Form Of Probability Distribution Research Articles

Monocular Depth Estimation with Augmented Ordinal Depth Relationships.

Most existing algorithms for depth estimation from single monocular images need large quantities of metric groundtruth depths for supervised learning. We show that relative depth can be an informative cue for metric depth estimation and can be easily obtained from vast stereo videos. Acquiring metric depths from stereo videos is sometimes impracticable due to the absence of camera parameters. In this paper, we propose to improve the performance of metric depth estimation with relative depths collected from stereo movie videos using existing stereo matching algorithm.We introduce a new "Relative Depth in Stereo" (RDIS) dataset densely labelled with relative depths. We first pretrain a ResNet model on our RDIS dataset. Then we finetune the model on RGB-D datasets with metric ground-truth depths. During our finetuning, we formulate depth estimation as a classification task. This re-formulation scheme enables us to obtain the confidence of a depth prediction in the form of probability distribution. With this confidence, we propose an information gain loss to make use of the predictions that are close to ground-truth. We evaluate our approach on both indoor and outdoor benchmark RGB-D datasets and achieve state-of-the-art performance.

CoDDA: A Flexible Copula-based Distribution Driven Analysis Framework for Large-Scale Multivariate Data.

CoDDA (Copula-based Distribution Driven Analysis) is a flexible framework for large-scale multivariate datasets. A common strategy to deal with large-scale scientific simulation data is to partition the simulation domain and create statistical data summaries. Instead of storing the high-resolution raw data from the simulation, storing the compact statistical data summaries results in reduced storage overhead and alleviated I/O bottleneck. Such summaries, often represented in the form of statistical probability distributions, can serve various post-hoc analysis and visualization tasks. However, for multivariate simulation data using standard multivariate distributions for creating data summaries is not feasible. They are either storage inefficient or are computationally expensive to be estimated in simulation time (in situ) for large number of variables. In this work, using copula functions, we propose a flexible multivariate distribution-based data modeling and analysis framework that offers significant data reduction and can be used in an in situ environment. The framework also facilitates in storing the associated spatial information along with the multivariate distributions in an efficient representation. Using the proposed multivariate data summaries, we perform various multivariate post-hoc analyses like query-driven visualization and sampling-based visualization. We evaluate our proposed method on multiple real-world multivariate scientific datasets. To demonstrate the efficacy of our framework in an in situ environment, we apply it on a large-scale flow simulation.

Robust Chance Constrained Power Allocation Scheme for Multiple Target Localization in Colocated MIMO Radar System

Taking into account the probabilistic uncertainty on the target radar cross section (RCS) parameter, a robust chance constrained power allocation (RCC-PA) scheme is presented for multiple target localization in colocated multiple-input multiple-output radar system. Such a system adopts a multibeam working mode, in which multiple simultaneous transmit beams are synthesized to illuminate multiple targets independently. We formulate the RCC-PA problem into a chance constrained programming model, where the total power consumption of the multiple beams is minimized to meet a specified multitarget localization accuracy requirement with high probability. Various target RCS fluctuation models have been discussed with different forms of probability distributions. We analytically show that the chance constrained programming problem for each RCS fluctuation model can equivalently be formulated as a deterministic convex optimization problem. Then, by formulating the Karush-Kuhn-Tuckers conditions, we transform the convex optimization problem into a nonlinear equation solving problem, and then solve it by using the bisection method. Simulation results show that our RCC-PA scheme can enhance the power utilization efficiency, and is more robust than the existing deterministic PA schemes.

A Bayesian Active Learning Experimental Design for Inferring Signaling Networks.

Machine learning methods for learning network structure are applied to quantitative proteomics experiments and reverse-engineer intracellular signal transduction networks. They provide insight into the rewiring of signaling within the context of a disease or a phenotype. To learn the causal patterns of influence between proteins in the network, the methods require experiments that include targeted interventions that fix the activity of specific proteins. However, the interventions are costly and add experimental complexity. We describe an active learning strategy for selecting optimal interventions. Our approach takes as inputs pathway databases and historic data sets, expresses them in form of prior probability distributions on network structures, and selects interventions that maximize their expected contribution to structure learning. Evaluations on simulated and real data show that the strategy reduces the detection error of validated edges as compared with an unguided choice of interventions and avoids redundant interventions, thereby increasing the effectiveness of the experiment.

An improved incipient fault detection method based on Kullback-Leibler divergence

This paper presents an improved incipient fault detection method based on Kullback-Leibler (KL) divergence under multivariate statistical analysis frame. Different from the traditional multivariate fault detection methods, this methodology can detect slight anomalous behaviors by comparing the online probability density function (PDF) online with the reference PDF obtained from large scale off-line data set. In the principal and residual subspaces obtained via PCA, a symmetric evaluation function is defined for both single variate and multivariate cases. The uniform form of probability distribution and fault detection thresholds associated with all eigenvalues are given. In addition, the robust performance is analyzed with respect to a wide range of Signal to Noise Ratio (SNR). Case studies are conducted with three types of incipient faults on a numerical example; combining with two nonlinear projections, the proposed scheme is successfully used for incipient fault detection in non-Gaussian electrical drive system. The results can demonstrate the superiority of the proposed method than several other methods.

Verification in the presence of observation errors: Bayesian point of view

Verification in the presence of observation errors is approached from the Bayesian point of view. Like data assimilation (DA), Bayesian verification is shown to have a robust foundation established by Bayesian inference. Together, DA and Bayesian verification form two difference levels of Bayesian inference. Evaluation of a model is equivalent to inference on the plausibility of this model given observations. Relative performances between different models are measured by ratios of posterior plausibilities, which becomes ratios of likelihoods in the case of no prior information. These ratios are called the Bayes factors and are the standard verification method in Bayesian model comparison. Since verification scores are used intensively in numerical weather prediction, the verification scores derived from likelihoods are proposed to replace the Bayes factors in Bayesian verification. With two requirements that the verification scores are both strictly proper and local, the logarithm score, i.e. log‐likelihood, and its linear transformation are shown to be the unique class.Log‐likelihoods in Bayesian verification are determined by the form of forecast probability distributions from models. The empirical form is preferable because of its flexibility in incorporating not only observation errors but also other uncertainties in observation biases or observation error variances into calculation to obtain closed forms for log‐likelihoods. When applied to observations with Gaussian errors, the logarithm score induces the weighted mean‐squared error which is non‐dimensional and can be used for both univariate and multivariate observations. The most interesting application of Bayesian verification is to offer a new explanation for rank histograms and quantify flatness of rank histograms by a metric which turns out to be the Kullback–Leibler divergence between the rank distribution observed in reality and a uniform rank distribution. It is worthy of note that the two very different metrics come from the logarithm score.

Modeling the Dynamics of Community Resilience to Coastal Hazards Using a Bayesian Network

Studies on how variables of community resilience to natural hazards interact as a system that affects the final resilience (i.e., their dynamical linkages) have rarely been conducted. Bayesian network (BN), which represents the interdependencies among variables in a graph while expressing the uncertainty in the form of probability distributions, offers an effective way to investigate the interactions among different resilience components and addresses the natural–human system as a whole. This article employs a BN to study the interdependencies of ten resilience variables and population change in the Lower Mississippi River Basin (LMRB) at the census block group scale. A genetic algorithm was used to identify an optimal BN where population change, a cumulative resilience indicator, was the target variable. The genetic algorithm yielded an optimized BN model with a cross-validation accuracy of 67 percent over a period of 906 generations. Six variables were found to have direct impacts on population change, including level of threat from coastal hazards, hazard damage, distance to coastline, employment rate, percentage of housing units built before 1970, and percentage of households with a female householder. The remaining four variables were indirect variables, including percentage agriculture land, percentage flood zone area, percentage owner-occupied house units, and population density. Each variable has a conditional probability table so that its impacts on the probability of population change can be evaluated as it propagates through the network. These probabilities could be used for scenario modeling to help inform policies to reduce vulnerability and enhance disaster resilience.

A Novel Multiview Topic Model to Compute Correlation of Heterogeneous Data

With fast development of Internet technologies and sensor techniques, it is much easier to acquire data from different sources in different dates and times. However, how to compute the correlation of those heterogeneous data is a big challenge for data mining and information retrieval. Here, data feature from one source is called as a view, and the multiview features denote the same data point. In the paper, hidden correlation of two-view features is proposed to construct a Heterogeneous (multiview) Topic Model (HTM). In particular, probabilistic topic model is utilized for different views as usually, generative models provide much richer features when handling high-dimensional data such as texts. Nevertheless, it is necessary to know the form of probability distribution for most existent probabilistic topic models, such as latent Dirichlet allocation. By avoiding the limitation of probabilistic topic model, the HTM is reduced to solving a non-negative matrix tri-factorization problem with certain constraints such that the proposed approach can be used in terms of an arbitrary model.

A stochastic MILP energy planning model incorporating power market dynamics

This paper presents an optimization-based methodological approach to address the problem of the optimal planning of a power system at an annual level in competitive and uncertain power markets. More specifically, a stochastic mixed integer linear programming model (MILP) has been developed, combining advanced optimization techniques with Monte Carlo method in order to deal with uncertainty issues. The main focus of the proposed framework is the dynamic formulation of the strategy followed by all market participants in volatile market conditions, as well as detailed economic assessment of the power system’s operation. The applicability of the proposed approach has been tested on a real case study of the interconnected Greek power system, quantifying in detail all the relevant technical and economic aspects of the system’s operation. The proposed work identifies in the form of probability distributions the optimal power generation mix, electricity trade at a regional level, carbon footprint, as well as detailed total supply cost composition, according to the assumed market structure. The paper demonstrates that the proposed optimization approach is able to provide important insights into the appropriate energy strategies designed by market participants, as well as on the strategic long-term decisions to be made by investors and/or policy makers at a national and/or regional level, underscoring potential risks and providing appropriate price signals on critical energy projects under real market operating conditions.

Impact of technical and economic uncertainties on the economic performance of a deep geothermal heat system

This paper presents a techno-economic analysis of a deep, direct use geothermal heat system in a conductive geological setting (Groningen, NE Netherlands). The model integrates the previously discussed uncertainties of the initial reservoir state, geological and operational conditions with the economic uncertainties. These uncertainties are incorporated in the form of probability distributions and 20,000 iterations of the model are performed over a project lifetime of 40 years. A combination of Ex-Ante and Ex-Post criteria are used to evaluate the economic performance of the system based on the Net Present Value (NPV), Levelised Cost of Heat (LCOH) and Expected Monetary Value (EMV). The sensitivity analysis highlights the load factor (effective flowrate) as the most important parameter for the economic performance and energy costs. However, the differences between the NPV and LCOH sensitivities highlight the importance of using both metrics for the economic performance of such systems. The presented project remains economically challenging, exhibiting a 50% probability of marginal revenues over its lifetime. Systematic insights are drawn with regard to potential improvements of technical and economic aspects of such geothermal heat systems.

Probability distribution of convection zone depth of chloride in concrete in a marine tidal environment

Based on a field experiment of concrete exposed to a marine tidal environment and according to measured chloride ingress data, diffusion coefficients of chloride ion in concrete after different exposure time are fitted by Fick-second law. Concrete with different types of admixture are tested in this paper, with water-cement ratios of 0.40, 0.45, 0.50, 0.55 and 0.60, respectively. Based on 270 group chloride ingress curves of test concrete, the convection zone depth of chloride and peak value of chloride concentration in concrete are acquired. According to chloride ingress curves of concrete with different water-cement ratio under the same exposure time, the probability distribution forms of convection zone depth of chloride are investigated by statistical test using the log-normal distribution, the normal distribution and the maximum value distribution, respectively. The statistical results show that the mean value of convection zone depths of chloride is in a range from 4mm to 6mmin this paper, disregarding the difference in exposure time, water-cement ratio and with or without the admixture in the specimens. The majority of convection zone depths of chloride in different exposure time and water-cement ratios, as well as the admixture, follow a Gumbel distribution, and the convection zone depth of chloride in total 270 specimens follows a Gumbel distribution with the mean value of 3.99mm and the standard deviation of 1.05mm. The exposure time, water-cement ratio and different admixture have negligible effect on the mean value and the probabilistic characteristic of convection zone depth of chloride, however, different admixture and lower water-cement ratio can significantly reduce the diffusion coefficients and peak values of chloride concentration in concrete.

確率分布母数の不確実さが確率論的破壊力学評価結果に与える影響の簡易評価手法の開発

Probabilistic fracture mechanics (PFM) analysis is an evaluation method for the structural integrity of components containing a crack, with considering the random variability of the input physical parameters, such as crack growth rate. The characteristics of the variability are described in the form of probability distribution, which is defined by probabilistic parameters such as mean and variance. Without sufficient information about the random variability, the parameter of the probability distribution may contain uncertainty, so that evaluated failure probability also contains uncertainty. Therefore, as the output of PFM analyses, not only the failure probability but also their uncertainty derived from the parameter uncertainty should be evaluated. In this paper, we describe the parameter uncertainty in the form of the interval of the parameter. We propose the simple estimation method for upper and lower bound of the interval of the PFM result derived from the above parameter interval. Additionally, we propose the uncertainty index that denotes the interval of the result derived from the interval of each parameter. These proposals are based on the first order reliability method (FORM). The proposed estimation method and the uncertainty index are validated through the evaluations, whose conditions are based on past evaluation study. At the first stage, accuracy of the evaluated result by FORM is validated through comparison between FORM and the directional simulation method. And then, the proposed methods are validated through the comparison with the result by FORM.

Tiered risk assessment of chemical pollution caused by military activities

<i>The methodology of environmental risk is becoming more common to assess the impact of chemical pollution on human beings and the environment, providing information for making environmental remediation decisions. This article examines the impact on human health chemicals that penetrated into river water as a result of an accident at a military ammunition depot. The river is the source of drinking water for the population. Assessing the impact of chemicals on the health of adults, adolescents and children is carried out in stages (tiers), from simple to complex. Assessment is carried out both for carcinogenic and non-carcinogenic substances. The first tier is executed by a deterministic method – a method in which all biological, chemical, physical, and environmental parameters are assumed to be constant and can be accurately specified. Deterministic methods commonly apply to either a “most likely” value for a parameter, or a conservative value. When the obtained values are insufficient for making the decision, the second tier of a risk assessment begins. The values in this case have the form of probability distributions that determine their variability. Processing the risk model with the help of the one-dimensional Monte Carlo method gives more accurate data in the form of risk distribution. However, the method does not consider the lack of knowledge about the values of input variables, so, at the third tier of a risk assessment, the two-dimensional Monte Carlo method is used. In this case, the specifi ed values of risk look like trend charts and indicate the limits of probability of risk for a certain percentage of the population.</i>

Statistical Characterization of the Mechanical Parameters of Intact Rock Under Triaxial Compression: An Experimental Proof of the Jinping Marble

We investigated the statistical characteristics and probability distribution of the mechanical parameters of natural rock using triaxial compression tests. Twenty cores of Jinping marble were tested under each different levels of confining stress (i.e., 5, 10, 20, 30, and 40 MPa). From these full stress–strain data, we summarized the numerical characteristics and determined the probability distribution form of several important mechanical parameters, including deformational parameters, characteristic strength, characteristic strains, and failure angle. The statistical proofs relating to the mechanical parameters of rock presented new information about the marble’s probabilistic distribution characteristics. The normal and log-normal distributions were appropriate for describing random strengths of rock; the coefficients of variation of the peak strengths had no relationship to the confining stress; the only acceptable random distribution for both Young’s elastic modulus and Poisson’s ratio was the log-normal function; and the cohesive strength had a different probability distribution pattern than the frictional angle. The triaxial tests and statistical analysis also provided experimental evidence for deciding the minimum reliable number of experimental sample and for picking appropriate parameter distributions to use in reliability calculations for rock engineering.

Bayesian Combinatorial Auctions

We study the following simple Bayesian auction setting: m items are sold to n selfish bidders in m independent second-price auctions. Each bidder has a private valuation function that specifies his or her complex preferences over all subsets of items. Bidders only have beliefs about the valuation functions of the other bidders, in the form of probability distributions. The objective is to allocate the items to the bidders in a way that provides a good approximation to the optimal social welfare value. We show that if bidders have submodular or, more generally, fractionally subadditive (aka XOS) valuation functions, every Bayes-Nash equilibrium of the resulting game provides a 2-approximation to the optimal social welfare. Moreover, we show that in the full-information game, a pure Nash always exists and can be found in time that is polynomial in both m and n .

New methods of probabilistic and possibilistic interactive data processing

This paper presents the methods of processing interactive data describing different forms of uncertainty. Data can be expressed in the form of interactive possibility distribution or the part of data can be expressed in the form of interactive possibility distribution and the part in the form of pr obability distribution. The procedure of processing combines stochastic simulation with nonlinear programming or simulation of fuzzy systems. The interaction between data are modeled by the correlation matrices and the interval regression. Presented practical example indicates that an interaction between data have a significant impact on results of calculations. Data processing without consideration of these interrelations would bear a considerable, systematic error.

Investigation of modal identification and modal identifiability of a cable-stayed bridge with Bayesian framework

In this study, the Bayesian probabilistic framework is investigated for modal identification and modal identifiability based on the field measurements provided in the structural health monitoring benchmark problem of an instrumented cable-stayed bridge named Ting Kau Bridge (TKB). The comprehensive structural health monitoring system on the cable-stayed TKB has been operated for more than ten years and it is recognized as one of the best test-beds with readily available field measurements. The benchmark problem of the cable-stayed bridge is established to stimulate investigations on modal identifiability and the present paper addresses this benchmark problem from the Bayesian prospective. In contrast to deterministic approaches, an appealing feature of the Bayesian approach is that not only the optimal values of the modal parameters can be obtained but also the associated estimation uncertainty can be quantified in the form of probability distribution. The uncertainty quantification provides necessary information to evaluate the reliability of parametric identification results as well as modal identifiability. Herein, the Bayesian spectral density approach is conducted for output-only modal identification and the Bayesian model class selection approach is used to evaluate the significance of different modes in modal identification. Detailed analysis on the modal identification and modal identifiability based on the measurements of the bridge will be presented. Moreover, the advantages and potentials of Bayesian probabilistic framework on structural health monitoring will be discussed.

Frequency-domain fatigue life estimation with mean stress correction

Two frequency-domain fatigue life calculation methods are presented which take into account the impact of the mean stress effect. The emphasis is set on the algorithm for fatigue life assessment of the method proposed by the authors. It is supplemented with a mean stress effect correction. Correction method is based on the direct transformation of the zero mean stress Power Spectral Density (PSD) due to mean stress. The method is verified on the basis of own results for the S355JR steel. The authors analyze five models for the designation of the probability density function used in the calculation process. The results are presented in the form of probability distributions after PSD transformation and the calculated fatigue life is being compared with the experimental life in fatigue comparison graphs. An analysis of the choice of a mean stress correction model is also widely discussed and a fatigue life estimation is also performed. The method proposed by the authors is being compared with the Kihl–Sarkani method for mean stress correction in frequency domain.

Risk Assessment for Ecological Planning of Arid Inland River Basins Under Hydrological and Management Uncertainties

The Shiyanghe river basin, an arid inland basin of northwest China, is taken as an example to analyze the risk for achieving the ecological planning objective in arid inland river basins under uncertainty conditions. Hydrology and management uncertainties that affect the accomplishment of ecological planning objective are analyzed quantitatively with the methods of Bayesian theory based Probabilistic model, scenario analysis and interval analysis. Bayesian probabilistic analysis method was used to analyze the hydrological uncertainties in the form of probability and interval distributions in planning period, while the scenario analysis method and interval method were used to analyze the managing uncertainties in the form of interval numbers. Instead of the ecological risk analysis, which for arid inland river basin, of studying the impact of environmental and human factor on ecological system, water resources and environment, we focused on analysing the possible impact of hydrological and management uncertainty factor on the ecological planning, and forecasting the degree of the completion under the uncertainty. Our study provided the probabilities of achieving ecological planning objective and the possible deviation of different scenarios. The more local water resources and higher level of local water resource utilization and management appeared to lead higher probability to achieve the ecological objective. This study can help environment and water resource managers and planner to formulate a rational planning for arid inland river basins under hydrological and management uncertainty.

Preprocessing of centred logratio transformed density functions using smoothing splines

With large-scale database systems, statistical analysis of data, occurring in the form of probability distributions, becomes an important task in explorative data analysis. Nevertheless, due to specific properties of density functions, their proper statistical treatment of these data still represents a challenging task in functional data analysis. Namely, the usual metric does not fully accounts for the relative character of information, carried by density functions; instead, their geometrical features are captured by Bayes spaces of measures. The easiest possibility of expressing density functions in an space is to use centred logratio transformation, even though this results in functional data with a constant integral constraint that needs to be taken into account in further analysis. While theoretical background for reasonable analysis of density functions is already provided comprehensively by Bayes spaces themselves, preprocessing issues still need to be developed. The aim of this paper is to introduce optimal smoothing splines for centred logratio transformed density functions that take all their specific features into account and provide a concise methodology for reasonable preprocessing of raw (discretized) distributional observations. Theoretical developments are illustrated with a real-world data set from official statistics and with a simulation study.