Analysis Of Rare Events Research Articles

Rare Event Analysis Considering Data and Model Uncertainty

Abstract In risk analysis of rare events, there is a need to adopt data from different sources with varying levels of detail (e.g., local, regional, categorical data). Therefore, it is very important to identify, understand, and incorporate the uncertainty that accompanies the data. Hierarchical Bayesian analysis (HBA) addresses uncertainty among the aggregated data for each event through generating an informative prior distribution for the event's parameter of interest. The Bayesian network (BN) approach is used to model accident causation. BN enables both inductive and abductive reasoning, which helps to better understand and minimize model uncertainty. In this work, the methodology is proposed to integrate BN with HBA to model rare events, considering both data and model uncertainty. HBA considers data uncertainty, while BN uses an adaptive model to better represent and manage model uncertainty. Application of the proposed methodology is demonstrated using three types of offshore accidents. The proposed methodology provides a way to develop a dynamic risk analysis approach to rare events.

Rare-event analysis of modulated Ornstein–Uhlenbeck processes

This paper studies Ornstein–Uhlenbeck (OU) processes in a random environment. The OU model has found widespread use in networking, as a Gaussian approximation of the user-level dynamics that allows explicit analysis; adding modulation to it allows incorporating phenomena in which the users’ activity level is affected by exogenous factors. The focus lies on rare-event analysis: under a specific scaling of the parameters involved, we establish the large deviations asymptotics of the probability that the process reaches an extreme value. The decay rate of this probability is generally only implicitly available (as the solution to a variational problem), but specializing to the case of Markov modulation we succeed in devising efficient numerical procedures.

A Flexible Hierarchical Bayesian Modeling Technique for Risk Analysis of Major Accidents.

Safety analysis of rare events with potentially catastrophic consequences is challenged by data scarcity and uncertainty. Traditional causation-based approaches, such as fault tree and event tree (used to model rare event), suffer from a number of weaknesses. These include the static structure of the event causation, lack of event occurrence data, and need for reliable prior information. In this study, a new hierarchical Bayesian modeling based technique is proposed to overcome these drawbacks. The proposed technique can be used as a flexible technique for risk analysis of major accidents. It enables both forward and backward analysis in quantitative reasoning and the treatment of interdependence among the model parameters. Source-to-source variability in data sources is also taken into account through a robust probabilistic safety analysis. The applicability of the proposed technique has been demonstrated through a case study in marine and offshore industry.

Employing Scaled Sigma Sampling for Efficient Estimation of Rare Event Probabilities in the Absence of Input Domain Mapping

Traditional techniques for statistical analysis of rare events require a good understanding of the dependence of the outputs on the independent input variables. This can sometimes be an insurmountable challenge, especially when the dimensionality of the input variation space is high. In this paper, we present an innovative scaled sigma sampling (SSS) technique that is able to obtain an accurate quantification of the low probability tails without requiring visibility to the failure regions or their input dimensionality. SSS leverages the probability density differences produced by process sigma scale factors to uncover the nature of the population redistribution induced by the circuit. This understanding is used to construct an efficient transform for the circuit metric, one that has the same sigma scale factor dependency of the cumulative probabilities as the SPICE simulations. This transform is then used to obtain the low probability tails corresponding to the original process distribution. We present representative circuit applications to illustrate the large savings in computational costs that one can achieve with SSS and the transparency and accuracy of this approach.

Statistical Rare-Event Analysis and Parameter Guidance by Elite Learning Sample Selection

Accurately estimating the failure region of rare events for memory-cell and analog circuit blocks under process variations is a challenging task. In this article, we propose a new statistical method, called EliteScope , to estimate the circuit failure rates in rare-event regions and to provide conditions of parameters to achieve targeted performance. The new method is based on the iterative blockade framework to reduce the number of samples, but consists of two new techniques to improve existing methods. First, the new approach employs an elite-learning sample-selection scheme, which can consider the effectiveness of samples and well coverage for the parameter space. As a result, it can reduce additional simulation costs by pruning less effective samples while keeping the accuracy of failure estimation. Second, the EliteScope identifies the failure regions in terms of parameter spaces to provide a good design guidance to accomplish the performance target. It applies variance-based feature selection to find the dominant parameters and then determine the in-spec boundaries of those parameters. We demonstrate the advantage of our proposed method using several memory and analog circuits with different numbers of process parameters. Experiments on four circuit examples show that EliteScope achieves a significant improvement on failure-region estimation in terms of accuracy and simulation cost over traditional approaches. The 16b 6T-SRAM column example also demonstrates that the new method is scalable for handling large problems with large numbers of process variables.

Bayesian analysis of rare events

In many areas of engineering and science there is an interest in predicting the probability of rare events, in particular in applications related to safety and security. Increasingly, such predictions are made through computer models of physical systems in an uncertainty quantification framework. Additionally, with advances in IT, monitoring and sensor technology, an increasing amount of data on the performance of the systems is collected. This data can be used to reduce uncertainty, improve the probability estimates and consequently enhance the management of rare events and associated risks. Bayesian analysis is the ideal method to include the data into the probabilistic model. It ensures a consistent probabilistic treatment of uncertainty, which is central in the prediction of rare events, where extrapolation from the domain of observation is common. We present a framework for performing Bayesian updating of rare event probabilities, termed BUS. It is based on a reinterpretation of the classical rejection-sampling approach to Bayesian analysis, which enables the use of established methods for estimating probabilities of rare events. By drawing upon these methods, the framework makes use of their computational efficiency. These methods include the First-Order Reliability Method (FORM), tailored importance sampling (IS) methods and Subset Simulation (SuS). In this contribution, we briefly review these methods in the context of the BUS framework and investigate their applicability to Bayesian analysis of rare events in different settings. We find that, for some applications, FORM can be highly efficient and is surprisingly accurate, enabling Bayesian analysis of rare events with just a few model evaluations. In a general setting, BUS implemented through IS and SuS is more robust and flexible.

Meta-analysis framework for exact inferences with application to the analysis of rare events.

The usefulness of meta-analysis has been recognized in the evaluation of drug safety, as a single trial usually yields few adverse events and offers limited information. For rare events, conventional meta-analysis methods may yield an invalid inference, as they often rely on large sample theories and require empirical corrections for zero events. These problems motivate research in developing exact methods, including Tian et al.'s method of combining confidence intervals (2009, Biostatistics, 10, 275-281) and Liu et al.'s method of combining p-value functions (2014, JASA, 109, 1450-1465). This article shows that these two exact methods can be unified under the framework of combining confidence distributions (CDs). Furthermore, we show that the CD method generalizes Tian et al.'s method in several aspects. Given that the CD framework also subsumes the Mantel-Haenszel and Peto methods, we conclude that the CD method offers a general framework for meta-analysis of rare events. We illustrate the CD framework using two real data sets collected for the safety analysis of diabetes drugs.

Accelerated failure identification sampling for probability analysis of rare events

Critical engineering systems generally demand high reliability while considering uncertainties, which makes failure event identification and reliability analysis based on computer simulation codes computationally very expensive. Rare event can be defined as a failure event that has a small probability of failure value, normally less than 10ź5. This paper presents a new approach, referred to as Accelerated Failure Identification Sampling (AFIS), for probability analysis of rare events, enabling savings of vast computational efforts. To efficiently identify rare failure sample points in probability analysis, the proposed AFIS technique will first construct a Gaussian process (GP) model for system performance of interest and then utilize the developed model to predict unknown responses of Monte Carlo sample points. Second, a new quantitative measure, namely "failure potential", is developed to iteratively search sample points that have the best chance to be a failure sample point. Third, the identified sample points with highest failure potentials are evaluated for the true performance and then used to update the GP model. The failure identification process will be iteratively preceded and the Monte Carlo simulation will then be employed to estimate probabilities of rare events if the maximum failure potential of existing Monte Carlo samples falls below a given target value. Two case studies are used to demonstrate the effectiveness of the developed AFIS approach for rare events identification and probability analysis.

An island particle algorithm for rare event analysis

Estimating rare event probability with accuracy is of great interest for safety and reliability applications. In this paper, we focus on rare events which can be modeled by a threshold exceedance of a deterministic input–output function with random inputs. Some parameters of this function or density parameters of input random variables may be fixed by an experimenter for simplicity reasons. From a risk analysis point of view, it is not only interesting to evaluate the probability of a critical event but it is also important to determine the impact of such tuning of parameters on the realization of a critical event, because a bad estimation of these parameters can strongly modify rare event probability estimations. In the present paper, we present an example of island particle algorithm referred to as sequential Monte Carlo square (SMC2). This algorithm gives an estimate of the law of random phenomena that leads to critical events. The principles of this statistical technique are described throughout this article and its results are analysed on different realistic aerospace test cases.

Detection and Characterization of Rare Circulating Endothelial Cells by Imaging Flow Cytometry.

Circulating endothelial cells (CECs) are angiogenic cells that appear in increased numbers in the peripheral circulation either as a result of vascular injury or in response to angiogenic stimuli. Elevated levels of CECs have been correlated with various disease states, indicating the use of CECs as a biomarker of disease. Flow cytometry is a widely accepted method for detecting and quantitating CECs. Flow cytometry provides statistical information on large numbers of cells but no information on morphological characteristics. Imaging flow cytometry combines traditional flow cytometry and microscopy, providing a streamlined, multiparameter approach to characterize the biological properties and morphology of large numbers of cells, and is particularly amenable for rare event analysis such as CECs. This approach for identifying and characterizing CECs allows the morphological characterization of large numbers of live, nucleated, single CECs, and alleviates the need for prior enrichment.

T116: Advantages of acoustic focusing in flow cytometry and state of the art microscopy on your bench

The work describes advantages of our latest instrument developments in flow cytometry and microscopy. Characteristics of newly launched flow cytometer, which uses acoustic focusing to align the cells in the focus of the laser for analysis, allows to analyze samples at a much higher throughput rate without losing precision and sensitivity. This opens up new possibilities regarding sample preparation and analysis. These advantages we want to demonstrate on 2 examples, whole blood analysis and rare event analysis. Analysis of biological samples in the most physiologic state with minimal sample preparation and manipulation is a key objective to any workflow. However as whole blood samples generally require significant manipulation, such as wash/centrifugation steps and/or red blood cell lysis, we have developed multiple no-lyse, no-wash assays to minimize these manipulation steps to obtain more physiological results. Here we show how we utilize the rapid sample collection capabilities of the our instrument to characterize phagocyte function in human whole blood with a phagocytosis/phagosome acidification assay and also a dihydrorhodamine 123 superoxide production assay, in a no-lyse, no wash format. Another area where our technology can shift boundaries is the field of rare event analysis. Due to the low frequency of the target cell population a large number of total events (in the range of several millions) need to be acquired. Simply due to the enormous amount of data that needs to be acquired, time becomes a very limiting factor for rare event analysis. As Acoustic Focusing allows analyzing samples at an approximately 10× higher throughput rate without scarifying data quality and maintaining a low coincidence rate, it pushes the limits what can be done in this field. As an example we will show the characterization of human iNKT cells. In addition to flow cytometry we want to show how modern microscopes help to perform a variety of routine and specialty applications.

A4Correlative Light and Electron Microscopy in Cell Biology

In recent years correlative microscopy, combining the power and advantages of light and electron microscopy, has become an important tool for biomedical research. Light microscopy has the advantage of easily searching large areas, even volumes, for the cells of interest, e.g., a special cell type in tissue, astrocytes in brain, [ 1 ] or for cells that have been modified either by transfections or by RNAi in a large population of non-modified cells. Also on thin sections, the low magnification of light microscopy and therefore ease of searching large areas are very beneficial to speed-up the analysis of rare events [ 2 ]. The predominant disadvantage of this technique, however, is that only the fluorescently labelled structures can be imaged in relation to each other. Electron microscopy reveals the cellular ultrastructure a high resolution and individual organelles, cytoskeleton or ribosomes can unequivocally identified. Proteins of interest can be labelled with colloidal gold particles and localised to the visible ultrastructural features within the cells. Searching for a few gold particles within a few cells of a large tissue, however, is very cumbersome and can be extremely time consuming.

On computer-intensive simulation and estimation methods for rare-event analysis in epidemic models.

This article focuses, in the context of epidemic models, on rare events that may possibly correspond to crisis situations from the perspective of public health. In general, no close analytic form for their occurrence probabilities is available, and crude Monte Carlo procedures fail. We show how recent intensive computer simulation techniques, such as interacting branching particle methods, can be used for estimation purposes, as well as for generating model paths that correspond to realizations of such events. Applications of these simulation-based methods to several epidemic models fitted from real datasets are also considered and discussed thoroughly.

An exploratory analysis of occupational accidents and risks from nuclear reactors in India

Modeling analysis of rare events like occupational accidents from nuclear power plants are crucial to understand potential risks. India is poised for a major expansion of civil nuclear energy in the coming decades; such an analysis with this background becomes more important. With this background, this paper explores the pattern of the historical data on severity and frequency of accidents in the select nuclear power plants of India. Based on the historical trend, econometric projections have been undertaken on the estimates of fatality, severity rates within the different uncertainty limits. Results of the projection exercise seem to indicate that there is a probable likelihood of a rise in fatal accidents in nuclear power plants in the absence of incremental safety culture. Further, through a downscaled analysis of global nuclear accidents, the severity and frequency rates of accidents for the Indian nuclear power plants are estimated. Overall, appreciative of the fact that there has not been many major accidents in the past, the results however communicate there is a need to continuously step up policy interventions and safety culture to tackle fatal accidents in nuclear power plants of India.

Rare event counting of CD59- red cells in human blood: A 47-month experience using PNH consensus guidelines for WBC and RBC testing in a reference lab.

Paroxysmal nocturnal hemoglobinuria (PNH) is a rare acquired disorder characterized by increased complement-mediated lysis of erythrocytes (RBCs) because of low/absent glycophosphatidylinositol (GPI) anchors of numerous cell surface proteins. Rare event analysis was applied to 120 million RBCs (12 normal individuals) and 102 million RBCs (102 normal individuals) to establish a reference range and verify a methodology for rare event analysis. Patient PNH testing (n = 10,984) was performed over 47 months using the 2010 consensus guidelines with CD59-PE and glycophorin A-FITC for RBCs and FLAER-Alexa 488, CD33-PerCP-Cy5.5, CD15-APC, CD14-APC-Cy7, and CD24-PE for WBCs. The distribution of CD59- RBCs in the normal population was asymmetric with a mean of 5.9, median between 3 and 4, and mode of 2 per million RBCs. The normal range of CD59- RBCs was 0-17/million RBCs. A natural cutoff of 2.5% of the peak expression of CD59 delineates CD59+ from CD59- populations. The incidence of GPI- samples received by the laboratory was 6-7% without correlation to age (P = 0.35) or sex (P = 0.45). The percentage of GPI- neutrophils and monocytes were strongly correlated (R(2) = 0.96) and usually greater than the percentage of GPI- RBCs. PNH RBC testing is a good example of rare event analysis applied to clinical cytometry—only 2.5 min are required to collect 1 million RBCs. With an established normal range of CD59- RBCs, the correlation between total cell count and sensitivity for detecting an abnormal population can be calculated using Poisson statistics.

Moderate deviations for interacting processes

This article is concerned with moderate deviation principles of a class of interacting empirical processes. We derive an explicit description of the rate function, and we illustrate these results with Feynman-Kac particle models arising in nonlinear filtering, statistical machine learning, rare event analysis, and computational physics. We discuss functional moderate deviations of the occupation measures for both the strong τ -topology on the space of finite and bounded measures as well as for the corresponding stochastic processes on some class of functions equipped with the uniform topology, yielding the first results of this type for mean field interacting processes. Our approach is based on an original semigroup analysis combined with Orlicz norm inequalities, stochastic perturbation techniques, and projective limit large deviation methods.

Analysis and simulation of rare events for SPDEs

In this work, we consider the numerical estimation of the probability for a stochastic process to hit a set B before reaching another set A. This event is assumed to be rare. We consider reactive trajectories of the stochastic Allen-Cahn partial differential evolution equation (with double well potential) in dimension 1. Reactive trajectories are defined as the probability distribution of the trajectories of a stochastic process, conditioned by the event of hitting B before A. We investigate the use of the so-called Adaptive Multilevel Splitting algorithm in order to estimate the rare event and simulate reactive trajectories. This algorithm uses a \emph{reaction coordinate} (a real valued function of state space defining level sets), and is based on (i) the selection, among several replicas of the system having hit A before B, of those with maximal reaction coordinate; (ii) iteration of the latter step. We choose for the reaction coordinate the average magnetization, and for B the minimum of the well opposite to the initial condition. We discuss the context, prove that the algorithm has a sense in the usual functional setting, and numerically test the method (estimation of rare event, and transition state sampling).

Equation-free Model Reduction in Agent-based Computations: Coarse-grained Bifurcation and Variable-free Rare Event Analysis

We study the coarse-grained, reduced dynamics of an agent-based market model due to Omurtag and Sirovich []. We first describe the large agent number, deterministic limit of the system dynamics by performing numerical bifurcation calculations on a continuum approximation of their model. By exploring a broad parameter space, we observe several interesting phenomena including turning points leading to unstable stationary agent density distributions as well as a type of “termination point.” Close to these deterministic turning points we expect the stochastic underlying model to exhibit rare event transitions. We then proceed to discuss a coarse-grained approach to the quantitative study of these rare events. The basic assumption is that the dynamics of the system can be decomposed into fast (noise) and slow (single reaction coordinate) dynamics, so that the system can be described by an effective, coarse-grained Fokker-Planck(FP) equation. An explicit form of this effective FP equation is not available; in our computations we bypass the lack of a closed form equation by numerically estimating its components - the drift and diffusion coefficients - from ensembles of short bursts of microscopic simulations with judiciously chosen initial conditions. The reaction coordinate is first constructed based on our understanding of the continuum model close to the turning points, and it gives results reasonably close to those from brute-force direct simulations. When no guidelines for the selection of a good reaction coordinate are available, data-mining tools, in particular Diffusion Maps, can be used to determine a suitable reaction coordinate. In the third part of this work we demonstrate this “variable-free” approach by constructing a reaction coordinate simply based on the data from the simulation itself. This Diffusion Map based, empirical coordinate gives results consistent with the direct simulation.

Identifying Transport Behavior of Single-Molecule Trajectories

Models of biological diffusion-reaction systems require accurate classification of the underlying diffusive dynamics (e.g., Fickian, subdiffusive, or superdiffusive). We use a renormalization group operator to identify the anomalous (non-Fickian) diffusion behavior from a short trajectory of a single molecule. The method provides quantitative information about the underlying stochastic process, including its anomalous scaling exponent. The classification algorithm is first validated on simulated trajectories of known scaling. Then it is applied to experimental trajectories of microspheres diffusing in cytoplasm, revealing heterogeneous diffusive dynamics. The simplicity and robustness of this classification algorithm makes it an effective tool for analysis of rare stochastic events that occur in complex biological systems.

Fatalities above 30,000 feet: characterizing pediatric deaths on commercial airline flights worldwide.

We conducted this study to characterize in-flight pediatric fatalities onboard commercial airline flights worldwide and identify patterns that would have been unnoticed through single case analysis of these relative rare events. Retrospective cohort study of pediatric in-flight medical emergencies resulting in fatalities between January 2010 and June 2013. A ground-based medical support center providing remote medical support to commercial airlines worldwide. Children (age 0-18 yr) who experienced a medical emergency resulting in death during a commercial airline flight. None. There were a total of 7,573 in-flight medical emergencies involving children reported to the ground-based medical support center, resulting in 10 deaths (0.13% of all pediatric in-flight emergencies). The median subject age was 3.5 months with 90% being younger than 2 years, the age until which children are allowed to travel sharing a seat with an adult passenger, also known as lap infants. Six patients had no previous medical history, with one suffering cardiorespiratory arrest after developing acute respiratory distress during flight and five found asystolic (including four lap infants). Four subjects had preflight medical conditions, including two children traveling for the purpose of accessing advanced medical care. Pediatric in-flight fatalities are rare, but death occurs most commonly in infants and in subjects with a preexisting medical condition. The number of fatalities involving seemingly previously healthy children under the age of 2 years (lap infants) is intriguing and could indicate a vulnerable population at increased risk of death related to in-flight environmental factors, sleeping arrangements, or yet another unrecognized factor.