Bayesian Classification Procedure Research Articles

Processing Probability Information in Nonnumerical Settings - Teachers' Bayesian and Non-bayesian Strategies During Diagnostic Judgment.

A diagnostic judgment of a teacher can be seen as an inference from manifest observable evidence on a student’s behavior to his or her latent traits. This can be described by a Bayesian model of inference: The teacher starts from a set of assumptions on the student (hypotheses), with subjective probabilities for each hypothesis (priors). Subsequently, he or she uses observed evidence (students’ responses to tasks) and knowledge on conditional probabilities of this evidence (likelihoods) to revise these assumptions. Many systematic deviations from this model (biases, e.g., base-rate neglect, inverse fallacy) are reported in the literature on Bayesian reasoning. In a teacher’s situation, the information (hypotheses, priors, likelihoods) is usually not explicitly represented numerically (as in most research on Bayesian reasoning) but only by qualitative estimations in the mind of the teacher. In our study, we ask to which extent individuals (approximately) apply a rational Bayesian strategy or resort to other biased strategies of processing information for their diagnostic judgments. We explicitly pose this question with respect to nonnumerical settings. To investigate this question, we developed a scenario that visually displays all relevant information (hypotheses, priors, likelihoods) in a graphically displayed hypothesis space (called “hypothegon”)–without recurring to numerical representations or mathematical procedures. Forty-two preservice teachers were asked to judge the plausibility of different misconceptions of six students based on their responses to decimal comparison tasks (e.g., 3.39 > 3.4). Applying a Bayesian classification procedure, we identified three updating strategies: a Bayesian update strategy (BUS, processing all probabilities), a combined evidence strategy (CES, ignoring the prior probabilities but including all likelihoods), and a single evidence strategy (SES, only using the likelihood of the most probable hypothesis). In study 1, an instruction on the relevance of using all probabilities (priors and likelihoods) only weakly increased the processing of more information. In study 2, we found strong evidence that a visual explication of the prior–likelihood interaction led to an increase in processing the interaction of all relevant information. These results show that the phenomena found in general research on Bayesian reasoning in numerical settings extend to diagnostic judgments in nonnumerical settings.

Bayesian Discriminant Analysis Using a High Dimensional Predictor

We consider the problem of Bayesian discriminant analysis using a high dimensional predictor. In this setting, the underlying precision matrices can be estimated with reasonable accuracy only if some appropriate additional structure like sparsity is assumed. We induce a prior on the precision matrix through a sparse prior on its Cholesky decomposition. For computational ease, we use shrinkage priors to induce sparsity on the off-diagonal entries of the Cholesky decomposition matrix and exploit certain conditional conjugacy structure. We obtain the contraction rate of the posterior distribution for the mean and the precision matrix respectively using the Euclidean and the Frobenius distance, and show that under some milder restriction on the growth of the dimension, the misclassification probability of the Bayesian classification procedure converges to that of the oracle classifier for both linear and quadratic discriminant analysis. Extensive simulations show that the proposed Bayesian methods perform very well. An application to identify cancerous breast tumorbased on image data obtained using find needle aspirate is considered.

Identification and classification of small molecule kinases: insights into substrate recognition and specificity.

BackgroundMany prokaryotic kinases that phosphorylate small molecule substrates, such as antibiotics, lipids and sugars, are evolutionarily related to Eukaryotic Protein Kinases (EPKs). These Eukaryotic-Like Kinases (ELKs) share the same overall structural fold as EPKs, but differ in their modes of regulation, substrate recognition and specificity—the sequence and structural determinants of which are poorly understood.ResultsTo better understand the basis for ELK specificity, we applied a Bayesian classification procedure designed to identify sequence determinants responsible for functional divergence. This reveals that a large and diverse family of aminoglycoside kinases, characterized members of which are involved in antibiotic resistance, fall into major sub-groups based on differences in putative substrate recognition motifs. Aminoglycoside kinase substrate specificity follows simple rules of alternating hydroxyl and amino groups that is strongly correlated with variations at the DFG + 1 position.ConclusionsSubstrate specificity determining features in small molecule kinases are mostly confined to the catalytic core and can be identified based on quantitative sequence and crystal structure comparisons.Electronic supplementary materialThe online version of this article (doi:10.1186/s12862-015-0576-x) contains supplementary material, which is available to authorized users.

A Fovea Localization Scheme Using Vessel Origin-Based Parabolic Model

At the center of the macula, fovea plays an important role in computer-aided diagnosis. To locate the fovea, this paper proposes a vessel origin (VO)-based parabolic model, which takes the VO as the vertex of the parabola-like vasculature. Image processing steps are applied to accurately locate the fovea on retinal images. Firstly, morphological gradient and the circular Hough transform are used to find the optic disc. The structure of the vessel is then segmented with the line detector. Based on the characteristics of the VO, four features of VO are extracted, following the Bayesian classification procedure. Once the VO is identified, the VO-based parabolic model will locate the fovea. To find the fittest parabola and the symmetry axis of the retinal vessel, an Shift and Rotation (SR)-Hough transform that combines the Hough transform with the shift and rotation of coordinates is presented. Two public databases of retinal images, DRIVE and STARE, are used to evaluate the proposed method. The experiment results show that the average Euclidean distances between the located fovea and the fovea marked by experts in two databases are 9.8 pixels and 30.7 pixels, respectively. The results are stronger than other methods and thus provide a better macular detection for further disease discovery.

Predicting torsion angles in amino acid protein sequences based on a bayesian classification procedure on markov chains

Torsion angles formed by C ? atoms of four neighboring residues are predicted using a Bayesian classification procedure on nonstationary Markov chains. The predicted sequence of torsion angles is used to construct a three-dimensional protein structure on Z 3 lattice.

Bayesian approach, theory of empirical risk minimization. Comparative analysis

Error estimates of empirical-risk minimization methods for an infinite number of decision rules are analyzed. Optimal deterministic estimates of the error of the Bayesian classification procedure for independent features are obtained based on averaging over a great number of training samples as a control. For the Boolean case, the Bayesian procedure is equivalent to a classification procedure based on a separating hyperplane.

A Bayesian Networks in Intrusion Detection Systems

Intrusion detection systems (IDSs) have been widely used to overcome security threats in computer networks. Anomaly-based approaches have the advantage of being able to detect previously unknown attacks, but they suffer from the difficulty of building robust models of acceptable behaviour which may result in a large number of false alarms caused by incorrect classification of events in current systems. We propose a new approach of an anomaly Intrusion detection system (IDS). It consists of building a reference behaviour model and the use of a Bayesian classification procedure associated to unsupervised learning algorithm to evaluate the deviation between current and reference behaviour. Continuous re-estimation of model parameters allows for real time operation. The use of recursive Log-likelihood and entropy estimation as a measure for monitoring model degradation related with behavior changes and the associated model update show that the accuracy of the event classification process is significantly improved using our proposed approach for reducing the missing- alarm.

Automatic identification of Mycobacterium tuberculosis by Gaussian mixture models

Tuberculosis and other kinds of mycobacteriosis are serious illnesses for which early diagnosis is critical for disease control. Sputum sample analysis is a common manual technique employed for bacillus detection but current sample-analysis techniques are time-consuming, very tedious, subject to poor specificity and require highly trained personnel. Image-processing and pattern-recognition techniques are appropriate tools for improving the manual screening of samples. Here we present a new technique for sputum image analysis that combines invariant shape features and chromatic channel thresholding. Some feature descriptors were extracted from an edited bacillus data set to characterize their shape. They were statistically represented by using a Gaussian mixture model representation and a minimal error Bayesian classification procedure was employed for the last identification stage. This technique constitutes a step towards automating the process and providing a high specificity.

Wurst: a protein threading server with a structural scoring function, sequence profiles and optimized substitution matrices.

Wurst is a protein threading program with an emphasis on high quality sequence to structure alignments (http://www.zbh.uni-hamburg.de/wurst). Submitted sequences are aligned to each of about 3000 templates with a conventional dynamic programming algorithm, but using a score function with sophisticated structure and sequence terms. The structure terms are a log-odds probability of sequence to structure fragment compatibility, obtained from a Bayesian classification procedure. A simplex optimization was used to optimize the sequence-based terms for the goal of alignment and model quality and to balance the sequence and structural contributions against each other. Both sequence and structural terms operate with sequence profiles.

Adaptive Bayesian contextual classification based on Markov random fields

An adaptive Bayesian contextual classification procedure that utilizes both spectral and spatial interpixel dependency contexts in estimation of statistics and classification is proposed. Essentially, this classifier is the constructive coupling of an adaptive classification procedure and a Bayesian contextual classification procedure. In this classifier, the joint prior probabilities of the classes of each pixel and its spatial neighbors are modeled by the Markov random field. The estimation of statistics and classification are performed in a recursive manner to allow the establishment of the positive-feedback process in a computationally efficient manner. Experiments with real hyperspectral data show that, starting with a small training sample set, this classifier can reach classification accuracies similar to that obtained by a pixelwise maximum likelihood pixel classifier with a very large training sample set. Additionally, classification maps are produced that have significantly less speckle error.

Efficiency of the Bayesian Classification Procedure: The Discrete Case

An upper-bound estimate of the error of the Bayesian procedure of solution of classification problems depending on the volume of training samples is given. The suboptimality of the Bayesian approach is proved and the complexity of the class of problems considered is determined.

Efficiency of Bayesian classification procedure

Efficiency of Bayesian classification procedure

Adaptive Bayesian Classification of Spatial Data

Abstract A two-dimensional scene is analyzed statistically by superimposing on it a rectangular grid and studying each square picture element (pixel) as one unit of the entire picture. With each pixel we want to associate one of K labels, but the label must be determined. Labels may be related to one another spatially, reflecting an underlying pattern in the scene. There is a noisy observation vector associated with each pixel, and these vectors are used contextually to classify the pixels; that is, to determine their labels in an effort to reconstruct the true scene. The discretized picture and the K labels constitute a lattice structure. We assume there is prior information available to assist in the reconstruction. The adaptive Bayesian classification (ABC) procedure proposed is iterative. It starts with a formal predictive contextual Bayesian classification of the entire map, then proceeds by adaptively reclassifying all of the labels in the map at each iteration using an empirical Bayesian updating a...

Adaptive Bayesian Classification of Spatial Data

Abstract A two-dimensional scene is analyzed statistically by superimposing on it a rectangular grid and studying each square picture element (pixel) as one unit of the entire picture. With each pixel we want to associate one of K labels, but the label must be determined. Labels may be related to one another spatially, reflecting an underlying pattern in the scene. There is a noisy observation vector associated with each pixel, and these vectors are used contextually to classify the pixels; that is, to determine their labels in an effort to reconstruct the true scene. The discretized picture and the K labels constitute a lattice structure. We assume there is prior information available to assist in the reconstruction. The adaptive Bayesian classification (ABC) procedure proposed is iterative. It starts with a formal predictive contextual Bayesian classification of the entire map, then proceeds by adaptively reclassifying all of the labels in the map at each iteration using an empirical Bayesian updating algorithm. The ABC algorithm provides an approximation to a local maximum for the joint posterior classification probability of all pixels in the map. The procedure attempts to improve on other such iterative procedures by reestimating parameters and reclassifying pixels by conditioning initially on prior information via the predictive Bayesian paradigm. It is “adaptive Bayesian” in that its initial reconstruction stage is formal Bayesian, and it also uses a Bayes theorem-type argument for updating the data at each iteration. Applications include image processing of remotely sensed satellite data, photon emission tomography, and computer vision.

Model of human sound localization based on spectral pattern recognition

In the course of our research on sound localization we have measured direction‐dependent pinna transfer functions of eight observers. The magnitudes of these functions have peaks and valleys that vary in spectral locus across subject and across source location. We addressed the question of whether these spectral patterns contain sufficient information for accurate localization of sounds in space. We used standard multivariate statistical techniques to develop a model of sound localization based on pattern recognition principles. A Bayesian classification procedure is employed to make a decision as to the most probable source location. The errors made by this procedure are compared to the errors made by subjects when judging source location in free‐field listening conditions. Preliminary results are extremely encouraging. The source positions for which the model makes errors match quite well those for which the subjects make errors. [Work supported by NSF and NIH.]

Cross-validation of a patient classification procedure: an application of the U method.

The objective of this article is to present the methods used for the validation of a patient classification system that was based on the concept of types of care (PCTC system). The PCTC system was developed to improve placement decisions for long-term care patients and also to provide information required for planning in the field of long-term care. A sample of long-term care patients was selected from various institutions/programs and the patients in the sample were assessed and classified by the program practitioners (users) as well as an independent panel (criterion team) composed of a physician, a nurse, and a social worker, using prototype forms specially designed for the project. An objective and empiric classification model was developed by applying discriminant analysis, Bayesian classification procedure, and cluster analysis techniques. The classification validity was evaluated by the use of the R, H, and U methods.

Validation and Comparison of Homogeneous and Occupational Interest Scales

Occupational interest scales and homogeneous scales were developed and compared in a double cross-validation design. A sample of 3,072 Air Force personnel was randomly divided for study purposes. Homogeneous scales were developed in each half-sample using a backward item selection procedure. Occupational scales were developed by selecting items which discriminated satisfied per sonnel within a career field from a "men-in- general" group. A Bayesian classification procedure was then used to cross-validate the scales developed in each half-sample. The results indicated that the occupational scales were slightly superior in cor rectly classifying satisfied personnel versus men-in- general. However, correlations between all interest scales and job satisfaction indicated generally higher validity for relevant homogeneous scales than for occupational scales. It was concluded that where prediction of group membership or occupa tional choice is desired, occupational keying should probably be the preferred approach. However, when concern is with a broader range of criteria, homo geneous scales may offer more general utility.

Clinical application of a second generation electrocardiographic computer program

An electrocardiographic computer program based on multivariate analysis of orthogonal leads (Frank) was applied to records transmitted daily by telephone from the Veterans Administration Hospital, West Roxbury, Mass., to the Veterans Administration Hospital, Washington, D.C. A Bayesian classification procedure was used to compute probabilities for all diagnostic categories that might be encountered in a given record. Computer results were compared with interpretations of conventional 12 lead tracings. Of 1,663 records transmitted, 1,192 were selected for the study because the clinical diagnosis in these cases could be firmly established on the basis of independent, nonelectrocardiographic information. Twenty-one percent of the records were obtained from patients without evidence of cardiac disease and 79 percent from patients with various cardiovascular illnesses. Diagnostic electrocardiographic classifications were considered correct when in agreement with documented clinical diagnoses. Of the total sample of 1,192 recordings, 86 percent were classified correctly by computer as compared with 68 percent by conventional 12 lead electrocardiographic analysis. Improvement in diagnostic recognition by computer was most striking in patients with hypertensive cardiovascular disease or chronic obstructive lung disease. The multivariate classification scheme functioned most efficiently when a problem-oriented approach to diagnosis was simulated. This was accomplished by a simple method of adjusting prior probabilities according to the diagnostic problem under consideration.

Discrimination Function Analysis and Bayesian Classification Approach to Muddy Sandstone Exploration, Wyoming: ABSTRACT

Stratigraphically trapped petroleum deposits occurring in the Muddy Formation of Campbell County, Wyoming, were studied by using discriminant function analysis followed by Bayesian classification analysis. The data used in this study were obtained from over 600 productive and nonproductive wells in a 720-sq mi area. A total of 15 quantitative measures (variables) of lithology, porosity, and salinity were computed from the S.P., gamma ray, and density logs from each well. Discriminant and Bayesian classification analyses were used to compute discriminant and probability maps. Discriminant-scores maps were made by two methods: (1) using the total data set of both productive and nonproductive wells, and (2) using only the nonproductive wells. The second type of map more closely simulates the exploration situation. A map showing probability of oil occurrence was constructed by first partitioning the study area into 64 cells of 9 sq mi each, and then establishing a control area and a test area. In the control area the cells were divided into productive and nonproductive subsets; a discriminant function then was computed. The discriminant function derived from the control area was used as the input for a Bayesian classification procedure to compute probabilities of petroleum occurrence in the test area. The predictions made by the statistical analyses are compared to the actual production in the test area. End_of_Article - Last_Page 615------------

Bayesian Classification Procedures in Analyzing Customer Characteristics

Traditionally, discriminant functions have been used to classify individuals according to a linear function of the individuals’ measured characteristics. This article develops a Bayesian classification procedure which explicitly takes into account the costs of misclassification and attribute measurement. The article presents the results of a computer program designed to determine the optimal number of characteristics to measure and discusses the results’ implications for consumer research.