Highest Probability Density Research Articles

An active failure-pursuing Kriging modeling method for time-dependent reliability analysis

Abstract Some time-dependent reliability analysis methods use surrogate models to approximate the implicit limit state functions of complex systems. However, the performance of these methods is usually affected by the situations that the used models are not accurate and some samples have no significant contribution to the accuracy improvement. To construct a more suitable model for reliability analysis, this work proposes an active failure-pursuing Kriging modeling method to identify the most valuable samples for improving the accuracy of the predicted failure probability. On the one hand, a global predicted failure probability error index calculated through the real-time reliability result is proposed to pursue the sensitive sample and the corresponding local region that is most likely to maximize the improvement of the accuracy of the reliability result. A fault-tolerant scheme is further applied to ensure the accuracy of the failure-pursuing process. On the other hand, the correlation-based screening and space partition strategy is developed to describe the local regions and avoid the clustering of samples. In each iteration, the Kriging model is updated with the exploitation of new sample from the local regions around the sensitive samples. Additionally, an equivalent stochastic process transformation is developed to form a uniform high probability density sampling space. The results of three cases demonstrate the efficiency, accuracy and stability of the proposed method.

Estimation of reliability of multicomponent stress-strength inverted exponentiated Rayleigh model

ABSTRACTIn this paper, we consider the estimation of the multicomponent reliability by assuming the inverted exponentiated Rayleigh distribution. Both stress and strength are assumed to have an inverted exponentiated Rayleigh distribution with common scale parameter. The random variable representing the stress experienced by the system and representing the strength of system available to overcome the stress. The system works flawlessly only if at least out of strength variables exceed the random stress. The multicomponent reliability of the system is given by . We estimate by using frequentist and Bayesian approaches. Bayes estimates of have been obtained by using Markov Chain Monte Carlo methods since joint posteriors of the parameters does not have the explicit forms. We also construct asymptotic and highest probability density credible intervals for . The behavior of the proposed estimators is studied on the basis of estimated risks through Monte Carlo simulations. Finally, a data set is analyzed for illustrative purposes.Abbreviations: PDF: Probability Density Function; CDF: Cumulative Density Function; IER: Inverted Exponentiated Rayleigh; MLE: Maximum likelihood estimators; HPD: Highest Posterior Density; UBT: Upside down Bathtub; HNC: Head and Neck Cancer data; MCMC: Monte-Carlo Markov Chains; CP: Coverage Probability; KS: Kolmogorov - Smirnov.

Balanced design for the feasible super rocket fuels: A first-principle study on gauche CHN7 and CHN3

On the basis of the framework of cubic gauche nitrogen (cg-N), six one-eighth methanetriyl groups (>CH-) substitutes and fifteen one-fourth >CH- substitutes were optimized using the first-principle calculations based on density functional theory (DFT). Both one-eighth and one-fourth substitutes still keep the gauche structures with the simple formula CHN7 and CHN3, respectively. The most thermodynamic stable gauche CHN7 and CHN3 are P21 qtg-C2H2N14 I and P21 qtg-C4H4N12 III, respectively. No probability density of C-C single bonds and high probability densities of C-N-C structures were found in the two substitutes. Although gauche CHN7 and CHN3 lose energy density in contrast to cg-N, they win kinetic stability and combustion temperature (Tc). Thus, they are more feasible than cg-N, and more effective than the traditional rocket fuels.

Discrimination of seismic sources in an underground mine using full waveform inversion

To discriminate the type of the induced seismicity in the underground mine, full waveform inversion and statistical methods were used to investigate the different microseismic source mechanisms in a more quantitative way. To eliminate possible effects caused by specific configuration of monitoring network, potential error in source location and wave propagation mismodelling, Jackknife resampling was used to obtain the probability density functions of inversion results and the moment tensor uncertainties. Firstly, the expected prior probability functions for mining blast, cavity collapse, fault slip, and tensional failure were defined, which are related to the percentage of the double couple, the compensated linear vector dipole, and the isotropic components. Secondly, the likelihood of a given candidate event to a certain source model was calculated, and the source type was determined according to the moment tensor decomposition of the case with the highest probability density. Tests with synthetic datasets were performed to evaluate the stability of the inversion in case of poor data quality and inaccurate source location. The calculated results with noise levels from 0% to 20% are all clustered closely around the initial source in the source type diagram, which indicates the reliability of the derived focal mechanism. The discrimination method of seismic sources in underground mine using full waveform inversion was verified by 8 events of field investigations in the Yongshaba Phosphate Mine, China. Results show that events 1, 5, 6 and 8 are tagged as fault slip events. Their probability of fault slip events are 0.53, 0.57, 0.37 and 0.60 respectively. The events 2, 3 and 7 are recognized as the cavity collapse events corresponding the probability 0.46, 0.51 and 0.50, respectively. The mechanism of the event 4 is recognized as a tensional failure with the probability 0.57.

Re‐Weighting Firefly Samples for Improved Finite‐Sample Monte Carlo Estimates

AbstractSamples with high contribution but low probability density, often called fireflies, occur in all practical Monte Carlo estimators and are part of computing unbiased estimates. For finite‐sample estimates, however, they can lead to excessive variance. Rejecting all samples classified as outliers, as suggested in previous work, leads to estimates that are too low and can cause undesirable artefacts. In this paper, we show how samples can be re‐weighted depending on their contribution and sampling frequency such that the finite‐sample estimate gets closer to the correct expected value and the variance can be controlled. For this, we first derive a theory for how samples should ideally be re‐weighted and that this would require the probability density function of the optimal sampling strategy. As this probability density function is generally unknown, we show how the discrepancy between the optimal and the actual sampling strategy can be estimated and used for re‐weighting in practice. We describe an efficient algorithm that allows for the necessary analysis of per‐pixel sample distributions in the context of Monte Carlo rendering without storing any individual samples, with only minimal changes to the rendering algorithm. It causes negligible runtime overhead, works in constant memory and is well suited for parallel and progressive rendering. The re‐weighting runs as a fast post‐process, can be controlled interactively and our approach is non‐destructive in that the unbiased result can be reconstructed at any time.

Bayesian filtering based on solving the Fokker-Planck equation

PurposeThis paper aims to propose Bayesian filtering based on solving the Fokker–Planck equation, to improve the accuracy of filtering in non-Gauss case. Nonlinear filtering plays an important role in many science and engineering fields for estimating the state of dynamic system, but the existing filtering algorithms are mainly used for solving the problem of Gauss system.Design/methodology/approachUnder the Bayesian framework, the time update of this filtering is based on solving Fokker–Planck equation, while the measurement update uses the Bayes formula directly. Therefore, this novel algorithm can be applied to nonlinear, non-Gaussian estimation. To reduce the computational complexity due to standard meshing, an adaptive meshing algorithm proposed which includes the coarse meshing, significant domain determination that is generated using extended Kalman filtering and Chebyshev’s inequality theorem, and value assignment for significant domain. Simulations are conducted on a reentry body tracking problem to demonstrate the effectiveness of this novel algorithm.FindingsIn this way, finer grid points can be placed in the regions with high conditional probability density, while the grid points with low conditional probability density can be neglected. The simulation results indicate that the novel algorithm can reduce the computational burden significantly compared to the standard meshing, while achieving similar accuracy.Practical implicationsA novel Bayesian filtering based on solving the Fokker–Planck equation using adaptive meshing is proposed, and the simulations show that algorithm can reduce the computational burden significantly compared to the standard meshing, while achieving similar accuracy.Originality/valueA novel nonlinear filtering based on solving the Fokker–Planck equation is proposed. The novel algorithm is suitable for non-Gauss system, and can achieve similar accuracy compared to the standard meshing with the significant reduction of computational burden.

Uncertainty Quantification of geochemical and mechanical compaction in layered sedimentary basins

In this work we propose an Uncertainty Quantification methodology for sedimentary basins evolution under mechanical and geochemical compaction processes, which we model as a coupled, time-dependent, non-linear, monodimensional (depth-only) system of PDEs with uncertain parameters. While in previous works (Formaggia et al. 2013, Porta et al. 2014) we assumed a simplified depositional history with only one material, in this work we consider multi-layered basins, in which each layer is characterized by a different material, and hence by different properties. This setting requires several improvements with respect to our earlier works, both concerning the deterministic solver and the stochastic discretization. On the deterministic side, we replace the previous fixed-point iterative solver with a more efficient Newton solver at each step of the time-discretization. On the stochastic side, the multi-layered structure gives rise to discontinuities in the dependence of the state variables on the uncertain parameters, that need an appropriate treatment for surrogate modeling techniques, such as sparse grids, to be effective. We propose an innovative methodology to this end which relies on a change of coordinate system to align the discontinuities of the target function within the random parameter space. The reference coordinate system is built upon exploiting physical features of the problem at hand. We employ the fact that the locations of the material interfaces display a smooth dependence on the random parameters and are therefore amenable to sparse grid polynomial approximations. We showcase the capabilities of our numerical methodologies through two synthetic test cases. In particular, we show that our methodology reproduces with high accuracy multi-modal probability density functions displayed by target state variables (e.g., porosity).

Tracing hepatitis B virus (HBV) genotype B5 (formerly B6) evolutionary history in the circumpolar Arctic through phylogeographic modelling.

BackgroundIndigenous populations of the circumpolar Arctic are considered to be endemically infected (>2% prevalence) with hepatitis B virus (HBV), with subgenotype B5 (formerly B6) unique to these populations. The distinctive properties of HBV/B5, including high nucleotide diversity yet no significant liver disease, suggest virus adaptation through long-term host-pathogen association.MethodsTo investigate the origin and evolutionary spread of HBV/B5 into the circumpolar Arctic, fifty-seven partial and full genome sequences from Alaska, Canada and Greenland, having known location and sampling dates spanning 40 years, were phylogeographically investigated by Bayesian analysis (BEAST 2) using a reversible-jump-based substitution model and a clock rate estimated at 4.1 × 10−5 substitutions/site/year.ResultsFollowing an initial divergence from an Asian viral ancestor approximately 1954 years before present (YBP; 95% highest probability density interval [1188, 2901]), HBV/B5 coalescence occurred almost 1000 years later. Surprisingly, the HBV/B5 ancestor appears to locate first to Greenland in a rapid coastal route progression based on the landscape aware geographic model, with subsequent B5 evolution and spread westward. Bayesian skyline plot analysis demonstrated an HBV/B5 population expansion occurring approximately 400 YBP, coinciding with the disruption of the Neo-Eskimo Thule culture into more heterogeneous and regionally distinct Inuit populations throughout the North American Arctic.DiscussionHBV/B5 origin and spread appears to occur coincident with the movement of Neo-Eskimo (Inuit) populations within the past 1000 years, further supporting the hypothesis of HBV/host co-expansion, and illustrating the concept of host-pathogen adaptation and balance.

Fault detection and diagnosis of rotating machinery using modified particle filter

In order to effectively monitor condition and detect fault types of high nonlinear system, and extract the features of system state under strong noise background, this paper proposes a novel fault detection and diagnosis (FDD) method based on modified particle filter (PF). The artificial neural network is incorporated in PF for adaptively adjusting weight of particle. In the modified PF, the large weight particles are split into several small weight particles, the particles with smaller weight is adjusted by using artificial neural network. By which the particles in the low probability density region are adjusted to the high probability density region, and the problem of particle leanness is solved effectively. Moreover, this paper also uses time-varying auto regressive (TVAR) and Akaike information criterion (AIC) methods to establish state space model for state estimation. Finally, the proposed method is implemented for fault diagnosis on a roller bearing. Good results are obtained, and the bearing faults, such as the outer race, the inner race and the roller element defects, have been effectively discriminated.

Distance based resampling of imbalanced classes: With an application example of speech quality assessment

This paper presents a new general methodological approach to imbalanced learning as one of the challenging problems in pattern classification. The presented method is founded on maximization of the sample entropy. The method involves detection of distributive properties of ideally balanced regular lattice sample and acceptable transfer of these properties to an arbitrary imbalanced sample increasing its representativeness. The proposed procedure assumes undersampling applied on areas of high probability density in the sample space combined with oversampling in the areas of low density. The main achievement of this method is the increased sample class entropy which reduces the inductive learner’s tendency to favor prominent class, or cluster. In addition to class balancing, this method can be useful for function approximation, clustering, and sample dimension reduction. The high degree of generality of the method implies its applicability on data of various complexity and imbalance. The presented theoretical foundation of the method was verified on a set of proper synthetic samples. The method’s practical usability is confirmed by a comparative classification of a large set of databases including speech signal samples.

A Study of the Dynamic Relation between Physiological Changes and Spontaneous Expressions

Recent progress in Affective Computing (AC) has enabled integration of physiological cues and spontaneous expressions to reveal a subject’s emotional state. Due to the lack of an effective technique for evaluating multimodal correlations, experience and intuition play a main role in present AC studies when fusing affective cues or modalities, resulting in unexpected outcomes. This study seeks to demonstrate a dynamic correlation between two such affective cues, physiological changes and spontaneous expressions, which were obtained by a combination of stereo vision based tracking and imaging photoplethysmography (iPPG), with a designed protocol involving 20 healthy subjects. The two cues obtained were sampled into a Statistical Association Space (SAS) to evaluate their dynamic correlation. It is found that the probability densities in the SAS increase as the peaks in two cues are approached. Also the complex form of the high probability density region in the SAS suggests a nonlinear correlation between two cues. Finally the cumulative distribution on the zero time-difference surface is found to be small (<0.047) demonstrating a lack of simultaneity. These results show that the two cues have a close interrelation, that is both asynchronous and nonlinear, in which a peak of one cue heralds a peak in the other.

Was Kaposi's sarcoma-associated herpesvirus introduced into China via the ancient Silk Road? An evolutionary perspective.

Kaposi's sarcoma-associated herpesvirus (KSHV) has become widely dispersed worldwide since it was first reported in 1994, but the seroprevalence of KSHV varies geographically. KSHV is relatively ubiquitous in Mediterranean areas and the Xinjiang Uygur Autonomous Region, China. The origin of KSHV has long been puzzling. In the present study, we collected and analysed 154 KSHV ORF-K1 sequences obtained from samples originating from Xinjiang, Italy, Greece, Iran and southern Siberia using Bayesian evolutionary analysis in BEAST to test the hypothesis that KSHV was introduced into Xinjiang via the ancient Silk Road. According to the phylogenetic analysis, 72 sequences were subtype A and 82 subtype C, with C2 (n = 56) being the predominant subtype. The times to the most recent common ancestors (tMRCAs) of KSHV were 29,872 years (95% highest probability density [HPD], 26,851-32,760 years) for all analysed sequences and 2037 years (95% HPD, 1843-2229 years) for Xinjiang sequences in particular. The tMRCA of Xinjiang KSHV was exactly matched with the time period of the ancient Silk Road approximately two thousand years ago. This route began in Chang'an, the capital of the Han dynasty of China, and crossed Central Asia, ending in the Roman Empire. The evolution rate of KSHV was slow, with 3.44 × 10-6 substitutions per site per year (95% HPD, 2.26 × 10-6 to 4.71 × 10-6), although 11 codons were discovered to be under positive selection pressure. The geographic distances from Italy to Iran and Xinjiang are more than 4000 and 7000 kilometres, respectively, but no explicit relationship between genetic distance and geographic distance was detected.

Selected aspects of prior and likelihood information for a Bayesian classifier in a road safety analysis

The development of the Bayesian logistic regression model classifying the road accident severity is discussed. The already exploited informative priors (method of moments, maximum likelihood estimation, and two-stage Bayesian updating), along with the original idea of a Boot prior proposal, are investigated when no expert opinion has been available. In addition, two possible approaches to updating the priors, in the form of unbalanced and balanced training data sets, are presented. The obtained logistic Bayesian models are assessed on the basis of a deviance information criterion (DIC), highest probability density (HPD) intervals, and coefficients of variation estimated for the model parameters. The verification of the model accuracy has been based on sensitivity, specificity and the harmonic mean of sensitivity and specificity, all calculated from a test data set. The models obtained from the balanced training data set have a better classification quality than the ones obtained from the unbalanced training data set. The two-stage Bayesian updating prior model and the Boot prior model, both identified with the use of the balanced training data set, outperform the non-informative, method of moments, and maximum likelihood estimation prior models. It is important to note that one should be careful when interpreting the parameters since different priors can lead to different models.

Nonparametric estimation of simplified vine copula models: comparison of methods

Abstract In the last decade, simplified vine copula models have been an active area of research. They build a high dimensional probability density from the product of marginals densities and bivariate copula densities. Besides parametric models, several approaches to nonparametric estimation of vine copulas have been proposed. In this article, we extend these approaches and compare them in an extensive simulation study and a real data application. We identify several factors driving the relative performance of the estimators. The most important one is the strength of dependence. No method was found to be uniformly better than all others. Overall, the kernel estimators performed best, but do worse than penalized B-spline estimators when there is weak dependence and no tail dependence.

A Severity Function Approach to Scenario Selection

The function approach (abbreviated SFA) is a method of selecting adverse from a multivariate density. It requires the scenario user (e.g. an agency that runs banking sector stress tests) to specify a severity function, which maps candidate into a scalar metric. The higher the value of this metric, the more harmful a scenario is. In selecting a scenario the SFA proceeds as follows: First, it isolates a set of equally severe scenario candidates. This set is determined by the condition that more severe only occur with some user-specified probability. Second, from this set it selects the candidate with the highest probability density, i.e. the most plausible scenario. The approach hence operationalizes the mantra that scenarios should be severe yet plausible.

Understanding the evolution and spread of chikungunya virus in the Americas using complete genome sequences.

Local transmission of chikungunya virus (CHIKV) was first detected in the Americas in December 2013, after which it spread rapidly throughout the Caribbean islands and American mainland, causing a major chikungunya fever epidemic. Previous phylogenetic analysis of CHIKV from a limited number of countries in the Americas suggests that an Asian genotype strain was responsible, except in Brazil where both Asian and East/Central/South African (ECSA) lineage strains were detected. In this study, we sequenced thirty-three complete CHIKV genomes from viruses isolated in 2014 from fourteen Caribbean islands, the Bahamas and two mainland countries in the Americas. Phylogenetic analyses confirmed that they all belonged to the Asian genotype and clustered together with other Caribbean and mainland sequences isolated during the American outbreak, forming an ‘Asian/American’ lineage defined by two amino acid substitutions, E2 V368A and 6K L20M, and divided into two well-supported clades. This lineage is estimated to be evolving at a mean rate of 5 × 10−4 substitutions per site per year (95% higher probability density, 2.9–7.9 × 10−4) and to have arisen from an ancestor introduced to the Caribbean (most likely from Oceania) in about March 2013, 9 months prior to the first report of CHIKV in the Americas. Estimation of evolutionary rates for individual gene regions and selection analyses indicate that (in contrast to the Indian Ocean Lineage that emerged from the ECSA genotype followed by adaptive evolution and with a significantly higher substitution rate) the evolutionary dynamics of the Asian/American lineage are very similar to the rest of the Asian genotype and natural selection does not appear to have played a major role in its emergence. However, several codon sites with evidence of positive selection were identified within the non-structural regions of Asian genotype sequences outside of the Asian/American lineage.

Fuzzy Grey Prediction-Based Particle Filter for Object Tracking

A particle filter is a powerful tool for object tracking based on sequential Monte Carlo methods under a Bayesian estimation framework. A major challenge for a particle filter in object tracking is how to allocate particles to a high-probability density area. A particle filter does not take into account the historical prior information on the generation of the proposal distribution and, thus, it cannot approximate posterior density well. Therefore, a new fuzzy grey prediction-based particle filter (called FuzzyGP-PF) for object tracking is proposed in this paper. First, a new prediction model which was based on fuzzy mathematics theory and grey system theory was established, coined the Fuzzy-Grey-Prediction (FGP) model. Then, the history state sequence is utilized as prior information to predict and sample a part of particles for generating the proposal distribution in the particle filter. Simulations are conducted in the context of two typical maneuvering motion scenarios and the results indicate that the proposed FuzzyGP-PF algorithm can exhibit better overall performance in object tracking.

Reliability analysis of masked data in adaptive step-stress partially accelerated lifetime tests with progressive removal

ABSTRACTBy combining the progressive hybrid censoring with the step-stress partially accelerated lifetime test, we propose an adaptive step-stress partially accelerated lifetime test, which allows random changing of the number of step-stress levels according to the pre-fixed censoring number and time points. Thus, the time expenditure and economic cost of the test will be reduced greatly. Based on the Lindley-distributed tampered failure rate (TFR) model with masked system lifetime data, the BFGS method is introduced in the expectation maximization (EM) algorithm to obtain the maximum likelihood estimation (MLE), which overcomes the difficulties of the vague maximization procedure in the M-step. Asymptotic confidence intervals of components' distribution parameters are also investigated according to the missing information principle. As comparison, the Bayesian estimation and the highest probability density (HPD) credible intervals are obtained by using adaptive rejection sampling. Furthermore, the reliability of the system and components are estimated at a specified time under usual and severe operating conditions. Finally, a numerical simulation example is presented to illustrate the performance of our proposed method.

Tales of dracula ants: the evolutionary history of the ant subfamily Amblyoponinae (Hymenoptera: Formicidae)

AbstractThe ants in the subfamily Amblyoponinae are an old, relictual group with an unusual suite of morphological and behavioural features. Adult workers pierce the integument of their larvae to imbibe haemolymph, earning them the vernacular name ‘dracula ants’. We investigate the phylogeny of this group with a data set based on 54 ingroup taxa, 23 outgroups and 11 nuclear gene fragments (7.4 kb). We find that the genus Opamyrma has been misplaced in this subfamily: it is a member of the leptanilline clade and sister to all other extant Leptanillinae. Transfer of Opamyrma to Leptanillinae renders the Amblyoponinae monophyletic. The enigmatic Afrotropical genus Apomyrma is sister to all other amblyoponines, and the latter cleave into two distinct and well‐supported clades, here termed POA and XMMAS. The POA clade, containing Prionopelta, Onychomyrmex and Amblyopone, is well resolved internally, and its structure supports synonymy of the genus Concoctio under Prionopelta (syn.n.). The XMMAS clade comprises two well‐supported groups: (i) a predominantly Neotropical clade, for which we resurrect the genus name Fulakora (stat.r., stat.n.), with junior synonyms Paraprionopelta (syn.n.) and Ericapelta (syn.n.); and (ii) the remaining taxa, or ‘core XMMAS’, which are manifested in our study as a poorly resolved bush of about a dozen lineages, suggesting rapid radiation at the time of their origin. Most of these XMMAS lineages have been assigned to the catch‐all genus Stigmatomma, but the more distinctive elements have been treated as separate genera (Xymmer, Mystrium, Myopopone and Adetomyrma). Resolution of basal relationships in the core XMMAS clade and reconfiguration of ‘Stigmatomma’ to restore monophyly of all named genera will require more extensive genetic data and additional morphological analysis. However, the genus Bannapone can be synonymized under Stigmatomma (syn.n.) because it is embedded within a clade that contains S. denticulatum, the type species of Stigmatomma. Divergence dating analysis indicates that crown Amblyoponinae arose in the mid‐Cretaceous, about 107 Ma (95% highest probability density: 93–121 Ma). The POA and XMMAS clades have estimated crown ages of 47 and 73 Ma, respectively. The initial burst of diversification in the core XMMAS clade occurred in the Late Paleocene/Early Eocene (50–60 Ma). Ancestral range reconstruction suggests that amblyoponines originated in the Afrotropics, and dispersed to the Indo‐Malayan region and to the New World. During none of these dispersal events did the ants break out of their cryptobiotic lifestyle.

Understanding taxi travel patterns

Taxis play important roles in modern urban transportation systems, especially in mega cities. While providing necessary amenities, taxis also significantly contribute to traffic congestion, urban energy consumption, and air pollution. Understanding the travel patterns of taxis is thus important for addressing many urban sustainability challenges. Previous research has primarily focused on examining the statistical properties of passenger trips, which include only taxi trips occupied with passengers. However, unoccupied trips are also important for urban sustainability issues because they represent potential opportunities to improve the efficiency of the transportation system. Therefore, we need to understand the travel patterns of taxis as an integrated system, instead of focusing only on the occupied trips. In this study we examine GPS trajectory data of 11,880 taxis in Beijing, China for a period of three weeks. Our results show that taxi travel patterns share similar traits with travel patterns of individuals but also exhibit differences. Trip displacement distribution of taxi travels is statistically greater than the exponential distribution and smaller than the truncated power-law distribution. The distribution of short trips (less than 30 miles) can be best fitted with power-law while long trips follow exponential decay. We use radius of gyration to characterize individual taxi’s travel distance and find that it does not follow a truncated power-law as observed in previous studies. Spatial and temporal regularities exist in taxi travels. However, with increasing spatial coverage, taxi trips can exhibit dual high probability density centers.