchestrate learning in a more unified system. To this end, a Hebbian learning rule for spiking neurons inspired by Bayesian statistics is proposed. In this model, synaptic weights and intrinsic currents are adapted on-line upon arrival of single spikes, which initiate a cascade of temporally interacting memory traces that locally estimate probabilities associated with relative neuronal activation levels. Trace dynamics enable synaptic learning to readily demonstrate a spike-timing dependence, stably return to a set-point over long time scales, and remain competitive despite this stability. Beyond unsupervised learning, linking the traces with an external plasticity-modulating signal enables spike-based reinforcement learning. At the postsynaptic neuron, the traces are represented by an activity-dependent ion channel that is shown to regulate the input received by a postsynaptic cell and generate intrinsic graded persistent firing levels. We show how spike-based Hebbian-Bayesian learning can be performed in a simulated inference task using integrate-and-fire (IAF) neurons that are Poisson-firing and background-driven, similar to the preferred regime of cortical neurons. Our results support the view that neurons can represent information in the form of probability distributions, and that probabilistic inference could be a functional by-product of coupled synaptic and nonsynaptic mechanisms operating over several timescales. The model provides a biophysical realization of Bayesian computation by reconciling several observed neural phenomena whose functional effects are only partially understood in concert.

I outline an argument for a subjective Bayesian interpretation of quantum probabilities as degrees of belief distributed subject to consistency constraints on a quantum rather than a classical event space. I show that the projection postulate of quantum mechanics can be understood as a noncommutative generalization of the classical Bayesian rule for updating an initial probability distribution on new information, and I contrast the Bayesian interpretation of quantum probabilities sketched here with an alternative approach defended by Chris Fuchs.

This paper compares two methods to estimate the position of a mobile robot in an indoor environment using only odometric calculus and the WiFi energy received from the wireless communication infrastructure. In both cases we use a well-known probabilistic method based on the Bayes rule to accumulate localization probability as the robot moves on with an experimental WiFi map, and with a theoretically built WiFi map. We will show several experiments made in our university building to compare both methods using a Pioneer robot. The two major contributions of the presented work are that the self-localization error achieved with WiFi energy is bounded, and that no significant degradation is observed when the expected WiFi energy at each point is taken from radio propagation model instead of an a priori experimental intensity map of the environment.

This paper describes a hybrid fuzzy weights-of-evidence (WofE) model for mineral potential mapping that generates fuzzy predictor patterns based on (a) knowledge-based fuzzy membership values and (b) data-based conditional probabilities. The fuzzy membership values are calculated using a knowledge-driven logistic membership function, which provides a framework for treating systemic uncertainty and also facilitates the use of multiclass predictor maps in the modeling procedure. The fuzzy predictor patterns are combined using Bayes' rule in a log-linear form (under an assumption of conditional independence) to update the prior probability of target deposit-type occurrence in every unique combination of predictor patterns. The hybrid fuzzy WofE model is applied to a regional-scale mapping of base-metal deposit potential in the south-central part of the Aravalli metallogenic province (western India). The output map of fuzzy posterior probabilities of base-metal deposit occurrence is classified subsequently to delineate zones with high-favorability, moderate favorability, and low-favorability for occurrence of base-metal deposits. An analysis of the favorability map indicates (a) significant improvement of probability of base-metal deposit occurrence in the high-favorability and moderate-favorability zones and (b) significant deterioration of probability of base-metal deposit occurrence in the low-favorability zones. The results demonstrate usefulness of the hybrid fuzzy WofE model in representation and in integration of evidential features to map relative potential for mineral deposit occurrence. abilities of B, given the presence or absence of D (Agterberg, :

This paper states necessary and sufficient conditions for the existence, uniqueness, and updating according to Bayes' rule, of subjective probabilities representing individuals' beliefs. The approach is preference based, and the result is an axiomatic subjective expected utility model of Bayesian decision making under uncertainty with statedependent preferences. The theory provides foundations for the existence of prior probabilities representing decision makers' beliefs about the likely realization of events and for the updating of these probabilities according to Bayes' rule.

This work presents an automated method for chromosome segmentation and classifieation. It takes the advantage of t b multi-spectral information in M-FISH chromosome images and d i z e s the Discrete Wavelet Transform (DWT) and Bayes rule. The results of the suggested method have shown a high performance of 100%, 92%, and 95% correct classification for three different imaging systems.

Regularization methods are characterized by loss functions measuring data fits and penalty terms constraining model parameters. The commonly used quadratic loss is not suitable for classification with binary responses, whereas the loglikelihood function is not readily applicable to models where the exact distribution of observations is unknown or not fully specified. We introduce the penalized Bregman divergence by replacing the negative loglikelihood in the conventional penalized likelihood with Bregman divergence, which encompasses many commonly used loss functions in the regression analysis, classification procedures and machine learning literature. We investigate new statistical properties of the resulting class of estimators with the number p n of parameters either diverging with the sample size n or even nearly comparable with n, and develop statistical inference tools. It is shown that the resulting penalized estimator, combined with appropriate penalties, achieves the same oracle property as the penalized likelihood estimator, but asymptotically does not rely on the complete specification of the underlying distribution. Furthermore, the choice of loss function in the penalized classifiers has an asymptotically relatively negligible impact on classification performance. We illustrate the proposed method for quasilikelihood regression and binary classification with simulation evaluation and real-data application.

An objective pilling evaluation method based on the multi-scale two-dimensional dual-tree complex wavelet transform and linear discriminant function of Bayes' Rule was developed. The surface fuzz and pills are identified from the high-frequency noise, fabric textures, fabric surface unevenness, and illuminative variation of a pilled fabric image by the two-dimensional dual-tree complex wavelet decomposition and reconstruction. The energies of the reconstructed subimages in six spatial orientations (±15º, ±45º, ±75º) are calculated as the elements of the pilling feature vector, whose dimension is reduced by principal component analysis. A linear discriminant function of Bayes' Rule was used as a classifier to establish classification rules among the five pilling grades. A new pilled sample with the same physical construction can then be automatically assigned to one of the five pilling grades by the classification rules. A general evaluation of the proposed method was conduct...

The slippage problem occurs when an unspecified observation in a given random sample is from a distribution other than that for all the remaining observations. This paper studies the problem in terms of the 'slip' in the mean direction of a circular normal distribution. The slippage problem is first treated as a multiple decision problem with a prior which is invariant under the permutations of the hypotheses. The probabilities of accepting the various hypotheses for the Bayes rule with respect to this prior are explicitly obtained. The likelihood ratio tests for this slippage problem, for the cases when the mean directions are both known and unknown, are shown to be easily computable. The tests are illustrated through two well-known datasets. The performances of a range of tests are compared using extensive simulation.

The Non-Use of Bayes Rule: Representative Evidence on Bounded Rationality * The ability to process new information and to compute conditional probabilities is crucial for making appropriate decisions under uncertainty. In this paper, we investigate the capability of inferring conditional probabilities in a representative sample of the German population. Our results show that only a small fraction of the population responds consistently with Bayes' rule. Instead, most individuals either neglect the base probability, or the arrival of new information, in their responses. The probability to give normatively correct answers decreases with the level of education.

Dental age estimation methods based on the radiologically detected third molar developmental stages are implemented in forensic age assessments to discriminate between juveniles and adults considering the judgment of young unaccompanied asylum seekers. Accurate and unbiased age estimates combined with appropriate quantified uncertainties are the required properties for accurate forensic reporting. In this study, a subset of 910 individuals uniformly distributed in age between 16 and 22 years was selected from an existing dataset collected by Gunst et al. containing 2,513 panoramic radiographs with known third molar developmental stages of Belgian Caucasian men and women. This subset was randomly split in a training set to develop a classical regression analysis and a Bayesian model for the multivariate distribution of the third molar developmental stages conditional on age and in a test set to assess the performance of both models. The aim of this study was to verify if the Bayesian approach differentiates the age of maturity more precisely and removes the bias, which disadvantages the systematically overestimated young individuals. The Bayesian model offers the discrimination of subjects being older than 18 years more appropriate and produces more meaningful prediction intervals but does not strongly outperform the classical approaches.

When resources are divided among agents, the characteristics of the agents are taken into consideration. A simple example is the bankruptcy problem, where the liquidation value of a bankrupt firm is divided among the creditors based on their claims. We characterize division rules under which no group of agents can increase the total amount they receive by transferring their characteristics within the group. By allowing agents' characteristics to be multi-dimensional and choosing the meaning of variables appropriately, our model can subsume a number of existing and new allocation problems, such as cost sharing, social choice with transferable utilities, income redistribution, bankruptcy with multiple types of assets, probability updating, and probability aggregation. A number of existing and new results in specific problems are obtained as corollaries. JEL Classification: C71, D30, D63, D71, H26. 1 The class of bankruptcy problems with a single type of assets was introduced by O'Neill [20], and since then a large literature has been developed. See Moulin [19] and Thomson [24, 26] for surveys. 2 Formally, the rule assigns

Information processing in the nervous system involves the activity of large populations of neurons. It is possible, however, to interpret the activity of relatively small numbers of cells in terms of meaningful aspects of the environment. 'Bayesian inference' provides a systematic and effective method of combining information from multiple cells to accomplish this. It is not a model of a neural mechanism (neither are alternative methods, such as the population vector approach) but a tool for analysing neural signals. It does not require difficult assumptions about the nature of the dimensions underlying cell selectivity, about the distribution and tuning of cell responses or about the way in which information is transmitted and processed. It can be applied to any parameter of neural activity (for example, firing rate or temporal pattern). In this review, we demonstrate the power of Bayesian analysis using examples of visual responses of neurons in primary visual and temporal cortices.We show that interaction between correlation in mean responses to different stimuli (signal) and correlation in response variability within stimuli (noise) can lead to marked improvement of stimulus discrimination using population responses. Trends Neurosci. (1998) 21, 259-265 I T IS GENERALLY AGREED that perceptions and actions arise from the activity pattern of populations of neurons. In this article, we address the issue of decoding the activity pattern of identified neurons. How the nervous system might decode the population activity is not considered here, but methods by which experimentalists can interpret the relationship between the population activity and either stimulus input or behavioural output are reviewed. Biologically plausible networks have been proposed that implement or approximate the two analysis methods discussed here 1,2 ; indeed, it might not be necessary for the nervous system to carry out explicit decoding. Our aim as experimentalists is to determine what information is present and hence available to the nervous system. Examination of changes in the information content of neural populations allows the underlying processing to be determined. Methods for interpreting the code of an identified population of neurons are therefore a matter of theoretical and practical importance.

Resumen: Cada vez son más numerosas las investigaciones que trabajan con un amplio número de variables donde existen relaciones complejas entre ellas. Las redes bayesianas son herramientas estadísticas surgidas en el campo de la Inteligencia Artificial que nos permiten afrontar situaciones de investigación de estas características. Una red bayesiana es un grafo dirigido acíclico que codifica relaciones probabilísticas de dependencia e independencia condicional y que actualiza el modelo con base en las evidencias muestrales mediante la regla de Bayes. Este artículo describirá los principios matemático-estadísticos esenciales de las redes bayesianas y las ventajas que tienen frente a otras herramientas multivariantes. Finalmente, revisaremos las aplicaciones, que desde la Psicología, se han aportado, así como se describen sus usos potenciales. Palabras clave: Redes bayesianas; sistemas expertos; estadística bayesiana y modelado estadístico.

A whole body counter (WBC) designed to measure bremsstrahlung from 90Y, the short-lived daughter of 90Sr, has been used since 1974 to measure 90Sr-body burdens in residents along the Techa River, which was contaminated by releases from the Mayak Production Association. Bayes' rule has been applied to the a posteriori WBC data in order to derive the uncertainties associated with the data: The lower limit of reliable detection is 2.0 kBq and the uncertainty of routine measurements is 1.6 kBq.

Individual classifiers predict unknown objects. Although, these are usually domain specific, and lack the property of scaling up prediction while handling data sets with huge size and high-dimensionality or imbalance class distribution. This article introduces an accuracy-based learning system called DTGA (decision tree and genetic algorithm) that aims to improve prediction accuracy over any classification problem irrespective to domain, size, dimensionality and class distribution. More specifically, the proposed system consists of two rule inducing phases. In the first phase, a base classifier, C4.5 (a decision tree based rule inducer) is used to produce rules from training data set, whereas GA (genetic algorithm) in the next phase refines them with the aim to provide more accurate and high-performance rules for prediction. The system has been compared with competent non-GA based systems: neural network, Naïve Bayes, rule-based classifier using rough set theory and C4.5 (i.e., the base classifier of DTGA), on a number of benchmark datasets collected from UCI (University of California at Irvine) machine learning repository. Empirical results demonstrate that the proposed hybrid approach provides marked improvement in a number of cases.

The exploration for oil and gas requires real-time petrophysical expertise to interpret measurement data acquired in boreholes and to recommend further steps. High time pressure and the far reaching nature of these decisions, as well as the limited opportunity to gain in depth petrophysical experience suggests that a decision support system that can aid the petrophysicist will be very useful. In this paper we describe a Bayesian approach for obtaining compositional estimates that combines expert knowledge with information obt ained from measurements. We define a prior model for the compositional volume fractions and observation models for each of the measurement tools. Both prior and observation models are based on domain expertise. These models are combined in a joint probability model. To deal with the nonlinearities in the model, Bayesian inference is implemented by using the hybrid Monte Carlo algorithm. In the system, tool measurement values can entered and the posterior probability distribution of the compositional fractions can be obtained by applying Bayes' rule. Bayesian inference is also used for optimal tool selection, using conditional entropy to select the most informative tool to obtain better estimates of the reservoir. Reliability and consistency of the method is demonstrated by inference on synthetically generated data.

Load forecasting is significantly important for the electricity production in the deregulated economy. It has many applications including energy purchasing and generation, load switching, contract evaluation, and infrastructure development. A large variety of mathematical methods have been developed for load forecasting. This paper presents a load forecast methodology using the Bayesian Belief Network (BBN) that is suitable for power system operational planning studies. Bayesian Belief Network is a powerful tool for combining different knowledge sources with various degrees of uncertainty in a mathematical sound and computationally efficient way. In this paper bayesian estimation is used for predicting maximum load growth per year.

This paper concerns the problem of classification based on training data. A framework of information geometry is given to elucidate the characteristics of discriminant functions including logistic discrimination and AdaBoost. We discuss a class of loss functions from a unified viewpoint.

This paper describes a method to estimate the position of a mobile robot in an indoor scenario using the odometric calculus and the WiFi energy received from the wireless infrastructure. This energy will be measured by wireless network card on-board a mobile robot, and it will be used as another regular sensor to improve position estimation. The Bayes rule will be used to accumulate localization probability as the robot moves on. In this paper several experiments in a university building are shown. The two major contributions of the presented work are that the self-localization error achieved is bounded, and that no significant degradation is observed when the theoretical WiFi energy at each point is taken from radio propagation model instead of an a priori experimental intensity map of the environment.

This paper presents a new method to forecast the short term electricity price as a kind of time series. A clustering based forecasting method is introduced. The proposed method contains input-output decomposition and using a simple clustering approach to classify them and then for a new input (a specified number of past time series values), these clusters are sorted according to the probabilities calculated by using the Bayes' formula. The prediction is then generated using the weighted average of the forecasted outputs of M clusters with highest probabilities.