Construction of nonparametric Bayesian models from parametric Bayes equations

We consider the general problem of constructing nonparametric Bayesian models on infinite-dimensional random objects, such as functions, infinite graphs or infinite permutations. The problem has generated much interest in machine learning, where it is treated heuristically, but has not been studied in full generality in non-parametric Bayesian statistics, which tends to focus on models over probability distributions. Our approach applies a standard tool of stochastic process theory, the construction of stochastic processes from their finite-dimensional marginal distributions. The main contribution of the paper is a generalization of the classic Kolmogorov extension theorem to conditional probabilities. This extension allows a rigorous construction of nonparametric Bayesian models from systems of finite-dimensional, parametric Bayes equations. Using this approach, we show (i) how existence of a conjugate posterior for the nonparametric model can be guaranteed by choosing conjugate finite-dimensional models in the construction, (ii) how the mapping to the posterior parameters of the nonparametric model can be explicitly determined, and (iii) that the construction of conjugate models in essence requires the finite-dimensional models to be in the exponential family. As an application of our constructive framework, we derive a model on infinite permutations, the nonparametric Bayesian analogue of a model recently proposed for the analysis of rank data.

An examination of strain space versus stress space for the formulation of elastoplastic constitutive models

Several elastoplastic soil models have been proposed over the years that are formulated in strain space rather than stress space due to certain analytical and computational advantages. One such model, BRICK (Simpson 1992), has been continuously utilized and developed for industrial applications within Arup Geotechnics for more than two decades. This paper aims to describe the advantages and difficulties associated with strain space modeling. In addition, it will show how recent advances in modeling the effects of stress history, stiffness anisotropy, strength anisotropy and time-dependence in conventional stress space models can be transferred to the BRICK model. © 2010 Taylor & Francis Group, London.

Auto-calibration of a camera system using Image Alignment

Calibration of a camera system is a necessary step in any stereo metric process. It correlates all cameras to a common coordinate system by measuring the intrinsic and extrinsic parameters of each camera. Currently, manual calibration of a camera system is the only way to achieve calibration in civil engineering operations that require stereo metric processes (photogrammetry, videogrammetry, vision based asset tracking, etc). This type of calibration however is time-consuming and labor-intensive. Furthermore, in civil engineering operations, camera systems are exposed to open, busy sites. In these conditions, the position of presumably stationary cameras can easily be changed due to external factors such as wind, vibrations or due to an unintentional push/touch from personnel on site. In such cases manual calibration must be repeated. In order to address this issue, several self-calibration algorithms have been proposed. These algorithms use Projective Geometry, Absolute Conic and Kruppa Equations and variations of these to produce processes that achieve calibration. However, most of these methods do not consider all constraints of a camera system such as camera intrinsic constraints, scene constraints, camera motion or varying camera intrinsic properties. This paper presents a novel method that takes all constraints into consideration to auto-calibrate cameras using an image alignment algorithm originally meant for vision based tracking. In this method, image frames are taken from cameras. These frames are used to calculate the fundamental matrix that gives epipolar constraints. Intrinsic and extrinsic properties of cameras are acquired from this calculation. Test results are presented in this paper with recommendations for further improvement.

Calibration of the spring constant of cantilevers of arbitrary shape using the phase signal in an atomic force microscope.

The measurement of cantilever parameters is an essential part of performing a calibrated measurement with an atomic force microscope (AFM). The thermal motion method is a widely used technique for calibrating the spring constant of an AFM cantilever, which can be applied to non-rectangular cantilevers. Given the trend towards high frequency scanning, calibration of non-rectangular cantilevers is of increasing importance. This paper presents two results relevant to cantilever calibration via the thermal motion method. We demonstrate the possibility of using the AFM's phase signal to acquire the thermal motion. This avoids the challenges associated with connecting the raw photodiode signal to a separate spectrum analyser. We also describe how numerical calculations may be used to calculate the parameters needed in a thermal motion calibration of a non-rectangular cantilever. Only accurate knowledge of the relative size of the in-plane dimensions of the cantilever is needed in this computation. We use this pair of results in the calibration of a variety of rectangular and non-rectangular cantilevers. We observe an average difference between the Sader and thermal motion values of cantilever stiffness of 10%.

Factorial comparison of working memory models.

Three questions have been prominent in the study of visual working memory limitations: (a) What is the nature of mnemonic precision (e.g., quantized or continuous)? (b) How many items are remembered? (c) To what extent do spatial binding errors account for working memory failures? Modeling studies have typically focused on comparing possible answers to a single one of these questions, even though the result of such a comparison might depend on the assumed answers to both others. Here, we consider every possible combination of previously proposed answers to the individual questions. Each model is then a point in a 3-factor model space containing a total of 32 models, of which only 6 have been tested previously. We compare all models on data from 10 delayed-estimation experiments from 6 laboratories (for a total of 164 subjects and 131,452 trials). Consistently across experiments, we find that (a) mnemonic precision is not quantized but continuous and not equal but variable across items and trials; (b) the number of remembered items is likely to be variable across trials, with a mean of 6.4 in the best model (median across subjects); (c) spatial binding errors occur but explain only a small fraction of responses (16.5% at set size 8 in the best model). We find strong evidence against all 6 documented models. Our results demonstrate the value of factorial model comparison in working memory.

Automatic construction and natural-language description of nonparametric regression models

Copyright © 2014, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. This paper presents the beginnings of an automatic statistician, focusing on regression problems. Our system explores an open-ended space of statistical models to discover a good explanation of a data set, and then produces a detailed report with figures and natural- language text. Our approach treats unknown regression functions non- parametrically using Gaussian processes, which has two important consequences. First, Gaussian processes can model functions in terms of high-level properties (e.g. smoothness, trends, periodicity, changepoints). Taken together with the compositional structure of our language of models this allows us to automatically describe functions in simple terms. Second, the use of flexible nonparametric models and a rich language for composing them in an open-ended manner also results in state- of-the-art extrapolation performance evaluated over 13 real time series data sets from various domains.

Comparison of moment-curvature models for fiber-reinforced polymer plate-end debonding studies using global energy balance approach

This paper compares a number of different moment-curvature models for cracked concrete sections that contain both steel and external fiber-reinforced polymer (FRP) reinforcement. The question of whether to use a whole-section analysis or one that considers the FRP separately is discussed. Five existing and three new models are compared with test data for moment-curvature or load deflection behavior, and five models are compared with test results for plate-end debonding using a global energy balance approach (GEBA). A proposal is made for the use of one of the simplified models. The availability of a simplified model opens the way to the production of design aids so that the GEBA can be made available to practicing engineers through design guides and parametric studies. Copyright © 2014, American Concrete Institute.

Model structure and uncertainty for stochastic non-point source modelling applications

The uncertainty associated with a rainfall-runoff and non-point source loading (NPS) model can be attributed to both the parameterization and model structure. An interesting implication of the areal nature of NPS models is the direct relationship between model structure (i.e. sub-watershed size) and sample size for the parameterization of spatial data. The approach of this research is to find structural limitations in scale for the use of the conceptual NPS model, then examine the scales at which suitable stochastic depictions of key parameter sets can be generated. The overlapping regions are optimal (and possibly the only suitable regions) for conducting meaningful stochastic analysis with a given NPS model. Previous work has sought to find optimal scales for deterministic analysis (where, in fact, calibration can be adjusted to compensate for sub-optimal scale selection); however, analysis of stochastic suitability and uncertainty associated with both the conceptual model and the parameter set, as presented here, is novel; as is the strategy of delineating a watershed based on the uncertainty distribution. The results of this paper demonstrate a narrow range of acceptable model structure for stochastic analysis in the chosen NPS model. In the case examined, the uncertainties associated with parameterization and parameter sensitivity are shown to be outweighed in significance by those resulting from structural and conceptual decisions. © 2011 Copyright IAHS Press.

The assembly of computational models for the collaborative development of virtual prototypes

In the context of collaborative product development, new requirements need to be accommodated for Virtual Prototyping Simulation (VPS), such as distributed processing and the integration of models created using different tools or languages. Existing solutions focus mainly on the implementation of distributed processing, but this paper explores the issues of combining different models (some of which may be proprietary) developed in different software environments. In this paper, we discuss several approaches for developing VPS, and suggest how it can best be integrated into the design process. An approach is developed to improve collaborative work in a VPS development by combining disparate computational models. Specifically, a system framework is proposed to separate the system-level modeling from the computational infrastructure. The implementation of a simple prototype demonstrates that such a paradigm is viable and thus provides a new means for distributed VPS development. © 2009 by ASME.

Information models used to manage engineering change: A review of the literature 2005-2010

Engineering change is a significant part of any product development programme. Changes can arise at many points throughout the product life-cycle, resulting in rework which can ripple through different stages of the design process. Managing change processes is thus a critical aspect of any design project, especially in complex design. Through a literature review, this paper shows the diversity of information models used by different change management methods proposed in the literature. A classification framework for organising these change management approaches is presented. The review shows an increase in the number of cross-domain models proposed to help manage changes.

Visual pattern recognition models for remote sensing of civil infrastructure

As-built models have been proven useful in many project-related applications, such as progress monitoring and quality control. However, they are not widely produced in most projects because a lot of effort is still necessary to manually convert remote sensing data from photogrammetry or laser scanning to an as-built model. In order to automate the generation of as-built models, the first and fundamental step is to automatically recognize infrastructure-related elements from the remote sensing data. This paper outlines a framework for creating visual pattern recognition models that can automate the recognition of infrastructure-related elements based on their visual features. The framework starts with identifying the visual characteristics of infrastructure element types and numerically representing them using image analysis tools. The derived representations, along with their relative topology, are then used to form element visual pattern recognition (VPR) models. So far, the VPR models of four infrastructure-related elements have been created using the framework. The high recognition performance of these models validates the effectiveness of the framework in recognizing infrastructure-related elements.