Bayesian Predictive Framework Research Articles

Leveraging the ETAS model to forecast mining microseismicity

SUMMARY Mining operations result in changes of the subsurface stress field that can lead to the occurrence of microseismic events. The development of strategies for forecasting and avoidance of significant events is crucial for safe and efficient operations of mines. One such example, discussed here is the observed induced microseismicity in soft rock potash mines. It is primarily driven by the rock excavations but can also be triggered by preceding events or can result from the delayed effects of plastic creep of soft rocks. Therefore, it is important from seismic hazard assessment and risk mitigation points of view to understand the statistical aspects of microseismicity in potash or other types of mines. In this study, the temporal evolution of the induced microseismicity from a potash mine in Saskatchewan is analysed and modelled. Specifically, the epidemic type aftershock sequence model is used to approximate the occurrence rate of the induced mining microseismicity. The estimated parameters signify that the microseismicity displays swarm-type characteristics with limited inter-event triggering. Moreover, the Bayesian predictive framework is used to compute the probabilities of the occurrences of the largest expected events above a certain magnitude for prescribed forecasting time intervals during the evolution of the sequence. This approach for computing the probabilities allows one to incorporate fully the uncertainties of the model parameters. The Markov Chain Monte Carlo sampling of the posterior distribution are used to generate parameter chains to quantify their variability. Furthermore, several statistical tests are conducted to assess the credibility of the obtained retrospective forecasts compared to the observed microseismicity. The obtained results show that the developed approach can accurately forecast the number of events and intensity of the sequence. It also provides a framework for computing the probabilities for the largest expected events.

The Analysis of the Aftershock Sequences of the Recent Mainshocks in Alaska

The forecasting of the evolution of natural hazards is an important and critical problem in natural sciences and engineering. Earthquake forecasting is one such example and is a difficult task due to the complexity of the occurrence of earthquakes. Since earthquake forecasting is typically based on the seismic history of a given region, the analysis of the past seismicity plays a critical role in modern statistical seismology. In this respect, the recent three significant mainshocks that occurred in Alaska (the 2002, Mw 7.9 Denali; the 2018, Mw 7.9 Kodiak; and the 2018, Mw 7.1 Anchorage earthquakes) presented an opportunity to analyze these sequences in detail. This included the modelling of the frequency-magnitude statistics of the corresponding aftershock sequences. In addition, the aftershock occurrence rates were modelled using the Omori–Utsu (OU) law and the Epidemic Type Aftershock Sequence (ETAS) model. For each sequence, the calculation of the probability to have the largest expected aftershock during a given forecasting time interval was performed using both the extreme value theory and the Bayesian predictive framework. For the Bayesian approach, the Markov Chain Monte Carlo (MCMC) sampling of the posterior distribution was performed to generate the chains of the model parameters. These MCMC chains were used to simulate the models forward in time to compute the predictive distributions. The calculation of the probabilities to have the largest expected aftershock to be above a certain magnitude after a mainshock using the Bayesian predictive framework fully takes into account the uncertainties of the model parameters. Moreover, in order to investigate the credibility of the obtained forecasts, several statistical tests were conducted to compare the performance of the earthquake rate models based on the OU formula and the ETAS model. The results indicate that the Bayesian approach combined with the ETAS model produced more robust results than the standard approach based on the extreme value distribution and the OU law.

Statistics and Forecasting of Aftershocks During the 2019 Ridgecrest, California, Earthquake Sequence

AbstractThe 2019 Ridgecrest, California, earthquake sequence represents a complex pattern of seismicity that is characterized by the occurrence of a well‐defined foreshock sequence followed by a mainshock and subsequent aftershocks. In this study, a detailed statistical analysis of the sequence is performed. Particularly, the parametric modeling of the frequency‐magnitude statistics and the earthquake occurrence rate is carried out. It is shown that the clustering of earthquakes plays an important role during the evolution of this sequence. In addition, the problem of constraining the magnitude of the largest expected aftershocks to occur during the evolution of the sequence is addressed. In order to do this, two approaches are considered. The first one is based on the extreme value theory, whereas the second one uses the Bayesian predictive framework. The latter approach has allowed to incorporate the complex earthquake clustering through the Epidemic Type Aftershock Sequence (ETAS) process and the uncertainties associated with the model parameters into the computation of the corresponding probabilities. The results indicate that the inclusion of the foreshock sequence into the analysis produces higher probabilities for the occurrence of the largest expected aftershocks after the M7.1 mainshock compared to the approach based on the extreme value distribution combined with the Omori‐Utsu formula for the earthquake rate. Several statistical tests are applied to verify the forecast.

Evaluating regional climate-electricity demand nexus: A composite Bayesian predictive framework

Climatic variations significantly influence the shape of end-use electricity demand curves. Although the climate sensitivity of end-use electricity demand is well-established, projecting medium- and long-term future demand remains a significant challenge—mostly due to a multitude of uncertainties involved in the modeling process. In this paper, we leveraged a state-of-the-art Bayesian approach to develop rigorously validated regional prediction models of the climate–demand nexus conditioned on the intensity level of demand. The prediction models were developed for the residential and commercial sectors for the top eight energy-intensive states in the U.S. A key contribution of this work was to illustrate the asymmetry in the sensitivity of load to climate. More specifically, our results demonstrated a greater sensitivity of the high-intensity end-use demand to climate variability as compared to the moderate-intensity end-use demand. In addition, our results helped identify mean dew point temperature as the key predictor of the climate-sensitive portion of both residential and commercial electricity demands, irrespective of the demand intensity levels. Wind speed was identified as the second most important predictor of the high-intensity (i.e., ≥3rd quartile) end-use demand, while electricity price was found to be the key predictor of the moderate-intensity (i.e., <3rd quartile) end-use demand. The influence of precipitation on the residential and commercial sectors’ moderate end-use demand was found to be more variable. Precipitation was found to influence the commercial sector’s electricity demand more significantly compared to the residential sector's demand.

Can the experimental study of religion be advanced using a Bayesian predictive framework?

ABSTRACTWe propose a Bayesian framework as an important theoretical and methodological tool to improve the scientific study of religion. At a theoretical level, the Bayesian predictive processing framework has the potential to provide a unifying account of religious beliefs and experience by stressing the central role of error monitoring and error correction in belief maintenance. At a methodological level, Bayesian statistics are needed to provide the extraordinary evidence for the extraordinary theoretical claims regarding the causes and consequences of religion.

Bayesian predictive modeling for genomic based personalized treatment selection.

Efforts to personalize medicine in oncology have been limited by reductive characterizations of the intrinsically complex underlying biological phenomena. Future advances in personalized medicine will rely on molecular signatures that derive from synthesis of multifarious interdependent molecular quantities requiring robust quantitative methods. However, highly parameterized statistical models when applied in these settings often require a prohibitively large database and are sensitive to proper characterizations of the treatment-by-covariate interactions, which in practice are difficult to specify and may be limited by generalized linear models. In this article, we present a Bayesian predictive framework that enables the integration of a high-dimensional set of genomic features with clinical responses and treatment histories of historical patients, providing a probabilistic basis for using the clinical and molecular information to personalize therapy for future patients. Our work represents one of the first attempts to define personalized treatment assignment rules based on large-scale genomic data. We use actual gene expression data acquired from The Cancer Genome Atlas in the settings of leukemia and glioma to explore the statistical properties of our proposed Bayesian approach for personalizing treatment selection. The method is shown to yield considerable improvements in predictive accuracy when compared to penalized regression approaches.

A Bayesian Predictive Model for Clustering Data of Mixed Discrete and Continuous Type.

Advantages of model-based clustering methods over heuristic alternatives have been widely demonstrated in the literature. Most model-based clustering algorithms assume that the data are either discrete or continuous, possibly allowing both types to be present in separate features. In this paper, we introduce a model-based approach for clustering feature vectors of mixed type, allowing each feature to simultaneously take on both categorical and real values. Such data may be encountered, for instance, in chemical and biological analyses, in the analysis of survey data, as well as in image analysis. Our model is formulated within a Bayesian predictive framework, where clustering solutions correspond to random partitions of the data. Using conjugate analysis, the posterior probability for each possible partition can be determined analytically, enabling the utilization of efficient computational search strategies for finding the posterior optimal partition. The derived model is illustrated using several synthetic and real datasets.

Hierarchical Factor Models for Large Spatially Misaligned Data: A Low‐Rank Predictive Process Approach

This article deals with jointly modeling a large number of geographically referenced outcomes observed over a very large number of locations. We seek to capture associations among the variables as well as the strength of spatial association for each variable. In addition, we reckon with the common setting where not all the variables have been observed over all locations, which leads to spatial misalignment. Dimension reduction is needed in two aspects: (i) the length of the vector of outcomes, and (ii) the very large number of spatial locations. Latent variable (factor) models are usually used to address the former, although low-rank spatial processes offer a rich and flexible modeling option for dealing with a large number of locations. We merge these two ideas to propose a class of hierarchical low-rank spatial factor models. Our framework pursues stochastic selection of the latent factors without resorting to complex computational strategies (such as reversible jump algorithms) by utilizing certain identifiability characterizations for the spatial factor model. A Markov chain Monte Carlo algorithm is developed for estimation that also deals with the spatial misalignment problem. We recover the full posterior distribution of the missing values (along with model parameters) in a Bayesian predictive framework. Various additional modeling and implementation issues are discussed as well. We illustrate our methodology with simulation experiments and an environmental data set involving air pollutants in California.

SPECIAL ISSUE DEDICATED TO THE 1ST INTERNATIONAL SYMPOSIUM ON UNCERTAINTY QUANTIFICATION AND STOCHASTIC MODELING (UNCERTAINTIES 2012)

International Symposium on Uncertainty Quantification and Stochastic Modeling(Uncertainties 2012), which has taken place at Maresias, city of S˜ao Sebastiao, state of S ˜ao Paulo, Brazil, fromFebruary 26 to March 2, 2012.The meeting was organized on behalf of the Brazilian Society of Mechanical Sciences and Engineering’s (ABCM)Committee on Uncertainty Quantification and Stochastic Modeling, with the objective of providing a proper forumfor discussion of academic, scientific and technical aspects of uncertainty quantification in mechanical systems. Fi-nancial support was provided by the Brazilian Funding Agencies CAPES, FAPESP and CNPq, which are gratefullyacknowledged. Additional operational support from the Structural Engineering Department of S˜ao Carlos Schoolof Engineering (EESC) and from the Brazilian Societies of Applied and Computational Mathematics (SBMAC) andComputational Methods in Engineering (ABMEC) was essential for the meeting’s success.The symposium consisted of 59 oral presentations and 9 keynote lectures covering practical and theoretical aspectsof uncertainty quantification and stochastic modeling, with applications to structural dynamics, nonlinear dynamics,corrosion and damage, structural reliability, optimization, acoustics and vibroacoustics. Based on their contributionsand editorial guidelines, selected presenters were invited to prepare full papers for publication in this special issue.All manuscripts underwent scientific and technical peer review according to the journal standards.The contributions in this special issue include studies on model reduction for dynamics of complex structuresusing a probabilistic approach (Batou and Soize, 2013), reliability-based design optimization of reinforced concretestructures (Aoues et al., 2013), multi-stage bayesian framework for prediction of porous media flow (Ginting et al.,2013), effect of uncertainties on the performance of discrete spatial modal filters (Trindade et al., 2013) and design-point excitation for crack propagation under random loading (Moustapha et al., 2013).In conclusion, we thank the authors for their valuable contributions and also the reviewers for their commentswhich undoubtedly improved the formal and technical value of the articles presented in this special issue.

A Bayesian Framework for Prediction of Seismic Ground Motion

Abstract Current needs of the site-specific hazard and risk analysis for critical facilities and accumulation of the observed records make the development of site-specific ground-motion attenuation relationship feasible. The use of the site-specific attenuation relationship has two advantages: lack of bias and representation of the specific site. This study develops the site-specific attenuation relationship within the Bayesian updating framework. Rather than developing new attenuation relationships, we develop a correction term to the existing past attenuation equation within the Bayesian framework. The correction term is described as a linear function of source magnitude and distance. New data are those observed at the specific site in recent years. Although the use of a prior distribution is one of the most controversial issues of the Bayes’ theorem, both the noninformative prior and the informative prior in terms of the gamma-normal prior are used to develop the posterior distribution for the prediction of ground motion. We feel that the reader should focus on the development of the site-specific attenuation relationship and quantification of the uncertainty of ground-motion prediction. Statistical uncertainty has been ignored in the existing attenuation relationships, while it is not ignorable in the site-specific attenuation relationship due to the limited number of data available at the specific site. This is particularly notable for the ground-motion prediction of large-magnitude-near-source earthquakes where seismic hazard is sensitive. Because the unknown parameters are treated as random variables in the Bayesian approach, the statistical uncertainty associated with them can be quantified in terms of the posterior distribution. The Bayesian methodology will be an effective approach to updating the attenuation relationship on a site basis when new data from observations become available.

Bayesian framework for prediction of future number of failures from a single group of units in the field

This paper considers prediction of unknown number of failures in a future inspection of a group of in-service units based on number of failures observed from an earlier inspection. We develop a flexible Bayesian model and calculate Bayesian estimator for this unknown number and other quantities of interest. The paper also includes an illustration of our method in an example about heat exchanger. A main advantage of our approach is in its nonparametric nature. By nonparametric here we simply mean that no assumption is required about the failure time distribution of a unit.