Conditional Distribution Model Research Articles

Uncertainty quantification for seismic response using dimensionality reduction‐based stochastic simulator

AbstractThis paper introduces a stochastic simulator for seismic uncertainty quantification, which is crucial for performance‐based earthquake engineering. The proposed simulator extends the recently developed dimensionality reduction‐based surrogate modeling method (DR‐SM) to address high‐dimensional ground motion uncertainties and the high computational demands associated with nonlinear response history analyses. By integrating physics‐based dimensionality reduction with multivariate conditional distribution models, the proposed simulator efficiently propagates seismic input into multivariate response quantities of interest. The simulator can incorporate both aleatory and epistemic uncertainties and does not assume distribution models for the seismic responses. The method is demonstrated through three finite element building models subjected to synthetic and recorded ground motions. The proposed method effectively predicts multivariate seismic responses and quantifies uncertainties, including correlations among responses.

Why Do Semianalytic Models Predict Higher Scatter in the Stellar Mass–Halo Mass Relation Than Cosmological Hydrodynamic Simulations?

Semianalytic models (SAMs) systematically predict higher-stellar mass scatter at a given halo mass than hydrodynamical simulations and most empirical models. Our goal is to investigate the physical origin of this scatter by exploring modifications to the physics in the SAM Dark Sage. We design two black hole formation models that approximate results from the IllustrisTNG 300-1 hydrodynamical simulation. In the first model, we assign a fixed black hole mass of 106 M ⊙ to every halo that reaches 1010.5 M ⊙. In the second model, we disregard any black hole growth as implemented in the standard Dark Sage model. Instead, we force all black hole masses to follow the median z = 0 black hole mass–halo mass relation in IllustrisTNG 300-1 with an imposed fixed scatter. We find that each model on its own does not significantly reduce the scatter in stellar mass. To explore the effects of active galactic nucleus (AGN) feedback in addition to black hole seeding, we replace the native Dark Sage AGN feedback model with a simple model where we turn off cooling for galaxies with black hole masses above 108 M ⊙. With the additional modification in AGN feedback, we find that the supermassive black hole seeding and fixed conditional distribution models create a significant reduction in the scatter in stellar mass at halo masses between 1011–14 M ⊙. These results suggest that AGN feedback in SAMs acts in a qualitatively different way than feedback implemented in cosmological simulations. Either or both may require substantial modification to match the empirically inferred scatter in the stellar mass–halo mass relation.

An auxiliary correction model implemented by the Correction Property of intermediate layer against adversarial examples

In powerful adversarial attacks against deep neural networks (DNN), the generated adversarial example will mislead the DNN-implemented classifier by destroying the features of the last layer. To enhance the robustness of the classifier, in our paper, a Feature Analysis and Conditional Matching prediction distribution (FACM) model is proposed to utilize the features of intermediate layers to correct the misclassification. Specifically, we first prove that the intermediate layers of the classifier still retain effective features for the original category when the classifier is subjected to adversarial attacks, which is defined as the Correction Property in our paper. According to this, we propose the FACM model consisting of Feature Analysis (FA) correction module, Conditional Matching Prediction Distribution (CMPD) correction module and decision module. Specifically, the FA correction module is comprised of fully connected layers, which takes the features of the intermediate layers as the input to correct the misclassification of the classifier. The CMPD correction module is based on a conditional autoencoder, which not only uses the features of intermediate layers as the condition to accelerate convergence but also mitigates the negative effect of adversarial examples, trained with the Kullback–Leibler loss to match prediction distribution. Through the empirically verified Diversity Property among the individual correction modules, the decision module is proposed to integrate the proposed correction modules to enhance the DNN-implemented classifier’s robustness by reducing the dimensionality of adversarial subspace. That is, the input perturbed in certain directions (i.e., dimensions) that lead to misclassifications for the classifier can be correctly classified by the proposed correction modules. The extended experiments demonstrate our FACM model outperforms the existing methods against adversarial attacks, especially optimization-based white-box attacks and query-based black-box attacks.

ENVIRONMENTAL CONTOUR ESTABLISHMENT BASED ON OPENLY AVAILABLE EMODNET WAVE AND WIND DATA FOLLOWING HEFFERNAN AND TAWN METHODOLOGIES

In this paper, I present methodologies and routines for inference of environmental contours based on openly available data from the European EMODnet service, specifically wind and wave timeseries from oil platform 6200146. The conditional marginal distribution models, known as environmental contours, is established based on measured wind and wave heights, at platform 6200146 located in the North Sea. The data is provided through the openly available data platform, EMODnet. The environmental contour model is established by fitting univariate distributions to each data-series independently, whereafter an extremal dependence structure is established following methodologies outlined in (Janet E. heffernan, 2004).

Hydrological drought forecasting under a changing environment in the Luanhe River basin

Abstract. Forecasting the occurrence of hydrological drought according to a forecasting system is an important disaster reduction strategy. In this paper, a new drought prediction model adapted to changing environments was constructed. Taking the Luanhe River basin in China as an example, first, nonstationarity analysis of hydrological sequences in the basin was carried out. Then, conditional distribution models with the human activity factor as an exogenous variable were constructed to forecast hydrological drought based on meteorological drought, and the results were compared with the traditional normal distribution model and conditional distribution model. Finally, a scoring mechanism was applied to evaluate the performance of the three drought forecasting models. The results showed that the runoff series of the Luanhe River basin from 1961 to 2010 were nonstationary; moreover, when human activities were not considered, the hydrological drought class tended to be the same as the meteorological drought class. The calculation results of the models involving HI as an exogenous variable were significantly different from the models that did not consider human activities. When the current drought class tended towards less severe or normal, the meteorological drought tended to turn into more severe hydrological drought with the increase in human index values. According to the scores of the three drought forecasting models, the conditional distribution models involving the human index can further improve the forecasting accuracy of drought in the Luanhe River basin.

Bootstrap specification tests for dynamic conditional distribution models

This paper proposes bootstrap based tests for the specification of a given parametric conditional distribution in autoregressive time series with GARCH-type disturbances. The tests are based on an estimated residual empirical process and are implemented by parametric bootstrap. We show that the proposed tests are asymptotically valid, consistent, and have nontrivial asymptotic power against a large proportion of local alternatives. Our approach relies on non-primitive regularity conditions and certain properties of exponential almost sure convergence. The regularity conditions are shown to be satisfied by GARCH(p,q); this technique of verification is applicable to other models as well. In our Monte Carlo study, the proposed tests performed well and better than several competing tests, including the information matrix test. A real data example illustrates the testing procedure.

Design loads and reliability assessment of marine structures considering statistical models of metocean data

The objective of this study is to investigate the effect of statistical models for constructing the bivariate distribution of metocean data on design loads and reliability assessment of offshore structures. First, the conventional conditional joint distribution and single copula models are utilized for characterizing the statistical data. Additionally, a novel mixed copula model is developed using a linear combination of Gaussian, Clayton, Gumbel and Frank copula considering various tails characteristics, the parameter estimation is performed using expectation-maximization (EM) algorithm. Moreover, a mixed joint model based on linear combinations of simple statistical models is proposed. Then, the environmental contours are constructed based on various joint probability distribution of environmental variables. Finally, the reliability of marine structures is estimated using direct Monte Carlo simulation considering dependence structure and joint models of statistical data. The results indicate the reliability of offshore structure differs significantly because the bivariate distribution models of environmental variables could not be defined uniquely, the dependence structure has non-negligible effect on reliability assessment. A mixed copula can be suitable for describing variables with symmetrical or asymmetric, independent or correlative, upper or lower tails, or complex characteristics. The mixed joint model provides satisfactory results for marginal and joint fitting.

Flood frequency analysis of Manas River Basin in China under non‐stationary condition

AbstractIncorporating 50 years of flood data for the Manas River Kenswat Hydrological Station from 1957 to 2006, the Pettitt test and Mann–Kendall trend test are used to analyse non‐stationarity of the flood characteristic sequences. Moreover, the Pearson type‐III (P‐III) distribution, the mixed distribution (MD) and conditional probability distribution (CPD) models are employed to analyse frequency and to calculate the design flood process line. The results showed that the annual maximum peak discharge and the annual maximum flood volume are most likely to change in 1993. The MD model considering the non‐stationarity of the flood sequence is more accurate than the CPD model and the traditional P‐III distribution model. There are significant differences in the design flood process lines of the 1996 typical flood process obtained by the three methods using the same frequency scaling method. In addition, under different design standards, the design value of the MD model is 20–53% smaller than the design value approved in 2008 (approved by China Renewable Energy Engineering Institute) and 4–48% higher than the traditional P‐III distribution design value. The results can provide a new reference for the management of non‐stationary floods in Manas River.

Uniform convergence rate of the kernel regression estimator adaptive to intrinsic dimension in presence of censored data

ABSTRACT The focus of the present paper is on the uniform in bandwidth consistency of kernel-type estimators of the regression function derived by modern empirical process theory, under weaker conditions on the kernel than previously used in the literature. Our theorems allow data-driven local bandwidths for these statistics. We extend existing uniform bounds on kernel regression estimator and making it adaptive to the intrinsic dimension of the underlying distribution of which will be characterising by the so-called intrinsic dimension. Moreover, we show, in the same context, the uniform in bandwidth consistency for nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship. Statistical applications to the kernel-type estimators (density, regression, conditional distribution, derivative functions, entropy, mode and additive models) are given to motivate these results.

Estimating Design Loads with Environmental Contour Approach Using Copulas for an Offshore Jacket Platform

Jacket-type offshore platforms are widely used for oil, gas field, and energy development in shallow water. The design of a jacket structure is highly dependent on target environmental variables. This study focuses on a strategy to estimate design loads for offshore jacket structures based on an environmental contour approach. In addition to the popular conditional distribution model, various classes of bivariate copulas are adopted to construct joint distributions of environmental variables. Analytical formulations of environmental contours based on various models are presented and discussed in this study. The design loads are examined by dynamic response analysis of jacket platform. Results suggest that the conditional model is not recommended for use in estimating design loads in sampling locations due to poor fitting results. Independent copula produces conservative design loads and the extreme response obtained using the conditional model are smaller than those determined by copulas. The suitability of a model for contour construction varies with the origin of wave data. This study provides a reference for the design load estimation of jacket structures and offers an alternative procedure to determine the design criteria for offshore structures.

A navigation satellite selection algorithm for optimized positioning based on Gibbs sampler

In various applications of satellite navigation and positioning, it is a key topic to select suitable satellites for positioning solutions to reduce the computational burden of the receiver in satellite selection system. Moreover, in order to reduce the processing burden of receivers, the satellite selection algorithm based on Gibbs sampler is proposed. First, the visible satellites are randomly sampled and divided into a group. The group is regarded as an initial combination selection scheme. Then, the geometric dilution of precision is chosen as an objective function to evaluate the scheme’s quality. In addition, the scheme is updated by the conditional probability distribution model of the Gibbs sampler algorithm, and it gradually approaches the global optimal solution of the satellite combination with better geometric distribution of the space satellite. Furthermore, an “adaptive perturbation” strategy is introduced to improve the global searching ability of the algorithm. Finally, the extensive experimental results demonstrate that when the number of selected satellite is more than 6, the time that the proposed algorithm with the improvement of “adaptive perturbation” takes to select satellite once is 43.7% of the time that the primitive Gibbs sampler algorithm takes. And its solutions are always 0.1 smaller than the related algorithms in geometric dilution of precision value. Therefore, the proposed algorithm can be considered as a promising candidate for satellite navigation application systems.

A specification test for dynamic conditional distribution models with function-valued parameters

This paper proposes a practical and consistent specification test of conditional distribution models for dependent data in a general setting. Our approach covers conditional distribution models indexed by function-valued parameters, allowing for a wide range of useful models for risk management and forecasting, such as the quantile autoregressive model, the CAViaR model, and the distributional regression model. The new specification test (i) is valid for general linear and nonlinear conditional quantile models under dependent data, (ii) allows for dynamic misspecification of the past information set, (iii) is consistent against fixed alternatives, and (iv) has nontrivial power against Pitman deviations from the null hypothesis. As the test statistic is non-pivotal, we propose and theoretically justify a subsampling approach to obtain valid inference. Finally, we illustrate the applicability of our approach by analyzing models of the returns distribution and Value-at-Risk (VaR) of two major stock indexes.

A monitoring and prediction system for compound dry and hot events

Compound dry and hot events (i.e. concurrent or consecutive occurrences of dry and hot events), which may cause larger impacts than those caused by extreme events occurring in isolation, have attracted wide attention in recent decades. Increased occurrences of compound dry and hot events in different regions around the globe highlight the importance of improved understanding and modeling of these events so that they can be tracked and predicted ahead of time. In this study, a monitoring and prediction system of compound dry and hot events at the global scale is introduced. The monitoring component consists of two indicators (standardized compound event indicator and a binary variable) that incorporate both dry and hot conditions for characterizing the severity and occurrence. The two indicators are shown to perform well in depicting compound dry and hot events during June–July–August 2010 in western Russia. The prediction component consists of two statistical models, including a conditional distribution model and a logistic regression model, for predicting compound dry and hot events based on El Niño–Southern Oscillation, which is shown to significantly affect compound events of several regions, including northern South America, southern Africa, southeast Asia, and Australia. These models are shown to perform well in predicting compound events in large regions (e.g. northern South America and southern Africa) during December–January–February 2015–2016. This monitoring and prediction system could be useful for providing early warning information of compound dry and hot events.

Ultra short‐term probability prediction of wind power based on LSTM network and condition normal distribution

AbstractConsidering the inevitable prediction errors in the traditional point predictions of wind power, in this paper, a new ultra short‐term probability prediction method for wind power is proposed, in which the long short‐term memory (LSTM) network, wavelet decomposition (WT), and principal component analysis (PCA) are combined together for ultra short‐term probability prediction of wind power, a conditional normal distribution model that is developed to describe the uncertainty of prediction errors. First, WT and PCA are jointly used to smooth the original time series, then the point prediction model for subsequence data based on LSTM network is proposed. It is worth pointing out that the input matrix of the model includes many features, such as wind power and wind speed, which will be helpful for improving prediction performance. After optimizing the index of the ultra short‐term probability prediction interval (PI) of wind power by particle swarm optimization (PSO), the conditional normal distribution model of prediction errors is developed. Thus, the ultra short‐term PIs for wind power are obtained. Finally, based on the data of two wind farms in China, simulation results are provided to illustrate the usefulness of the proposed prediction model. It follows from those results that the proposed method can improve the accuracy of prediction, and the reliability of probability prediction for wind power is also improved.

Coordinated Energy Dispatch of Autonomous Microgrids With Distributed MPC Optimization

With the increased penetration of renewable energy sources (RESs) and plug-and-play loads, Microgrids (MGs) bring direct challenges in energy management due to the uncertainties in both supply and demand sides. In this paper, we present a coordinated energy dispatch based on Distributed Model Predictive Control (DMPC), where the upper level provides an optimal scheduling for energy exchange between Distribution Network Operator (DNO) and MGs, whereas the lower level guarantees a satisfactory tracking between supply and demand. With the proposed scheme, not only we maintain a supply–demand balance in an economic way, but also improve the renewable energy utilization of distributed MG systems. To describe the dynamic process of energy trading, a novel conditional probability distribution model is introduced, which can characterize randomness of charging/discharging and uncertainties of energy dispatch. Moreover, we formulate a two-layer optimization problem and the corresponding algorithm is given. Finally, simulation results show the effectiveness of the proposed method.

Toward parsimonious modeling of frequency of areal runoff from heavy-to-extreme precipitation in large urban areas under changing conditions: a derived moment approach

Translating changes in land surface conditions and climate into changes in precipitation, runoff and flood frequencies over a range of catchment scales is a pressing challenge for hydrologic design and flood risk management today. In this paper, we describe a novel approach for modeling areal runoff frequency from heavy-to-extreme precipitation in large urban areas using a simple but general stochastic model for runoff at point scale and bi- and univariate parametric probability distributions for positive point precipitation and areal runoff, respectively. We apply the approach to the Dallas–Fort Worth area using a 22-year historical multisensor precipitation dataset from the National Weather Service to characterize how the different factors that specify the second-order statistics of precipitation, imperviousness and soil water holding capacity at point scale may shape areal runoff frequency, and to assess how changes in precipitation climatology and land surface conditions may change areal runoff frequency as a function of catchment scale and magnitude of precipitation. The results indicate that areal runoff frequency is impacted most significantly by changes in climatological mean and coefficient of variation of positive point precipitation, water holding capacity of soil, imperviousness, and spatial correlation scale of positive point precipitation given the probability of occurrence of heavy-to-extreme precipitation, and that a very small number of low-order statistics of point precipitation may describe areal runoff frequency given the conditional probability distribution models for point precipitation and areal runoff. The approach presented hence offers a parsimonious physically-based alternative to purely numerical approaches based on integrated modeling, or empirical approaches based solely on statistical modeling toward predictive modeling of areal precipitation and runoff frequencies under changing hydroclimatological conditions.

Prevalence of active school transportation in the upper east and upper west regions of Ghana

<p>The use of active transportation such as walking to and from school is on the decline globally. The primary purpose of the study was to determine the prevalence of active school transportation among primary and junior high school students in the Upper East and Upper West regions of Ghana. The secondary purpose was to examine predictors for meeting the recommended daily number of steps. A total of 2505 (1117 boys and 1388 girls) primary (1583) and junior high school (922) students participated in the study. The distances from children’s homes to their schools, heights, and body weights were measured –their heights were used to estimate their stride lengths. The step count for each participant to and from school each day was calculated. Data were analyzed using conditional percentage distribution and Logit model. Analyses indicated that 98.96% of participants used active transportation to and from school. Over 63% of the students were within the normal BMI range. However, 26.47% of the participants were either thin or underweight while 9.9% were either overweight or obese. Overall, 46.47% of the participants met the recommended daily steps. The Logit model indicated that educational level, BMI, mode of transportation, region, height, and age were significant predictors for meeting the recommended daily number of steps<strong>. </strong>The prevalence of school active transportation in the present study was high compared to that reported in other studies. Furthermore, the prevalence of thinness and underweight were higher than in previous studies, while the prevalence in overweight and obesity were lower.</p>

Distribution free testing for conditional distributions given covariates

Given a sample (ξi,Xi)i=1n of i.i.d. pairs, consider Fx and Qx as two different models for conditional distribution of ξi given Xi=x. The paper shows how the empirical process for testing Fx can be transformed into a process with the same asymptotic behavior as the empirical process for testing Qx thereby rendering the two testing problems equivalent.

Blind Bleed-Through Removal for Scanned Historical Document Image With Conditional Random Fields.

Scanned images of historical documents often suffer from bleed-through, which refers to the ink on one side seeping through the paper and appearing on the other side. In this paper, a new conditional random field (CRF)-based method is proposed to remove the bleed-through from the scanned images of historical images. The proposed method only requires the scanned image of one side, referred as a blind method. In general, the scanned historical document image is composed of three components: foreground, bleed-through, and background. By assuming Gaussian distributions of the three components, the proposed method establishes conditional probability distribution (CPD) models of the three components first. The parameters of the component CPD models are estimated based on an initial segmentation of the input image. Then, CRFs are used to capture the relations between observed pixels in the scanned image and the corresponding labels as well as the spatial relation between the adjacent labels. The belief propagation algorithm is used to calculate the probabilities of different labels for each pixel. Once the labeling is completed by choosing the most possible label for each pixel, the bleed-through component is removed from the input historical image by a random-filling inpainting algorithm. Experimental results on the real data set show that the proposed method preserves the foreground component very well and removes the bleed-through effectively.

Weighted simulated integrated conditional moment tests for parametric conditional distributions of stationary time series processes

ABSTRACTIn this article, we propose a weighted simulated integrated conditional moment (WSICM) test of the validity of parametric specifications of conditional distribution models for stationary time series data, by combining the weighted integrated conditional moment (ICM) test of Bierens (1984) for time series regression models with the simulated ICM test of Bierens and Wang (2012) of conditional distribution models for cross-section data. To the best of our knowledge, no other consistent test for parametric conditional time series distributions has been proposed yet in the literature, despite consistency claims made by some authors.