Network Models in Probability and Statistics

Network Models in Probability and Statistics

The artificial neural network, statistical and grey models are established for predicting the filtration properties of melt blown nonwoven fabrics from the processing parameters. The results show that the ANN model yields very accurate predictions and a reasonably good ANN model can be achieved with relatively few data points. The statistical model gives satisfactory prediction results for most cases, and the grey model needs to be improved for precise predictions. The results show great perspective of this research in the field of computer assisted design of melt blowing nonwoven technology.

Neural network prediction of performance parameters of an inclined plate seed metering device and its reverse mapping for the determination of optimum design and operational parameters

Analysis of Railroad Accident Prediction using Zero-truncated Negative Binomial Regression and Artificial Neural Network Model: A Case Study of National Railroad in South Korea

Statistical models are probability models and physical models are causal or deterministic or mixed causal-deterministic-probability models applied to observable propositions. It is observations which turn probability into statistics. Statistical and physical models are thus verifiable, and all use statistics in their verification. All models should be verified, but most aren’t. Classical modeling emphasizes hypothesis or “significance” testing and estimation. No hypothesis test, Bayesian or frequentist, should ever be used. Death to all p-values or Bayes factors! Hypothesis testing does not prove or show cause; therefore, embedded in every test used to claim cause is a fallacy. If cause is known, probability isn’t needed. Neither should parameter-centric (estimation, etc.) methods be used. Instead, use only probability, make probabilistic predictions of observables given observations and other premises, then verify these predictions. Measures of model goodness and observational relevance are given in a language which requires no sophisticated mathematical training to understand. Speak only in terms of observables and match models to measurement. Hypothesis-testing and parameter estimation are responsible for a pandemic of over-certainty in the sciences. Decisions are not probability, a fact with many consequences.

Based on the standardized precipitation index data of 89 meteorological stations in southwest China (Sichuan Province, Yunnan Province, Guizhou Province, Chongqing) during 1961-2010, probability model containing drought duration and drought severity is established by using the theory of run and the Copula function. The influences of the drought sample number on the distribution parameters, the probability and drought return period are discussed. The result shows that the stability of distribution parameters needs larger sample number. The sample number is greater than 50 in some regions and the requirements for sample number of each parameter is not consistent. The sample number of severity distribution parameters is largest. The probability and return period obtained in the case where the sample number is about 10 have no significant difference (the significant level is 0.05) from those in the case where the sample number is 40 in most of region. With the results used as the standard, statistical model can greatly reduce the requirements for the sample number. And then it demonstrates that the distribution function of drought duration and drought severity can still be established in the lack of measurement data and the inconsistency between starting and ending time. Climate warming has no influence on the minimum of sample number. The fluctuation is mostly between -5 to 5. Statistical model has a certain stability. Meanwhile, the division of climate state reduces the need for distribution test sample number and makes it easier to build model.

: Statistical data modeling is a field of statistical reasoning that seeks to fit models to data without using models based on prior theory; rather one seeks to learn the model by a process which could be called statistical model identification. When analyzing a sample X sub 1, ..., X sub n, statisticians should not confine themselves to either fitting a Gaussian distribution, or transforming the data to be Gaussian. Such an approach ignores the importance of bimodality as a feature of observed data, and also ignores the need to fit to data probability model based distributions which could suggest probability models for the causes generating the data. This paper describes an approach to statistical data modeling which emphasizes estimation of quantile and density-quantile functions; it treats the Gaussian distribution as just one of the available distributions. (Author)

A mathematical description of catastrophe in complex systems modeled as a network is presented with emphasis on network topology and its relationship to risk and resilience. We present mathematical formulas for computing risk, resilience, and likelihood of faults in nodes/links of network models of complex systems and illustrate the application of the formulas to simulation of catastrophic failure. This model is not related to nonlinear “Catastrophe theory” by René Thom, E.C. Zeeman and others. Instead, we present a strictly probabilistic network model for estimating risk and resilience—two useful metrics used in practice. We propose a mathematical model of exceedance probability, risk, and resilience and show that these properties depend wholly on vulnerability, consequence, and properties of the network representation of the complex system. We use simulation of the network under simulated stress causing one or more nodes/links to fail, to extract properties of risk and resilience. In this paper two types of stress are considered: viral cascades and flow cascades. One unified definition of risk, MPL, is proposed, and three kinds of resilience illustrated—viral cascading, blocking node/link, and flow resilience. The principal contributions of this work are new equations for risk and resilience and measures of resilience based on vulnerability of individual nodes/links and network topology expressed in terms of spectral radius, bushy, and branchy metrics. We apply the model to a variety of networks—hypothetical and real—and show that network topology needs to be included in any definition of network risk and resilience. In addition, we show how simulations can identify likely future faults due to viral and flow cascades. Simulations of this nature are useful to the practitioner.

A projective network model is a model that enables predictions to be made based on a subsample of the network data, with the predictions remaining unchanged if a larger sample is taken into consideration. An exchangeable model is a model that does not depend on the order in which nodes are sampled. Despite a large variety of non-equilibrium (growing) and equilibrium (static) sparse complex network models that are widely used in network science, how to reconcile sparseness (constant average degree) with the desired statistical properties of projectivity and exchangeability is currently an outstanding scientific problem. Here we propose a network process with hidden variables which is projective and can generate sparse power-law networks. Despite the model not being exchangeable, it can be closely related to exchangeable uncorrelated networks as indicated by its information theory characterization and its network entropy. The use of the proposed network process as a null model is here tested on real data, indicating that the model offers a promising avenue for statistical network modelling.

<div class="section abstract"><div class="htmlview paragraph">The ergonomic design of automobiles has changed over in the last years. It is increasingly being transferred from the usage of two-dimensional templates of the human shape to computer-aided manmodels. So far these models were mainly used for static anthropometric investigations on the drivers workplace. Dynamic questions can be answered only very insufficiently.</div><div class="htmlview paragraph">In the context of this work a methodology was developed to precalculate target directed human movements in a motor vehicle environment with the CAD-manmodel RAMSIS.</div><div class="htmlview paragraph">A new two-piece model was developed. In this model dynamic boundary conditions, so called dynamic restrictions, for any movement in a car are determined, concerning outside parameters. In the following, the entire bodyposture is determined by a statistical posture probability model, considering these dynamic restrictions.</div><div class="htmlview paragraph">A control theory of human movements was derived from the field of neurophysiology. It was adapted to the problems for the application in a manmodel. This theory is used, to generate the necessary dynamic restrictions.</div><div class="htmlview paragraph">For the first time, a statistical angle probability model is used to make the posture prognosis. The model was generated in a preceding work and its suitability to answer dynamic questions was validated within two test series.</div><div class="htmlview paragraph">Altogether 12 different experiments, with in each case 15 test subjects, were carried out within all fields of this work. More than 500 “dynamic “ postures were measured and analysed as well as more than 2500 movements.</div><div class="htmlview paragraph">Within this report the developed strategy, that enables a technical designer to precalculate movements of humans within the manmodel RAMSIS realistically, will be shown. This enables the designer to regard also dynamic questions for the ergonomic design of an automobile.</div></div>

This special issue contains a selection of articles from the Second International Symposium on Imprecise Probabilities and Their Applications (ISIPTA ’01) [4]. The symposium was held at Cornell University, USA, in June 2001, and was chaired by Gert de Cooman, Terrence L. Fine, and Teddy Seidenfeld. It was a successor of the first successful ISIPTA meeting [3]. This was held in 1999, and was intended to promote interaction and communication between researchers in a great diversity of fields but with common interests in imprecise probabilities. ISIPTA ’01 was no exception in this respect: the 47 papers presented there covered a wide and heterogeneous range of topics, such as algorithms, belief change, civil engineering, pattern recognition, coherence, combination of uncertainties, conditioning, credal nets, decision making, economics and finance, elicitation, foundations, independence, mathematical models for uncertainty, probabilistic logic, reliability, and statistical inference. This heterogeneity as well as lively discussions during the meeting, turned ISIPTA ’01 into successful attempt to bring together an interdisciplinary community of researchers actively involved in advancing and promoting a generalized view of probability theories. Shortly after ISIPTA ’01, in February 2002, a few active members in this community decided to found SIPTA, the Society for Imprecise Probability: Theories and Applications. This society manages the organization of the ISIPTA meetings, nowadays a well-established international forum for discussing imprecise probabilities. And, being aware that the field of imprecise probabilities is not always easily accessible, due to its heterogeneity and the related variety of different Flanguages_ used to talk about imprecise probabilities, the Society has also recently started organizing the SIPTA Schools in Imprecise Probabilities, the next of which is due to be held in July 2006 in Madrid, Spain. At this point it is useful to be more precise about the subject of the ISIPTA meetings, namely, imprecise probabilities. The name Fimprecise probability_ was intended from the beginnings in a very wide sense, as a generic term for the many mathematical or statistical models that measure chance or uncertainty without sharp numerical probabilities. These models can be qualitative, such as comparative probability models and partial preference orderings, or quantitative, such as interval probabilities, belief functions, upper and lower expectations or previsions, just to name a few. More important, though, is that imprecise probability models are needed in inference problems characterized by scarce, vague or conflicting information. These

In the Cochrane Database of Systematic Reviews (CDSR) 75% of reported meta-analyses contain five or fewer studies. For a small dataset a reasonable goodness-of-fit test on a statistical model cannot be performed since either it requires a large sample size for the validity of asymptotic approximation or it might be not powerful enough to detect a deviation from the target model. Random effects model under the assumption of normality is commonly used in many fields of science. It also appears to be a classical approach for data reduction in interlaboratory studies in metrology and in meta-analysis in medicine. However, the assumption of normality might not be fulfilled in many practical applications. If a data set is small, then no statistical test on distribution will perform well. The intrinsic Bayes factor is used for selecting an appropriate probability model among several competitors, which not necessarily have to be nested. We apply the proposed methodology to the measurement results used to determine the Newtonian constant of gravitation and the Planck constant.

Enhancing riverine load prediction of anthropogenic pollutants: Harnessing the potential of feed-forward backpropagation (FFBP) artificial neural network (ANN) models

This paper focuses on the application of the principle of demographic gravitation to estimate link-level annual average daily traffic (AADT) based on land-use characteristics. According to the principle, the effect of a variable on AADT of a link decreases with an increase in distance from the link. The spatial variations in land-use characteristics were captured and integrated for each study link using the principle of demographic gravitation. The captured land-use characteristics and on-network characteristics were used as independent variables. Traffic count data available from the permanent count stations in the city of Charlotte, North Carolina, were used as the dependent variable to develop statistical and neural network models. Negative binomial count statistical models (with log-link) were developed as data were observed to be over-dispersed while neural network models were developed based on a multilayered, feed-forward, back-propagation design for supervised learning. The results obtained indicate that statistical and neural network models ensured significantly lower errors when compared to outputs from traditional four-step method used by regional modelers. Overall, the neural network model yielded better results in estimating AADT than any other approach considered in this research. The neural network approach can be particularly suitable for their better predictive capability, whereas the statistical models could be used for mathematical formulation or understanding the role of explanatory variables in estimating AADT.

Inflammation-associated cytokine analysis identifies presence of respiratory bacterial pathogens in the nasopharynx.