Alternative Probabilistic Models Research Articles

The Generalized Long-Term Fault Memory Model and Applications to Paleoseismic Records

ABSTRACT Paleoseismic studies show large variability in earthquake interevent times along a fault, with short intervals often separated by long quiescent periods. Some paleoseismologists have interpreted this variability as a product of an earthquake’s partial strain release with the next earthquake occurring sooner than expected because of the remaining residual strain. However, commonly used probabilistic large earthquake recurrence models attribute this variability purely to chance, not the state of strain on the fault. Here, we present an alternative probabilistic model, built on the long-term fault memory model framework that better reflects the strain accumulation and release process. This generalized long-term fault memory model (GLTFM) predicts that this interevent time variability arises from both chance and the state of strain on the fault. Specifically, it estimates when residual strain is likely present and its impact on the timing of the next earthquake in the sequence. In addition, GLTFM assumes that additional accumulated strain always increases earthquake probability. In contrast, the commonly used lognormal and Brownian passage time models predict that the probability of a large earthquake stays constant or even decreases after it is “overdue” (past the observed average recurrence interval) so additional accumulated strain does not make an earthquake more likely. GLTFM’s simple implementation and versatility should make it a powerful tool in earthquake forecasting.

Impact of Probabilistic Modeling Alternatives on the Seismic Fragility Analysis of Reinforced Concrete Dual Wall–Frame Buildings towards Resilient Designs

Demands to advance toward more resilient and sustainable cities in terms of reducing casualties, economic losses, downtime, and environmental impacts derived from earthquake-induced damage are becoming more frequent. Indeed, accurate evaluations of the seismic performance of buildings via numerical simulations are crucial for the sustainable development of the built environment. Nevertheless, performance estimations could be influenced by alternative probabilistic methods that can be chosen throughout the procedure of building-specific risk assessment, specifically in the construction and validation of fragility functions. This study evaluates the numerical impacts of selecting different probabilistic models on seismic risk metrics for reinforced concrete dual wall–frame buildings. Specifically, alternative probabilistic models are implemented and evaluated for (i) the identification and elimination of unusual observations within the simulated data (i.e., outliers); (ii) the selection and implementation of different Probability Distribution Functions (PDFs) to estimate fragility functions at different limit states (LSs); and (iii) the application of goodness-of-fit tests and information criteria to assess the validity of proposed PDFs. According to the results, the risk measures showed large variability at the extreme building LS (collapse). On the other hand, for a lower LS (service level), the measures remain similar in all the cases despite the methods selected. Further, the variability observed in the collapse response is up to two times that after eliminating data outliers. Finally, the large variability obtained with the evaluated alternative probabilistic modeling methods suggests re-opening the technical discussion over the state of the practice often used in earthquake engineering to improve the decision-making process, mitigating earthquake-induced consequences in an environmentally, economically, and socially beneficial manner.

Block-Term Tensor Decomposition Model Selection and Computation: The Bayesian Way

The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of \emph{blocks} of rank higher than one, a scenario encountered in numerous and diverse applications. Uniqueness conditions and fitting methods have thus been thoroughly studied. Nevertheless, the challenging problem of estimating the BTD model structure, namely the number of block terms, $R$, and their individual ranks, $L_r$, has only recently started to attract significant attention, mainly through regularization-based approaches which entail the need to tune the regularization parameter(s). In this work, we build on ideas of sparse Bayesian learning (SBL) and put forward a fully automated Bayesian approach. Through a suitably crafted multi-level \emph{hierarchical} probabilistic model, which gives rise to heavy-tailed prior distributions for the BTD factors, structured sparsity is \emph{jointly} imposed. Ranks are then estimated from the numbers of blocks ($R$) and columns ($L_r$) of non-negligible energy. Approximate posterior inference is implemented, within the variational inference framework. The resulting iterative algorithm completely avoids hyperparameter tuning, which is a significant defect of regularization-based methods. Alternative probabilistic models are also explored and the connections with their regularization-based counterparts are brought to light with the aid of the associated maximum a-posteriori (MAP) estimators. We report simulation results with both synthetic and real-word data, which demonstrate the merits of the proposed method in terms of both rank estimation and model fitting as compared to state-of-the-art relevant methods.

Statistical Modeling of Networked Solar Resources for Assessing and Mitigating Risk of Interdependent Inverter Tripping Events in Distribution Grids

It is speculated that higher penetration of inverter-based distributed photo-voltaic (PV) power generators can increase the risk of tripping events due to voltage fluctuations. To quantify this risk utilities need to solve the interactive equations of tripping events for networked PVs in real-time. However, these equations are non-differentiable, nonlinear, and exponentially complex, and thus, cannot be used as a tractable basis for solar curtailment prediction and mitigation. Furthermore, load/PV power values might not be available in real-time due to limited grid observability, which further complicates tripping event prediction. To address these challenges, we have employed Chebyshev's inequality to obtain an alternative probabilistic model for quantifying the risk of tripping for networked PVs. The proposed model enables operators to estimate the probability of interdependent inverter tripping events using only PV/load statistics and in a scalable manner. Furthermore, by integrating this probabilistic model into an optimization framework, countermeasures are designed to mitigate massive interdependent tripping events. Since the proposed model is parameterized using only the statistical characteristics of nodal active/reactive powers, it is especially beneficial in practical systems, which have limited real-time observability. Numerical experiments have been performed employing real data and feeder models to verify the performance of the proposed technique.

Identifiability of tree-child phylogenetic networks under a probabilistic recombination-mutation model of evolution

Phylogenetic networks are an extension of phylogenetic trees which are used to represent evolutionary histories in which reticulation events (such as recombination and hybridization) have occurred. A central question for such networks is that of identifiability, which essentially asks under what circumstances can we reliably identify the phylogenetic network that gave rise to the observed data? Recently, identifiability results have appeared for networks relative to a model of sequence evolution that generalizes the standard Markov models used for phylogenetic trees. However, these results are quite limited in terms of the complexity of the networks that are considered. In this paper, by introducing an alternative probabilistic model for evolution along a network that is based on some ground-breaking work by Thatte for pedigrees, we are able to obtain an identifiability result for a much larger class of phylogenetic networks (essentially the class of so-called tree-child networks). To prove our main theorem, we derive some new results for identifying tree-child networks combinatorially, and then adapt some techniques developed by Thatte for pedigrees to show that our combinatorial results imply identifiability in the probabilistic setting. We hope that the introduction of our new model for networks could lead to new approaches to reliably construct phylogenetic networks.

Impact of Hydrogeological Uncertainty on Estimation of Environmental Risks Posed by Hydrocarbon Transportation Networks

AbstractUbiquitous hydrogeological uncertainty undermines the veracity of quantitative predictions of soil and groundwater contamination due to accidental hydrocarbon spills from onshore pipelines. Such predictions, therefore, must be accompanied by quantification of predictive uncertainty, especially when they are used for environmental risk assessment. We quantify the impact of parametric uncertainty on quantitative forecasting of temporal evolution of two key risk indices, volumes of unsaturated and saturated soil contaminated by a surface spill of light nonaqueous‐phase liquids. This is accomplished by treating the relevant uncertain parameters as random variables and deploying two alternative probabilistic models to estimate their effect on predictive uncertainty. A physics‐based model is solved with a stochastic collocation method and is supplemented by a global sensitivity analysis. A second model represents the quantities of interest as polynomials of random inputs and has a virtually negligible computational cost, which enables one to explore any number of risk‐related contamination scenarios. For a typical oil‐spill scenario, our method can be used to identify key flow and transport parameters affecting the risk indices, to elucidate texture‐dependent behavior of different soils, and to evaluate, with a degree of confidence specified by the decision‐maker, the extent of contamination and the correspondent remediation costs.

Variability of Compressive Strength of Concrete Cores

A comprehensive test program was conducted on the compressive strength of concrete cores. The tests involved eight mixes of concrete. Because over 200 tests were conducted, it was possible to undertake an analysis of the concrete cores using the probabilistic treatment of strength. The present work reports a comparative study of alternative probabilistic models to describe the compressive strength of concrete cores. A large class of probability models including two-parameter Weibull, three-parameter Weibull, normal, lognormal, and gamma distributions were validated using test data. This information is useful in the theoretical description of concrete failure. Furthermore, the results were compared in terms of modified Kolmogorov-Smirnov, log-likelihood, and minimum chi-square criterion. The results suggested that none of the described probability methods are adequate for determining the variability of the compressive strength of concrete cores.

Co-evolution Is Incompatible with the Markov Assumption in Phylogenetics

Markov models are extensively used in the analysis of molecular evolution. A recent line of research suggests that pairs of proteins with functional and physical interactions co-evolve with each other. Here, by analyzing hundreds of orthologous sets of three fungi and their co-evolutionary relations, we demonstrate that co-evolutionary assumption may violate the Markov assumption. Our results encourage developing alternative probabilistic models for the cases of extreme co-evolution.

Comment on “Stochastic Analysis of the Transport of Kinetically Sorbing Solutes in Aquifers with Randomly Heterogeneous Hydraulic Conductivity” by H. A. M. Quinodoz and A. J. Valocchi

In this comment the alternative probabilistic model for spatial moments of kinetically sorbing solutes was presented. The main advantage of the presented model is the full closed-form solution for general initial conditions which can be extended even for moments higher than second.The only disadvantage is in the accuracy of the first-order approximation in the residence time distribution for very early times. The comparison with the spatial moments obtained by Quinodoz and Valocchi (1993) for the point source case showed consistency in most parts of the transport timescale. The actual limitation of both theories was discussed from the point that they followed a single-particle discplacement concept. It was shown that to compare the stochastic theory, based on a single-particle displacement approach, with field data, either the ergodicity requirement has to be satisfied (very difficult to achive for the kinetically sorbing solutes) or one has to remove the inherent uncertainty in the mean centroid displacement.

Probabilistic Models for Risk Assessment

Recent concern with the potential for stray carbon fibers to damage electronic equipment and cause economic losses has led to the development of advanced risk‐assessment methods. Risk assessment often requires the synthesis of risk profiles which represent the probability distribution of total annual losses due to a certain set of events or activities. A number of alternative probabilistic models are presented which the authors have used to develop such profiles. Examples are given of applications of these methods to assessment of risk due to conductive fibers released from aircraft or automobile fires. These assessments usually involve a two‐stage approach: estimation of losses for several subclassifications of the overall process, and synthesis of the results into an aggregate risk profile. The methodology presented is capable of treating a wide variety of situations involving sequences of random physical events.

THE STRUCTURE OF PROBABILISTIC TRADE AREA DELIMITATION MODELS

Since D. L. Huff proposed a probabilistic trade area delimitation model for the delimitation of a trade area (the Huff model), a number of attempts applying the extentions of the Huff model have been devised to analyze competitive market behavior. These models are generally called the Huff type model or the multiplicative competitive interaction (M. C. I.) model. The theoretical basis of these models relies to a large extent on the Luce choice axiom. It assumes the one-to-one correspondence between choice ratio which is the probability of a consumer in an area shopping at a certain store and relative utility which is the utility ratio. of a certain store to an aggregate utility of all stores which the consumer can patronage. However, there is no proof of the existence of one-to-one correspondence. Therefore, the Huff' and Hufftype models which rely on the Luce choice axiom do not have the evident store choice mechanism. The purpose of this study is to build an alternative probabilistic model which is strictly defined in terms of consumer behavior, and to compare this model with the Huff and Huff-type models. Main charateristics of this new model are as follows: Let Xi be consumers' utility on the ith store in a given district. As the utility Xi is not the same to all consumers in the district, we assume that randam variable Xi is normally distributed with mean μi and variance σi2. Furthermore, we assume that the probability choosing a certain store is equal to the probability that a certain sore's utility is greater than the . other stores' utility. In case of three stores (denoted 1, 2, 3), the probability that store 1 would be chosen (P1) may be stated as follows _??_here fi(xi) is the probability density function of Xi, the function Zi=(Xi-μi)/σi is normally distributed with mean zero and variance one, and Kj=(X1-μj)/σj. The following results were obtained applying this model to the data about Matsuyama city. 1) Assuming that the consumers evaluations of store attraction is normally distributed and that the choice ratio in which consumers choose a certain store is equal to the probability that the evaluationn of the store is greater than those of the other stores, the author was able to build an alternative probabilistic model which has more clear choice mechanism than the usual ones. 2) The proposed model, as the probabilistic model satisfies the necessary conditions, _??_ 3) The R. M. S. error obtained from the Huff-type model is 9.5% and that obtained from the Huff model is 15.86%. In terms of fitness the former is about 6% better than the latter. This difference is considered to be caused by applying both models to close-by stores which have different selling space. Accordingly, if the Huff model is applied to this situation, it is expected that stores having greater selling space have larger expect ed values than observed ones. 4) As the R. M. S. error obtained from the proposed model is 10.5%, there is no significant difference in terms of the goodness of fit between the proposed model and the Huff-type model. Furthermore, both models have similar distributions of predicted values. 5) Therefore, the proposed model has the same performance as the Huff-type model, and at the same time it has more clear store choice mechanism than the usual probabilistic models.

The validity of the 'energy principle' for noise-induced hearing loss.

The energy principle for noise-induced hearing loss (Burns and Robinson) postulates that equal noise immission levels cause equal hearing losses. Three special variants of this principle (originated with Burns and Robinson) were tested by means of 270 multiple linear and nonlinear regression analyses. Out of a pool of 25 000 protocols, 649 industrial noise workers were selected who had been exposed to a constant daily noise environment. Persons with hearing damage that might be due to factors other than noise and age were excluded. The evidence from these analyses denied the energy principle in almost all cases. Theoretical considerations show that hearing losses in dB due to various causes (noise, age, gunfire, …) cannot be additive at all. Therefore, models with this kind of structure must necessarily fail. Some alternative probabilistic models are suggested