Obtain Probability Distributions Research Articles

Investigating the Relationship Between the Dynamics of the Structure of Intermediate Consumption and Output of Industries: Cross-Country Analysis

This paper examines one of the main prerequisites of the inter-industry balance methodology on the proportional dependence of the output of industries and their intermediate consumption. The statistical base of the study is the world input-output tables collected for the period from 2000 to 2014. According to the results of the work, it was revealed that the prerequisite of a proportional change in the vector of intermediate consumption with a change in output is not consistent. However, significant positive relationships were found between intermediate consumption and the output of industries. On the basis of the identified relationships, we conducted a clustering procedure on industries, where, in particular, clusters with strong, medium, and weak relationships between intermediate consumption and output are distinguished. Thus, the paper proposes to expand the input-output methodology by introducing proportionality coefficients for changes in the intermediate consumption of an industry with a change in its output. Proportionality coefficients are proposed to be obtained on the basis of regression equations built on statistical data from the input-output tables. It should be especially noted that in addition to obtaining point forecasts of intermediate consumption for each industry when its output changes, it is also possible to obtain probability distributions for the gross output of each industry, their value added, wages, taxes, and profits through Monte Carlo simulations based on the constructed regression equations, which will facilitate a scenario analysis of the development of the considered economic system. The results of this work can be useful to executive authorities in planning large state economic projects as well as in assessing the impact of external shocks on the countryʼs economy.

Modification of Ground-Motion Models to Estimate Orientation-Dependent Horizontal Response Spectra in Strike-Slip Earthquakes

ABSTRACT A model to estimate the 5% damped response spectra of horizontal components at specific orientations is presented. The model, which explicitly accounts for directionality, is based on prior research by the authors that identified that the orientation of maximum horizontal spectral response at a site in strike-slip earthquakes tends to occur at or close to the transverse orientation with respect to the epicenter. Using a database of 1962 ground motions recorded in shallow crustal earthquakes with strike-slip faulting, it is shown that there is a significantly larger probability of exceeding orientation-independent RotD50 intensities in the transverse orientation than in the radial orientation. Furthermore, the results indicate that, on average, spectral responses in the transverse orientation are significantly larger than those in the radial orientation and that these differences become more significant as the period of the oscillator increases. For example, spectral responses in the transverse orientation are, on average, 12% larger than those in the radial orientation for 1 s oscillators and 78% larger for 10 s oscillators. A period- and orientation-dependent model is developed and calibrated to estimate 5% damped response spectral ordinates at specific orientations by modifying orientation-independent RotD50 intensities. The proposed orientation-dependent model can explicitly account for directionality by modifying the means and standard deviations of any ground-motion model that estimates RotD50 response spectral ordinates for strike-slip earthquakes to obtain probability distributions of response spectral ordinates but now at specific horizontal orientations.

A hybrid Monte Carlo simulation risk model for oil exploration projects

A new 3-D Hybrid Monte Carlo Simulation (MCS) Risk Model is proposed in this study. The wind, wave, current, climate change, and tsunami sub-models of the Three-Dimensional Hydrodynamic Transport and Water Quality Model HYDROTAM-3D are interrelated with MCS, to obtain probability distributions for the simulation of environmental conditions. This is the only model that can incorporate the tsunami, storm, and sea level rise risks in oil exploration projects. The spill risk index (SRI) of 50 blue barrels spilled due to a blowout from the rig/port during fuel supply was circa 1 ton/ship as Tier I with an average annual occurrence probability of 1.0 × 10−6. The discharge of 4000 bbls for 6 h was modeled, resulting in the SRI of 546 metric tons from the riser blowout with SRI = 0.2 per meter, indicating a Tier II risk. The mean arrival time of this spill was found by MCS as 145 min.

The GeMS/GSAOI Galactic Globular Cluster Survey (G4CS). II. Characterization of 47 Tuc with Bayesian Statistics

We present a photometric analysis of globular cluster 47 Tuc (NGC 104) using near-IR imaging data from the GeMS/GSAOI Galactic Globular Cluster Survey (G4CS), which is in operation at Gemini-South telescope. Our survey is designed to obtain AO-assisted deep imaging with near diffraction-limited spatial resolution of the central fields of Milky Way globular clusters. The G4CS near-IR photometry was combined with an optical photometry catalog that was obtained from Hubble Space Telescope survey data to produce a high-quality color–magnitude diagram that reaches down to K s ≈ 21 Vega mag. We used the software suite BASE-9, which uses an adaptive Metropolis sampling algorithm to perform a Markov chain Monte Carlo Bayesian analysis, and obtained probability distributions and precise estimates for the age, distance, and extinction cluster parameters. Our best estimate for the age of 47 Tuc is ± 0.08 Gyr and our true distance modulus estimate is (m−M)0 = 13.250 ± 0.028 mag, which are in tight agreement with previous studies using Gaia DR2 parallax and detached eclipsing binaries.

An equivalent RBDO method under the hybrid of fuzzy and interval variables in the worst case

AbstractIn the reliability‐based design optimization (RBDO) problems of structures or systems, only a single type of variable involving is rare, and most of time are hybrid variables. Random variables are often used to describe uncertainty, and these random variables can usually be described by certain probability distributions. However, in practice, the probability distributions of some random variables are difficult or even impossible to be obtained, or the obtained probability distributions may be inaccurate, and can only be roughly described by fuzzy values or intervals. Therefore, this paper is committed to solving RBDO problems under the hybrid of fuzzy variables and interval variables. Firstly, the RBDO model of the structure under the hybrid variables is established. Secondly, the fuzzy variables are transformed to random variables according to entropy invariance. Finally, RBDO is carried out based on sequential single‐loop method in the worst case. A numerical example is presented to illustrate the feasibility of the proposed method.

Construction of a Probabilistic Model Describing Deterioration of Pumping Wells and Its Verification Using Actual Data

A probabilistic model is newly proposed for describing random deterioration of pumping wells, in consideration of application to efficient management of pumping wells using a concept of asset management procedure. First, introducing a health index for quantifying specific capacity, we formulate a differential equation describing mean deterioration of the helth index. Next, it is extended to a random differential equation, in which a Gaussian white noise is introduced for representing intensive fluctuation around the mean deterioration behavior, so that intensively random variation of the health index can be well reproduced. A probability distribution of the health index is then derived in an analytical form. Finally, the obtained probability distribution is compared with actual data of the health index for active eight pumping wells in Joyo area, Kyoto prefecture, Japan. It is clarified that the scatter of health index of actual pumping wells is quite well reproduced by the theoretically derived probability distribution from the newly proposed probabilistic model.

An improved approach for calculating energy landscape of gene networks from moment equations.

The energy landscape theory has widely been applied to study the stochastic dynamics of biological systems. Different methods have been developed to quantify the energy landscape for gene networks, e.g., using Gaussian approximation (GA) approach to calculate the landscape by solving the diffusion equation approximately from the first two moments. However, how high-order moments influence the landscape construction remains to be elucidated. Also, multistability exists extensively in biological networks. So, how to quantify the landscape for a multistable dynamical system accurately, is a paramount problem. In this work, we prove that the weighted summation from GA (WSGA), provides an effective way to calculate the landscape for multistable systems and limit cycle systems. Meanwhile, we proposed an extended Gaussian approximation (EGA) approach by considering the effects of the third moments, which provides a more accurate way to obtain probability distribution and corresponding landscape. By applying our generalized EGA approach to two specific biological systems: multistable genetic circuit and synthetic oscillatory network, we compared EGA with WSGA by calculating the KL divergence of the probability distribution between these two approaches and simulations, which demonstrated that the EGA provides a more accurate approach to calculate the energy landscape.

A Short‐Time Non‐Gaussian Probability Approximation Based Method for Response Transitions of a Lévy‐Driven Nonsmooth System

This paper proposes an efficient short‐time probability approximation with Lévy excitation to capture the transient probability distribution and its evolving path. Using principal component analysis (PCA), the method constructs a probability core to exclude outliers beyond it. The statistics of samples that fall inside the core are treated, with a prescribed fiducial probability, as an easy‐to‐estimate Gaussian type. The idea is verified numerically by compared with Monte‐Carlo results. Then, it is integrated into the path integral (PI) method, combined with evolving probabilistic vector (EPV) techniques, to efficiently obtain probability distributions in each time step of PI. This scheme is semianalytical, only dependent on a relatively small amount of response samples to form the probability core; thus, it can have very computational advantages over full Monte‐Carlo simulation to capture transient responses and probability distributions. The application to investigating response transitions of a nonsmooth system driven by Lévy shock and jump has revealed the performance of the proposed method. Also, the exit times of stochastic response are characterized quantitatively from the perspective of global dynamic transition. These investigations will be helpful to achieve the efficient probability estimation for nonlinear system with non‐Gaussian inputs and quantify the reliability of the mechanical system.

Data-driven photometric redshift estimation from type Ia supernovae light curves

ABSTRACT Redshift measurement has always been a constant need in modern astronomy and cosmology. And as new surveys have been providing an immense amount of data on astronomical objects, the need to process such data automatically proves to be increasingly necessary. In this article, we use simulated data from the Dark Energy Survey, and from a pipeline originally created to classify supernovae, we developed a linear regression algorithm optimized through novel automated machine learning (AutoML) frameworks achieving an error score better than ordinary data pre-processing methods when compared with other modern algorithms (such as xgboost). Numerically, the photometric prediction RMSE of type Ia supernovae events was reduced from 0.16 to 0.09 and the RMSE of all supernovae types decreased from 0.20 to 0.14. Our pipeline consists of four steps: through spectroscopic data points we interpolate the light curve using Gaussian process fitting algorithm, then using a wavelet transform we extract the most important features of such curves; in sequence we reduce the dimensionality of such features through principal component analysis, and in the end we applied super learning techniques (stacked ensemble methods) through an AutoML framework dedicated to optimize the parameters of several different machine learning models, better resolving the problem. As a final check, we obtained probability distribution functions (PDFs) using Gaussian kernel density estimations through the predictions of more than 50 models trained and optimized by AutoML. Those PDFs were calculated to replicate the original curves that used SALT2 model, a model used for the simulation of the raw data itself.

Sensitivity-based Parameter Calibration of Single- and Dual-continuum Coreflooding Simulation Models

Our study is keyed to the development of a viable framework for the stochastic characterization of coreflooding simulation models under two- and three-phase flow conditions taking place within a core sample in the presence of preferential flow of the kind that can be associated with the presence of a system of fractures. We do so considering various modeling strategies based on (spatially homogeneous or heterogeneous) single- and dual-continuum formulations of black-oil computational models and relying on a global sensitivity-driven stochastic parameter calibration. The latter is constrained through a set of data collected under a water alternating gas scenario implemented in laboratory-scale coreflooding experiments. We set up a collection of Monte Carlo (MC) numerical simulations while considering uncertainty encompassing (a) rock attributes (i.e., porosity and absolute permeability), as well as (b) fluid–fluid/ fluid–solid interactions, as reflected through characteristic parameters of relative permeability and capillary pressure formulations. Modern moment-based global sensitivity indices are evaluated on the basis of the MC model responses, with the aim of (i) quantifying sensitivity of the coreflooding simulation results to variations of the input uncertain model parameters and (ii) assessing the possibility of reducing the dimensionality of model parameter spaces. We then rest on a stochastic inverse modeling approach grounded on the acceptance–rejection sampling (ARS) algorithm to obtain probability distributions of the key model parameters (as identified through our global sensitivity analyses) conditional to the available experimental observations. The relative skill of the various candidate models to represent the system behavior is quantified upon relying on the deviance information criterion. Our findings reveal that amongst all tested models, a dual-continuum formulation provides the best performance considering the experimental observations available. Only a few of the parameters embedded in the dual-continuum formulation are identified as major elements significantly affecting the prediction (and associated uncertainty) of model outputs, petrophysical attributes and relative permeability model parameters having a stronger effect than parameters related to capillary pressure.

A risk-based approach to measuring population micronutrient status from blood biomarker concentrations.

BackgroundNutrient biomarkers and their definitive cut-offs are used to classify individuals as nutrient-deficient or sufficient. This determinism does not consider any uncertainty, and a probability approach, using biomarker distributions, is then preferable to define the risk of nutrition deficiency when in populations.MethodHealthy 1–19-year-old children and adolescents were selected from the Comprehensive National Nutrition Survey (CNNS), to obtain probability distributions of their retinol, zinc and vitamin B12, along with erythrocyte folate. Model-based estimates of location, scale and shape parameters of these distributions were obtained across ages. Subsequently, in the entire sample of 1–19 year old children of CNNS, the population risk of deficiency (PRD) which is average risk of deficiency in individuals in the population was computed, which is “of concern” when >50%. When individual risk of deficiency is >97.5% it is called “severe risk of deficiency” (SRD).ResultsIn the entire CNNS sample, the PRD of concern was low for serum retinol (3.6–8.2%), zinc (0–5.5%), and SRD of vitamin B12 and erythrocyte folate were 2.3–7.2% and 4.2–9.7%, respectively, across age and sex groups.ConclusionThis proposed method assesses the adequacy of nutrient exposures without relying on pre-defined deterministic biomarker cut-offs to define micronutrient deficiency and avoids errors in exposure assessment.

Image two-classification algorithm based on continuous-time quantum walk

To further improve the performance of image retrieval, we propose an image two-classification algorithm based on continuous-time quantum walk (CTQW) model. First, a weighted undirected complete graph is constructed based on a new weighted edge method, that is, the images in the image set are used to represent the nodes on the weighted complete graph, and every two images are connected to represent the edge on the weighted complete image, the weighted value of which represents the similarity between adjacent images. Then, the CTQW is executed to realize the image two-classification based on the quantum walk model of the weighted complete graph, that is, the CTQW is performed from two types of unrelated images, and the two-classification of images is realized that the relevant and unrelated labels are assigned to each image according to the obtained probability distribution two-classification. Finally, the experimental results show that the proposed two-classification algorithm based on CTQW has a good classification effect from the visual effect, and the evaluation indexes of image classification, such as the average precision rate, the recall rate, and the accuracy rate, are all higher than 0.85. In addition, the proposed image two-classification algorithm based on CTQW can be extended to image multiclassification if the quantum walk is performed using multiple irrelevant pictures as the starting point. Similarly, the extended image multiclassification method also has a better classification effect through the experiments and the evaluation indexes of image classification.

Prioritizing farm management interventions to improve climate change adaptation and mitigation outcomes—a case study for banana plantations

Intervening into agricultural systems necessarily includes risks, uncertainties, and ultimately unknown outcomes. Decision analysis embraces uncertainty through an interdisciplinary approach that involves relevant stakeholders in evaluating complex decisions. We applied decision analysis approaches to prioritize 21 farm management interventions, which could be considered in certification schemes for banana production. We estimated their contribution to climate change adaptation and mitigation as well as ecological outcomes. We used a general model that estimated the impacts of each intervention on adaptation (benefits minus costs), mitigation (global warming potential), ecological parameters (e.g., biodiversity and water and soil quality), and farming aspects (e.g., yield, implementation costs and production risks). We used expert and documented knowledge and presented uncertainties in the form of 90% confidence intervals to feed the model and forecast the changes in system outcomes caused by each intervention compared to a baseline scenario without the measure. By iterating the model function 10,000 times, we obtained probability distributions for each of the outcomes and farm management interventions. Our results suggest that interventions associated with nutrient management (e.g., composting and nutrient management plan) positively affect climate change adaptation, mitigation, and ecological aspects. Measures with no direct yield benefits (e.g., plastic reduction) correlate negatively with adaptation but have positive impacts on ecology. Creating buffer zones and converting low-productivity farmland (incl. unused land) also have positive ecological and adaptation outcomes. Decision analysis can help in prioritizing farm management interventions, which may vary considerably in their relationship with the expected outcomes. Additional work may be required to elaborate a comprehensive assessment of the underlying aspects modulating the impacts of a given measure on the evaluated outcome. Our analysis provides insights on the most promising interventions for banana plantations and may help practitioners and researchers in focusing further studies.

The prevalence of apraxia of speech in chronic aphasia after stroke: A bayesian hierarchical analysis

Apraxia of speech is a motor speech disorder that occurs after lesions to the left cerebral hemisphere, most often concomitant with aphasia. It requires specific approaches in the study of its physiological and neuroanatomical basis and special expertise in clinical care. Knowing its prevalence in patients with aphasia after stroke is therefore relevant for planning specific resources in clinical research and in health care provision. Systematic studies of the frequency of this condition are lacking.We examined the frequency of apraxia of speech in a representative sample of 156 patients with chronic post-stroke aphasia. Three experts classified the patients’ speech by best-practice auditory-perceptual methods. Bayesian hierarchical models were fitted to obtain probability distributions for prevalence estimates. A prior distribution was calculated in two steps, including Bayesian models for published frequency data (step 1) and prevalence estimates from experienced clinicians (step 2). Separate models were fitted for different severity ranges.Overall, a prevalence rate of .44 [.30, .58] was obtained. When only moderate and severe cases were taken into account, the rate was .35 [.23, .49]. After a further restriction to only severe impairment, prevalence dropped to .22 [.12, .34]. Patients identified with apraxia of speech had suffered more severe strokes according to clinical criteria and had more severe aphasias. The presence of apraxia of speech was predicted by the articulation/prosody and syntax rating scales of the Aachen Aphasia Test.Lower prevalence estimates published earlier are probably biased by low sensitivity of assessment instruments for mild speech impairment.

Physical Properties of 29 sdB+dM Eclipsing Binaries in Zwicky Transient Facility

The development of large-scale time-domain surveys provides an opportunity to study the physical properties as well as the evolutionary scenario of B-type subdwarfs (sdBs) and M-type dwarfs (dMs). Here, we obtained 33 sdB+dM eclipsing binaries based on the Zwicky Transient Facility (ZTF) light curves and Gaia Early Data Release 3 (EDR3) parallaxes. By using the PHOEBE code for light curve analysis, we obtain probability distributions for parameters of 29 sdB+dMs. R 1, R 2 and i are well determined, and the average uncertainty of mass ratio q is 0.08. Our parameters are in good agreement with previous works if a typical mass of sdB is assumed. Based on parameters of 29 sdB+dMs, we find that both the mass ratio q and the companion’s radius R 2 decrease with the shortening of the orbital period. For the three sdB+dMs with orbital periods less than 0.075 days, their companions are all brown dwarfs. The masses and radii of the companions satisfy the mass–radius relation for low-mass stars and brown dwarfs. Companions with radii between 0.12 R ⊙ and 0.15 R ⊙ seem to be missing in the observations. As more short-period sdB+dM eclipsing binaries are discovered and classified in the future with ZTF and Gaia, we will have more information to constrain the evolutionary ending of sdB+dMs.

Methodology for dynamic reliability assessment of team situation awareness of digital nuclear power plants

Team situation awareness (TSA) reliability is an important factor for team reliability. Moreover, situation awareness (SA) is a prominent problem in digital nuclear power plants (NPPs). Currently, since there is no suitable method to dynamically assess TSA reliability, we constructed a dynamical assessment method of TSA reliability based on a dynamic Bayesian network (DBN) to evaluate TSA reliability. First of all, a TSA causal concept model through qualitative analysis, expert group discussion and sample data analysis. On this basis, the quantitative assessment method of TSA reliability was constructed based on DBN and obtained probability distribution of variables. A standardized method was established to obtain the probability distribution of variables. Furthermore, we evaluated TSA dynamic reliability in a steam generator tube rupture (SGTR) accident. The results showed that the error probability of TSA decreased, and the level of TSA reliability continuously increased in SGTR. TSA reliability can be dynamically predicted by causal reasoning, the most important cause of TSA error could be identified by diagnostic reasoning, which provided theoretical support for the targeted prevention of human error. Finally, this established method was proved to be reasonable through sensitivity analysis.

A Multilayer CARU Framework to Obtain Probability Distribution for Paragraph-Based Sentiment Analysis

Paragraph-based datasets are hard to analyze by a simple RNN, because a long sequence always contains lengthy problems of long-term dependencies. In this work, we propose a Multilayer Content-Adaptive Recurrent Unit (CARU) network for paragraph information extraction. In addition, we present a type of CNN-based model as an extractor to explore and capture useful features in the hidden state, which represent the content of the entire paragraph. In particular, we introduce the Chebyshev pooling to connect to the end of the CNN-based extractor instead of using the maximum pooling. This can project the features into a probability distribution so as to provide an interpretable evaluation for the final analysis. Experimental results demonstrate the superiority of the proposed approach, being compared to the state-of-the-art models.

Sensitivities of heat-wave mortality projections: Moving towards stochastic model assumptions

This paper analyses the probabilistic future behaviour of heat-waves (HWs) in the city of Madrid in the twenty-first century, using maximum daily temperatures from twenty-one climate circulation models under two representative concentration pathways (RCP 8.5 & RCP 4.5). HWs are modelled considering three factors: number per annum, duration and intensity, characterised by three stochastic processes: Poisson, Gamma and truncated Gaussian, respectively. Potential correlations between these processes are also considered. The probabilistic temperature behaviour is combined with an epidemiological model with stochastic mortality risk following a generalized extreme value distribution (gev). The objective of this study is to obtain probability distributions of mortality and risk measures such as the mean value of the 5% of worst cases in the 21st century, in particular from 2025 to 2100. Estimates from stochastic models for characterising HWs and epidemiological impacts on human health can vary from one climate model to another, so relying on a single climate model can be problematic. For this reason, the calculations are carried out for 21 models and the average of the results is obtained. A sensitivity adaptation analysis is also performed. Under RCP 8.5 for 2100 for Madrid city a mean excess of 3.6 °C over the 38 °C temperature threshold is expected as the average of all models, with an expected attributable mortality of 1614 people, but these figures may be substantially exceeded in some cases if the highest-risk cases occur.

Plastic strain rate quantified from dislocation dynamics in dusty plasma shear flows.

Dynamics of dislocations and defects are investigated in 2D dusty plasma experiments with two counterpropagating flows. It is experimentally demonstrated that the Orowan equation is able to accurately determine the plastic strain rate from the motion of dislocations, well agreeing with the shear rate defined from the drift velocity gradient. For a higher shear rate, the studied system is in the liquidlike flow state, as a result, the determined shear rate from the Orowan equation deviates from its definition. The obtained probability distribution function of dislocations from the experiments clearly shows that the dislocation motion can be divided into the local and gliding ones. All findings above are further verified by the corresponding Langevin dynamical simulations with various levels of shear rates. The dislocation and defect analysis results from these simulations clearly indicate that the defect and dislocation dynamics in the sheared dusty plasmas clearly exhibit two stages as the shear rate increases.

Kinetics of heat-induced changes in foods: A workflow proposal

The goal of kinetic modeling is twofold: i) to increase scientific understanding of the process under study, and ii) to predict product properties in product and process design and shelf life. Reviewing food science literature shows that classical two-step kinetic analysis is most common, by first deriving rate constants for an assumed order of reaction (possibly after linearization to make linear regression possible) and then deriving Arrhenius parameters via linear regression, again after log-linearization. This two-step approach is not without problems and this article proposes an alternative general workflow on the untransformed data using nonlinear, global regression. The basic elements consist of: i) a full statistical analysis of the order of the reaction per temperature, ii) a global analysis of all data simultaneously to estimate Arrhenius parameters while characterizing a possibly varying order via multilevel modeling, iii) evaluation of the resulting model and parameters in terms of fitting and, even more importantly, predictive capacity. The proposed workflow is illustrated with a case study on thermal degradation of carnitin (described in literature as a first-order reaction). A Bayesian approach was used to obtain probability distributions of parameters rather than point estimates, but the common standard frequentist approach can also be applied. Kinetic analysis of the carnitin data for each temperature separately showed that the order varied with temperature between 0.9 and 1.6. Multilevel modeling on all data simultaneously was used to better characterize this variation along with the common Arrhenius parameters. Due to the nature of the Arrhenius equation, reparameterization and rescaling is necessary to avoid strong parameter correlation and numerical difficulties during nonlinear regression. Multilevel modeling of all data showed that the variation of the order with temperature was not that strong as suggested from the separate analyses but it did show that the global order was higher than one. The outcome of the suggested workflow was compared to that of the classical two-step kinetic analysis and showed considerable differences in Arrhenius parameters; this appeared to be due to linearization by taking logarithms of concentration data, at least for this case study. Furthermore, it is illustrated that Bayesian regression leads to better insight into behaviour of parameters and models than least-squares regression in terms of density distributions, parameter correlations and joint confidence intervals. Even more importantly, testing of predictive capacity of kinetic models can be done much more rigorously using the Bayesian approach. • Estimation of uncertainty in reaction order from kinetic data gives insight in reactions. • Multilevel modeling allows variation of reaction order per temperature. • Global regression leads to less uncertainty in model predictions. • Bayesian estimation gives more insight in regression parameters than least-squares. • Logarithmic transformation in Arrhenius regression leads to biased estimates.