We explore the effect of dimensionality on the nearest neighbor problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective, we present empirical results on both real and synthetic data sets that demonstrate that this effect can occur for as few as 10-15 dimensions. These results should not be interpreted to mean that high-dimensional indexing is never meaningful; we illustrate this point by identifying some high-dimensional workloads for which this effect does not occur. However, our results do emphasize that the methodology used almost universally in the database literature to evaluate high-dimensional indexing techniques is flawed, and should be modified. In particular, most such techniques proposed in the literature are not evaluated versus simple linear scan, and are evaluated over workloads for which nearest neighbor is not meaningful. Often, even the reported experiments, when analyzed carefully, show that linear scan would outperform the techniques being proposed on the workloads studied in high (10-15) dimensionality!.

When is nearest neighbor meaningful

Simulation and the monte carlo method

Filtering and smoothing methods are used to produce an accurate estimate of the state of a time-varying system based on multiple observational inputs (data). Interest in these methods has exploded in recent years, with numerous applications emerging in fields such as navigation, aerospace engineering, telecommunications, and medicine. This compact, informal introduction for graduate students and advanced undergraduates presents the current state-of-the-art filtering and smoothing methods in a unified Bayesian framework. Readers learn what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages. They also discover how state-of-the-art Bayesian parameter estimation methods can be combined with state-of-the-art filtering and smoothing algorithms. The book’s practical and algorithmic approach assumes only modest mathematical prerequisites. Examples include MATLAB computations, and the numerous end-of-chapter exercises include computational assignments. MATLAB/GNU Octave source code is available for download at www.cambridge.org/sarkka, promoting hands-on work with the methods.

贝叶斯滤波与平滑 (Bayesian filtering and smoothing)

Technical foundations introduction software reliability and system reliability the operational profile software reliability modelling survey model evaluation and recalibration techniques practices and experiences best current practice of SRE software reliability measurement experience measurement-based analysis of software reliability software fault and failure classification techniques trend analysis in validation and maintenance software reliability and field data analysis software reliability process assessment emerging techniques software reliability prediction metrics software reliability and testing fault-tolerant SRE software reliability using fault trees software reliability process simulation neural networks and software reliability. Appendices: software reliability tools software failure data set repository.

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Handbook of software reliability engineering

Estimation of fragility functions using dynamic structural analysis is an important step in a number of seismic assessment procedures. This paper discusses the applicability of statistical inferenc...

Efficient analytical fragility function fitting using dynamic structural analysis

MCMC algorithms for Subset Simulation

Risk based inspection planning for structural systems

Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion

A generic framework for stochastic modeling of deterioration processes is proposed, based on dynamic Bayesian networks. The framework facilitates computationally efficient and robust reliability analysis and, in particular, Bayesian updating of the model with measurements, monitoring, and inspection results. These properties make it ideally suited for near-real time applications in asset integrity management and deterioration control. The framework is demonstrated and investigated through two applications to probabilistic modeling of fatigue crack growth.

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Stochastic Modeling of Deterioration Processes through Dynamic Bayesian Networks

Bayesian updating is a powerful method to learn and calibrate models with data and observations. Because of the difficulties involved in computing the high-dimensional integrals necessary for Bayesian updating, Markov chain Monte Carlo (MCMC) sampling methods have been developed and successfully applied for this task. The disadvantage of MCMC methods is the difficulty of ensuring the stationarity of the Markov chain. We present an alternative to MCMC that is particularly effective for updating mechanical and other computational models, termed Bayesian updating with structural reliability methods (BUS). With BUS, structural reliability methods are applied to compute the posterior distribution of uncertain model parameters and model outputs in general. An algorithm for the implementation of BUS is proposed, which can be interpreted as an enhancement of the classic rejection sampling algorithm for Bayesian updating. This algorithm is based on the subset simulation, and its efficiency is not dependent on the number of random variables in the model. The method is demonstrated by application to parameter identification in a dynamic system, Bayesian updating of the material parameters of a structural system, and Bayesian updating of a random field–based finite-element model of a geotechnical site.

Daniel Straub

Papers

MCMC algorithms for Subset Simulation

Risk based inspection planning for structural systems

Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion

Stochastic Modeling of Deterioration Processes through Dynamic Bayesian Networks

Bayesian Updating with Structural Reliability Methods