Likelihood-based Imprecise Regression

We introduce a new approach to regression with imprecisely observed data, combining likelihood inference with ideas from imprecise probability theory, and thereby taking different kinds of uncertainty into account. The approach is very general and applicable to various kinds of imprecise data, not only to intervals. In the present paper, we propose a regression method based on this approach, where no parametric distributional assumption is needed and interval estimates of quantiles of the error distribution are used to identify plausible descriptions of the relationship of interest. Therefore, the proposed regression method is very robust. We apply our robust regression method to an interesting question in the social sciences. The analysis, based on survey data, yields a relatively imprecise result, reflecting the high amount of uncertainty inherent in the analyzed data set

A method of classification for multisource data in remote sensing based on interval-valued probabilities

An axiomatic approach to intervalued (IV) probabilities is presented, where the IV probability is defined by a pair of set-theoretic functions which satisfy some pre-specified axioms. On the basis of this approach representation of statistical evidence and combination of multiple bodies of evidence are emphasized. Although IV probabilities provide an innovative means for the representation and combination of evidential information, they make the decision process rather complicated. It entails more intelligent strategies for making decisions. The development of decision rules over IV probabilities is discussed from the viewpoint of statistical pattern recognition. The proposed method, so called evidential reasoning method, is applied to the ground-cover classification of a multisource data set consisting of Multispectral Scanner (MSS) data, Synthetic Aperture Radar (SAR) data, and digital terrain data such as elevation, slope, and aspect. By treating the data sources separately, the method is able to capture both parametric and nonparametric information and to combine them. Then the method is applied to two separate cases of classifying multiband data obtained by a single sensor. In each case a set of multiple sources is obtained by dividing the dimensionally huge data into smaller and more manageable pieces based on the global statistical correlation information. By a divide-and-combine process, the method is able to utilize more features than the conventional maximum likelihood method

Causal inference for data centric engineering

The paper reviews methods that seek to draw causal inference from observational data and demonstrates how they can be applied to empirical problems in engineering research. It presents a framework for causal identification based on the concept of potential outcomes and reviews core contemporary methods that can be used to estimate causal quantities. The paper has two aims: first, to provide a consolidated overview of the statistical literature on causal inference for the data centric engineering community; and second, to illustrate how causal concepts and methods can be applied. The latter aim is achieved through Monte Carlo simulations designed to replicate typical empirical problems encountered in engineering research. R code for the simulations is made available for readers to run and adapt and citations are given to real world studies. Causal inference aims to quantify effects that occur due to explicit intervention (or 'treatment') in non-experimental settings, typically for non-randomly assigned treatments. The paper argues that analyses of engineering interventions are often characterized by such conditions, and consequently, that causal inference has immediate and valuable applicability

A variance-based estimation of the resilience indices in the preliminary design optimisation of engineering systems under epistemic uncertainty

This paper presents novel heuristics for the fast conservative approximation of resilience indices in the preliminary design optimisation of engineering systems under uncertainty. Since the uncertain in the early phases of the design process is mainly of an epistemic nature, Dempster–Shafer theory of evidence is proposed as the reasoning framework. The heuristics proposed in this paper are used to partition the uncertainty space in a collection of subsets that is smaller than the full set of focal elements but still provides a good approximation of Belief and Plausibility. Under suitable assumptions, this methodology renders the approximation of the Belief and Plausibility curves cost-effective for large-scale evidence-based models. Its application to the preliminary-design sizing of a small spacecraft solar array under epistemic uncertainty will be demonstrated

Method of Classification for Multisource Data in Remote Sensing Based on Interval-VaIued Probabilities

This work was supported by NASA Grant No. NAGW-925 “Earth Observation Research - Using Multistage EOS-Iike Data” (Principal lnvestigators: David A. Landgrebe and Chris Johannsen). The Anderson River SAR/MSS data set was acquired, preprocessed, and loaned to us by the Canada Centre for Remote Sensing, Department of Energy Mines, and Resources, of the Government of Canada. The importance of utilizing multisource data in ground-cover^ classification lies in the fact that improvements in classification accuracy can be achieved at the expense of additional independent features provided by separate sensors. However, it should be recognized that information and knowledge from most available data sources in the real world are neither certain nor complete. We refer to such a body of uncertain, incomplete, and sometimes inconsistent information as “evidential information.” The objective of this research is to develop a mathematical framework within which various applications can be made with multisource data in remote sensing and geographic information systems. The methodology described in this report has evolved from “evidential reasoning,” where each data source is considered as providing a body of evidence with a certain degree of belief. The degrees of belief based on the body of evidence are represented by “interval-valued (IV) probabilities” rather than by conventional point-valued probabilities so that uncertainty can be embedded in the measures. There are three fundamental problems in the muItisource data analysis based on IV probabilities: (1) how to represent bodies of evidence by IV probabilities, (2) how to combine IV probabilities to give an overall assessment of the combined body of evidence, and (3) how to make a decision when the statistical evidence is given by IV probabilities. This report first introduces an axiomatic approach to IV probabilities, where the IV probability is defined by a pair of set-theoretic functions which satisfy some pre-specified axioms. On the basis of this approach the report focuses on representation of statistical evidence by IV probabilities and combination of multiple bodies of evidence. Although IV probabilities provide an innovative means for the representation and combination of evidential information, they make the decision process rather complicated. It entails more intelligent strategies for making decisions. This report also focuses on the development of decision rules over IV probabilities from the viewpoint of statistical pattern recognition The proposed method, so called “evidential reasoning” method, is applied to the ground-cover classification of a multisource data set consisting of Multispectral Scanner (MSS) data* Synthetic Aperture Radar (SAR) data, and digital terrain data such as elevation, slope, and aspect. By treating the data sources separately, the method is able to capture both parametric and nonparametric information and to combine them. Then the method is applied to two separate cases of classifying multiband data obtained by a single sensor, in each case, a set of multiple sources is obtained by dividing the dimensionally huge data into smaller and more manageable pieces based on the global statistical correlation information. By a Divide-and-Combine process, the method is able to utilize more features than the conventional Maximum Likelihood method

Dempster-Shafer's Basic Probability Assignment Based on Fuzzy Membership Functions

In this paper, an image segmentation method based on Dempster-Shafer evidence theory is proposed. Basic probability assignment (bpa) is estimated in unsupervised way using pixels fuzzy membership degrees derived from image histogram. No assumption is made about the images data distribution. bpa is estimated at pixel level. The effectiveness of the method is demonstrated on synthetic and real images

Active Learning with Statistical Models

For many types of machine learning algorithms, one can compute the statistically `optimal' way to select training data. In this paper, we review how optimal data selection techniques have been used with feedforward neural networks. We then show how the same principles may be used to select data for two alternative, statistically-based learning architectures: mixtures of Gaussians and locally weighted regression. While the techniques for neural networks are computationally expensive and approximate, the techniques for mixtures of Gaussians and locally weighted regression are both efficient and accurate. Empirically, we observe that the optimality criterion sharply decreases the number of training examples the learner needs in order to achieve good performance.Comment: See http://www.jair.org/ for any accompanying file

Preliminary space mission design under uncertainty

This paper proposes a way to model uncertainties and to introduce them explicitly in the design process of a preliminary space mission. Traditionally, a system margin approach is used in order to take them into account. In this paper, Evidence Theory is proposed to crystallise the inherent uncertainties. The design process is then formulated as an Optimisation Under Uncertainties (OUU). Three techniques are proposed to solve the OUU problem: (a) an evolutionary multi-objective approach, (b) a step technique consisting of maximising the belief for different levels of performance, and (c) a clustering method that firstly identifes feasible regions. The three methods are applied to the BepiColombo mission and their effectiveness at solving the OUU problem are compared