Relevance of a Posteriori Probability Errors in Bayesian Classification

Improving Viterbi Bayesian predictive classification via sequential bayesian learning in robust speech recognition

We consider a binary response which is potentially affected by a set of continuous variables. Of special interest is the causal effect on the response due to an intervention on a specific variable. The latter can be meaningfully determined on the basis of observational data through suitable assumptions on the data generating mechanism. In particular we assume that the joint distribution obeys the conditional independencies (Markov properties) inherent in a Directed Acyclic Graph (DAG), and the DAG is given a causal interpretation through the notion of interventional distribution. We propose a DAG-probit model where the response is generated by discretization through a random threshold of a continuous latent variable and the latter, jointly with the remaining continuous variables, has a distribution belonging to a zero-mean Gaussian model whose covariance matrix is constrained to satisfy the Markov properties of the DAG; the latter is assigned a DAG-Wishart prior through the corresponding Cholesky parameters. Our model leads to a natural definition of causal effect conditionally on a given DAG. Since the DAG which generates the observations is unknown, we present an efficient MCMC algorithm whose target is the posterior distribution on the space of DAGs, the Cholesky parameters of the concentration matrix, and the threshold linking the response to the latent. Our end result is a Bayesian Model Averaging estimate of the causal effect which incorporates parameter, as well as model, uncertainty. The methodology is assessed using simulation experiments and applied to a gene expression data set originating from breast cancer stem cells.

This paper proposes a novel approach for machine health condition prognosis based on neuro-fuzzy systems (NFSs) and Bayesian algorithms. The NFS, after training with machine condition data, is employed as a prognostic model to forecast the evolution of the machine fault state with time. An online model update scheme is developed on the basis of the probability density function (PDF) of the NFS residuals between the actual and predicted condition data. Bayesian estimation algorithms adopt the model's predicted data as prior information in combination with online measurements to update the degree of belief in the forecasting estimations. In order to simplify the implementation of the proposed approach, a recursive Bayesian algorithm called particle filtering is utilized to calculate in real time a posterior PDF by a set of random samples (or particles) with associated weights. When new data become available, the weights of all particles are updated, and then, predictions are carried out, which form the PDF of the predicted estimations. The developed method is evaluated via two experimental cases-a cracked carrier plate and a faulty bearing. The prediction performance is compared with three prevalent machine condition predictors-recurrent neural networks, NFSs, and recurrent NFSs. The results demonstrate that the proposed approach can predict machine conditions more accurately.

One comparative analysis method of English comparative literature based on big data Bayesian method has been proposed to improve the calculation accuracy of comparative analysis process of English comparative literature. Firstly, one multilayer Bayesian classification recognition algorithm mechanism has been proposed for the problem of low accuracy and poor calculation efficiency of Bayesian classification algorithm under the big data environment; Gabor multilayer feature extraction algorithm has been proposed for multilayer Bayesian algorithm, Gabor multilayer feature extraction Bayesian algorithm has been designed and realized. Secondly, the algorithm process of comparative analysis system of English comparative literature based on this improved algorithm has been designed and the success rate of comparative analysis of English comparative literature has been improved effectively based on the features of comparative analysis of English comparative literature. Finally, the effectiveness of algorithm has been verified through experimental simulation.

Auto-extraction of stratified interface in the underground space based on Bayesian detection algorithm with statistical fitting of probability density by actual data

Bayesian networks and intelligence technology applied to climate change: An application of fuzzy logic based simulation in avalanche simulation risk assessment using GIS in a Western Himalayan region

In the course of the Sloan Digital Sky Survey (SDSS-I), a large fraction of the surveyed area was observed more than once due to field tiling overlap, usually at different epochs. We utilize some of these data to perform a supernova (SN) survey at a mean redshift of z= 0.2. Our archival search, in ∼5 per cent of the SDSS-I overlap area, produces 29 SN candidates clearly associated with host galaxies. Using the Bayesian photometric classification algorithm of Poznanski et al., and correcting for classification bias, we find 17 of the 29 candidates are likely Type Ia SNe. Accounting for the detection efficiency of the survey and for host extinction, this implies a Type Ia SN rate of rIa= (14.0+2.5+1.4−2.5−1.1± 2.5) × 10−14h270 yr−1L−1⊙,g, where the errors are Poisson error, systematic detection efficiency error and systematic classification error, respectively. The volumetric rate is RIa= (1.89+0.42+0.18−0.34−0.15± 0.42) × 10−5yr−1h370 Mpc−3. Our measurement is consistent with other rate measurements at low redshift. An order of magnitude increase in the number of SNe is possible by analysing the full SDSS-I data base.

Identifying strategies to improve PANSS based dimensional models in schizophrenia: Accounting for multilevel structure, Bayesian model and clinical staging

Bayesian model updating provides a rigorous framework to account for uncertainty induced by lack of knowledge about engineering systems in their respective mathematical models through updates of the joint probability density function (PDF), the so-called posterior PDF, of the unknown model parameters. The Markov chain Monte Carlo (MCMC) methods are currently the most popular approaches for generating samples from the posterior PDF. However, these methods often found wanting when sampling from difficult distributions (e.g., high-dimensional PDFs, PDFs with flat manifolds, multimodal PDFs, and very peaked PDFs). This paper introduces a new multi-level sampling approach for Bayesian model updating, called Sequential Gauss-Newton algorithm, which is inspired by the Transitional Markov chain Monte Carlo (TMCMC) algorithm. The Sequential Gauss-Newton algorithm improves two aspects of TMCMC to make an efficient and effective MCMC algorithm for drawing samples from difficult posterior PDFs. First, the statistical efficiency of the algorithm is enhanced by use of the systematic resampling scheme. Second, a new MCMC algorithm, called Gauss-Newton MCMC algorithm, is proposed which is essentially an M-H algorithm with a Gaussian proposal PDF tailored to the posterior PDF using the gradient and Hessian information of the negative log posterior. The effectiveness of the proposed algorithm for solving the Bayesian model updating problem is illustrated using three examples with irregularly shaped posterior PDFs.

Application of Bayesian classifier to magnetic and gamma ray spectrometry data for targeting hydrocarbon microseepages

Biofeedback-EEG training to learn the mental control of an external device (e.g., a cursor on the screen) has been an important paradigm to attempt to understand the involvements of various areas of the brain in the volitional control and the modulation of intentional thought processes. Often the areas to adapt and to monitor progress are selected a priori. Less explored, however, has been the notion of automatically emerging activation in a particular area or subregions within that area recruited above and beyond the rest of the brain. Likewise, the notion of evoking such a signal as an amodal, abstract one remaining robust across different sensory modalities could afford some exploration. Here we develop a simple binary control task in the context of brain-computer interface (BCI) and use a Bayesian sparse probit classification algorithm to automatically uncover brain regional activity that maximizes task performance. We trained and tested 19 participants using the visual modality for instructions and feedback. Across training blocks we quantified coupling of the frontoparietal nodes and selective involvement of visual and auditory regions as a function of the real-time sensory feedback. The testing phase under both forms of sensory feedback revealed automatic recruitment of the prefrontal cortex with a parcellation of higher strength levels in Brodmann's areas 9, 10, and 11 significantly above those in other brain areas. We propose that the prefrontal signal may be a neural correlate of externally driven intended direction and discuss our results in the context of various aspects involved in the cognitive control of our thoughts.

Microarray information is crucial for the identification and categorisation of malignant tissues. The very limited sample size in the microarray has always been a challenge for classification design in cancer research. As a result, by pre-processing gene selection approaches and genes lacking their information, the microarray data are deleted prior to categorisation. In essence, an appropriate gene selection technique can significantly increase the accuracy of illness (cancer) classification. For the classification of high-dimensional microarray data, a novel approach based on the hybrid model of multi-objective particle swarm optimisation (MOPSO) is proposed in this research. First, a binary vector representing each particle's position is presented at random. A gene is represented by each bit. Bit 0 denotes the absence of selection of the characteristic (gene) corresponding to it, while bit 1 denotes the selection of the gene. Therefore, the position of each particle represents a set of genes, and the linear Bayesian discriminant analysis classification algorithm calculates each particle's degree of fitness to assess the quality of the gene set that particle has chosen. The suggested methodology is applied to four different cancer database sets, and the results are contrasted with those of other approaches currently in use. The proposed algorithm has been applied on four sets of cancer database and its results have been compared with other existing methods. The results of the implementation show that the improvement of classification accuracy in the proposed algorithm compared to other methods for four sets of databases is 25.84% on average. So that it has improved by 18.63% in the blood cancer database, 24.25% in the lung cancer database, 27.73% in the breast cancer database, and 32.80% in the prostate cancer database. Therefore, the proposed algorithm is able to identify a small set of genes containing information in a way choose to increase the classification accuracy. Our proposed solution is used for data classification, which also improves classification accuracy. This is possible because the MOPSO model removes redundancy and reduces the number of redundant and redundant genes by considering how genes are correlated with each other.

An accurate prediction of the probability density function (PDF) of the mixture fraction is crucial to the prediction of combustion since mixing plays an important role in turbulent non-premixed and partially premixed flames. This work provides an assessment of the large-eddy simulation (LES)/filtered density function (FDF) method for the prediction of the PDF of the mixture fraction. The advantage of the LES/FDF method is that it provides the full predictions of the statistical distribution of scalars including the mixture fraction. The predictive accuracy of the method for the PDF is yet to be fully validated. Assessing the prediction of the PDF of the mixture fraction, a conserved scalar, is an important starting point. The Sydney/Sandia inhomogeneous inlet jet flame is used as a test case. A quick comparison shows that the LES/FDF predicted PDF shapes of the mixture fraction deviate significantly from the commonly presumed Beta-PDF as well as from the experimental data in the flame. To examine the source of the discrepancy, we clarify the different PDF definitions used in the comparison among the predictions, measurements, and presumed shape PDFs. The discrepancy observed from the comparison is largely reconciled by clarifying the difference between the PDFs that are examined. The PDF of the resolved mixture fraction is shown to be close to the Beta-PDF in both the measurements and predictions, while the PDF directly deduced from the LES/FDF particles deviates significantly from the Beta-PDF. A multimodal PDF analysis and a pseudo convergence analysis are conducted to provide plausible evidence to support the predicted multimodal PDF shapes. The sub-filter scale FDF is shown to be close to the Beta-PDF too through the construction of a synthesised PDF, which supports the common presumed Beta-PDF assumption used in the presumed PDF methods when combined with LES.

The naive Bayesian classifier provides a simple and effective approach to classifier learning, but its attribute independence assumption is often violated in the real world. A number of approaches have sought to alleviate this problem. A Bayesian tree learning algorithm builds a decision tree, and generates a local naive Bayesian classifier at each leaf. The tests leading to a leaf can alleviate attribute inter-dependencies for the local naive Bayesian classifier. However, Bayesian tree learning still suffers from the small disjunct problem of tree learning. While inferred Bayesian trees demonstrate low average prediction error rates, there is reason to believe that error rates will be higher for those leaves with few training examples. This paper proposes the application of lazy learning techniques to Bayesian tree induction and presents the resulting lazy Bayesian rule learning algorithm, called LBR. This algorithm can be justified by a variant of Bayes theorem which supports a weaker conditional attribute independence assumption than is required by naive Bayes. For each test example, it builds a most appropriate rule with a local naive Bayesian classifier as its consequent. It is demonstrated that the computational requirements of LBR are reasonable in a wide cross-section of natural domains. Experiments with these domains show that, on average, this new algorithm obtains lower error rates significantly more often than the reverse in comparison to a naive Bayesian classifier, C4.5, a Bayesian tree learning algorithm, a constructive Bayesian classifier that eliminates attributes and constructs new attributes using Cartesian products of existing nominal attributes, and a lazy decision tree learning algorithm. It also outperforms, although the result is not statistically significant, a selective naive Bayesian classifier.

Two new algorithms for hydrometeor classification using polarimetric radar observations are developed based on prototypes derived by applying clustering techniques (Part I of this two-part paper). Each prototype is defined as a probability distribution of the polarimetric variables and ambient temperature corresponding to a hydrometeor type. The first algorithm is a maximum prototype likelihood classifier that uses all prototypes attributed to the different hydrometeor types in Part I. The hydrometeor type is assigned as the prototype with the highest likelihood when comparing the polarimetric variables and temperature with each prototype. The second algorithm is a Bayesian classifier that uses the probability density functions (PDFs) as derived from the prototype set associated with the identical hydrometeor type. The posteriori probability in the Bayesian method is calculated from a combination of the PDFs and the prior probability, the maximum of which corresponds to the most likely hydrometeor type. The respective merits of the two techniques are discussed. The two classifiers are applied to CP-2 S-band radar observations of two hailstorms that occurred between 16 and 20 November 2008, including the so-called Gap storm, which produced a devastating microburst and large hail at the ground. Results from the classifiers are compared with those derived using the well-established National Center for Atmospheric Research fuzzy logic classifier. In general, good agreement is found, yielding overall confidence in the robustness of the new classifiers. However, large differences are found for the melting ice and ice crystal categories, which will need to be studied further.