Likelihood Densities Research Articles

Technical diagnostic system in the maintenance of turbomachinery for ammonia synthesis in the process industries

Technical maintenance of machines and equipment in processing industry requires elaborate technical diagnostics systems to recognize the current state and forecast their future state. Creating such a system is a complex task due to multiple factors, with aging in aggressive exploitation environment being an important one. Statistical pattern recognition systems are very suitable to solve problems of technical diagnostics as they produce quantitative estimates of the states. We present the use of a hybrid Bayesian pattern recognition classifier that utilizes statistical and fuzzy paradigms and expresses the measurement information with four types of features (discrete, pseudo-discrete, multi-normal and independent continuous). It uses frequentist and subjective information (from training samples and expert opinion respectively) to identify the unknown parameters of the conditional likelihood density functions of each technical state. We discuss possible sources to collect learning information, and different methods to represent it. The classifier uses three different methods for parameter estimation of the conditional likelihood densities using data fusion. The classification is realised as a discriminant non-linear machine, which incorporates fuzzy approaches at different levels. We develop a novel algorithm for fault prediction without dynamic learning with four possible types of answers. A detailed example of technical diagnostics system for classification and prediction of states of turbomachinery for ammonia synthesis is presented. For the journal bearing diagnostics, we introduce modification of the hybrid Bayesian classifier using pseudo-priors to incorporate rule-based knowledge and improve the classification.

CERENKOV2: improved detection of functional noncoding SNPs using data-space geometric features

BackgroundWe previously reported on CERENKOV, an approach for identifying regulatory single nucleotide polymorphisms (rSNPs) that is based on 246 annotation features. CERENKOV uses the xgboost classifier and is designed to be used to find causal noncoding SNPs in loci identified by genome-wide association studies (GWAS). We reported that CERENKOV has state-of-the-art performance (by two traditional measures and a novel GWAS-oriented measure, AVGRANK) in a comparison to nine other tools for identifying functional noncoding SNPs, using a comprehensive reference SNP set (OSU17, 15,331 SNPs). Given that SNPs are grouped within loci in the reference SNP set and given the importance of the data-space manifold geometry for machine-learning model selection, we hypothesized that within-locus inter-SNP distances would have class-based distributional biases that could be exploited to improve rSNP recognition accuracy. We thus defined an intralocus SNP “radius” as the average data-space distance from a SNP to the other intralocus neighbors, and explored radius likelihoods for five distance measures.ResultsWe expanded the set of reference SNPs to 39,083 (the OSU18 set) and extracted CERENKOV SNP feature data. We computed radius empirical likelihoods and likelihood densities for rSNPs and control SNPs, and found significant likelihood differences between rSNPs and control SNPs. We fit parametric models of likelihood distributions for five different distance measures to obtain ten log-likelihood features that we combined with the 248-dimensional CERENKOV feature matrix. On the OSU18 SNP set, we measured the classification accuracy of CERENKOV with and without the new distance-based features, and found that the addition of distance-based features significantly improves rSNP recognition performance as measured by AUPVR, AUROC, and AVGRANK. Along with feature data for the OSU18 set, the software code for extracting the base feature matrix, estimating ten distance-based likelihood ratio features, and scoring candidate causal SNPs, are released as open-source software CERENKOV2.ConclusionsAccounting for the locus-specific geometry of SNPs in data-space significantly improved the accuracy with which noncoding rSNPs can be computationally identified.

Sequential Bayesian Analysis of Multivariate Count Data

We develop a new class of dynamic multivariate Poisson count models that allow for fast online updating. We refer to this class as multivariate Poisson-scaled beta (MPSB) models. The MPSB model allows for serial dependence in count data as well as dependence with a random common environment across time series. Notable features of our model are analytic forms for state propagation, predictive likelihood densities, and sequential updating via sufficient statistics for the static model parameters. Our approach leads to a fully adapted particle learning algorithm and a new class of predictive likelihoods and marginal distributions which we refer to as the (dynamic) multivariate confluent hyper-geometric negative binomial distribution (MCHG-NB) and the dynamic multivariate negative binomial (DMNB) distribution, respectively. To illustrate our methodology, we use a simulation study and empirical data on weekly consumer non-durable goods demand.

Beyond the Model Limit: Parameter Inference Across Scales

In multiscale studies of emergent phenomena, a common approach is to define a microscopic scale generative model and subsequently, by passing to a diffusion limit, to derive a mesoscopic or macroscopic model via a homogenization argument. Microscopic models are often inherently stochastic, while the diffusion limit model may represent distributions or mean field quantities. A canonical example of this type of limiting process is the classical diffusion equation as a limit of Brownian random motion. Being typically based on ordinary or partial differential equations formalism, large scale models are more amenable to inverse problems, where the model parameters are estimated from indirect observations. Due to the intrinsic ill-posed nature of inverse problems, the estimation of the parameters of large scale models may be itself a significant challenge. In some multiscale investigations, the quantities of primary interest are not those characterizing the large scale model, but rather the parameters of the associated microscopic model. The latter are sometimes related to our understanding of the processes that are described by the generative models. In many cases, there is no direct connection between the small scale parameters and the large scale parameters describing the aggregate effects of the underlying processes. Moreover, estimating the unknown parameters of a microscopic, stochastic model from the large scale observations poses a number of challenges, and requires the development of new methodological approaches. In the Bayesian statistical framework, stochastic forward models often lead to intractable likelihood densities, making standard statistical computations a challenge. Such models are addressed by approximate Bayesian computing (ABC). In this paper we propose an alternative approach combining Bayesian statistics and particle techniques for inference beyond the limits of model scales. The viability of the approach is demonstrated on three computed examples describing diffusion, chemical kinetics, and cell culture assay, and a connection with existing ABC methods is discussed.

Energy-based active contour method for image segmentation

The level set methods have given effective structures to medical image analysis. Nonetheless, to acquire exact limits of the objects, particularly when they have feeble edges or inhomogeneous forces, is still an extremely difficult undertaking. It is found that existing level set methodologies neglect to fragment the images with powerless edges. The hazy edges and inhomogeneous powers cause instability for segmentation. In this paper, a novel energy based level set approach is proposed in which the energy capacity is defined by contrast between the real and assessed likelihood densities of the powers and partial differential equation is determined for finding the base of the vital work. The proposed approach has been tried on medical images and find the genuine protest limits, low difference, and inhomogeneous forces. The technique determines profitable advantages like computerisation, invariance of force inhomogeneity and precise medical image portions.

Energy-based active contour method for image segmentation

The level set methods have given effective structures to medical image analysis. Nonetheless, to acquire exact limits of the objects, particularly when they have feeble edges or inhomogeneous forces, is still an extremely difficult undertaking. It is found that existing level set methodologies neglect to fragment the images with powerless edges. The hazy edges and inhomogeneous powers cause instability for segmentation. In this paper, a novel energy based level set approach is proposed in which the energy capacity is defined by contrast between the real and assessed likelihood densities of the powers and partial differential equation is determined for finding the base of the vital work. The proposed approach has been tried on medical images and find the genuine protest limits, low difference, and inhomogeneous forces. The technique determines profitable advantages like computerisation, invariance of force inhomogeneity and precise medical image portions.

Triply fuzzy function approximation for hierarchical Bayesian inference

We prove that three independent fuzzy systems can uniformly approximate Bayesian posterior probability density functions by approximating the prior and likelihood probability densities as well as the hyperprior probability densities that underly the priors. This triply fuzzy function approximation extends the recent theorem for uniformly approximating the posterior density by approximating just the prior and likelihood densities. This approximation allows users to state priors and hyper-priors in words or rules as well as to adapt them from sample data. A fuzzy system with just two rules can exactly represent common closed-form probability densities so long as they are bounded. The function approximators can also be neural networks or any other type of uniform function approximator. Iterative fuzzy Bayesian inference can lead to rule explosion. We prove that conjugacy in the if-part set functions for prior, hyperprior, and likelihood fuzzy approximators reduces rule explosion. We also prove that a type of semi-conjugacy of if-part set functions for those fuzzy approximators results in fewer parameters in the fuzzy posterior approximator.

Bayesian Inference With Adaptive Fuzzy Priors and Likelihoods

Fuzzy rule-based systems can approximate prior and likelihood probabilities in Bayesian inference and thereby approximate posterior probabilities. This fuzzy approximation technique allows users to apply a much wider and more flexible range of prior and likelihood probability density functions than found in most Bayesian inference schemes. The technique does not restrict the user to the few known closed-form conjugacy relations between the prior and likelihood. It allows the user in many cases to describe the densities with words and just two rules can absorb any bounded closed-form probability density directly into the rulebase. Learning algorithms can tune the expert rules as well as grow them from sample data. The learning laws and fuzzy approximators have a tractable form because of the convex-sum structure of additive fuzzy systems. This convex-sum structure carries over to the fuzzy posterior approximator. We prove a uniform approximation theorem for Bayesian posteriors: An additive fuzzy posterior uniformly approximates the posterior probability density if the prior or likelihood densities are continuous and bounded and if separate additive fuzzy systems approximate the prior and likelihood densities. Simulations demonstrate this fuzzy approximation of priors and posteriors for the three most common conjugate priors (as when a beta prior combines with a binomial likelihood to give a beta posterior). Adaptive fuzzy systems can also approximate non-conjugate priors and likelihoods as well as approximate hyperpriors in hierarchical Bayesian inference. The number of fuzzy rules can grow exponentially in iterative Bayesian inference if the previous posterior approximator becomes the new prior approximator.