Interval probability propagation

AbstractBelief networks are tried as a method for propagation of singleton interval probabilities. A convex polytope representation of the interval probabilities is shown to make the problem intractable even for small parameters. A solution to this is to use the interval bounds directly in computations of the propagation algorithm. The algorithm presented leads to approximative results but has the advantage of being polynomial in time. It is shown that the method gives fairly good results

An Exposition on Bayesian Inference

The Bayesian approach to probability and statistics is described, a brief history of Bayesianism is related, differences between Bayesian and Frequentist schools of statistics are defined, protential applications are investigated, and a literature survey is presented in the form of a machine-sort card file. Bayesian thought is increasing in favor among statisticians because of its ability to attack problems that are unassailable from the Frequentist approach. It should become more popular among practitioners because of the flexibility it allows experimenters and the ease with which prior knowledge can be combined with experimental data. (82 pages

Towards perceptual intelligence : statistical modeling of human individual and interactive behaviors

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Architecture, 2000.Includes bibliographical references (p. 279-297).This thesis presents a computational framework for the automatic recognition and prediction of different kinds of human behaviors from video cameras and other sensors, via perceptually intelligent systems that automatically sense and correctly classify human behaviors, by means of Machine Perception and Machine Learning techniques. In the thesis I develop the statistical machine learning algorithms (dynamic graphical models) necessary for detecting and recognizing individual and interactive behaviors. In the case of the interactions two Hidden Markov Models (HMMs) are coupled in a novel architecture called Coupled Hidden Markov Models (CHMMs) that explicitly captures the interactions between them. The algorithms for learning the parameters from data as well as for doing inference with those models are developed and described. Four systems that experimentally evaluate the proposed paradigm are presented: (1) LAFTER, an automatic face detection and tracking system with facial expression recognition; (2) a Tai-Chi gesture recognition system; (3) a pedestrian surveillance system that recognizes typical human to human interactions; (4) and a SmartCar for driver maneuver recognition. These systems capture human behaviors of different nature and increasing complexity: first, isolated, single-user facial expressions, then, two-hand gestures and human-to-human interactions, and finally complex behaviors where human performance is mediated by a machine, more specifically, a car. The metric that is used for quantifying the quality of the behavior models is their accuracy: how well they are able to recognize the behaviors on testing data. Statistical machine learning usually suffers from lack of data for estimating all the parameters in the models. In order to alleviate this problem, synthetically generated data are used to bootstrap the models creating 'prior models' that are further trained using much less real data than otherwise it would be required. The Bayesian nature of the approach let us do so. The predictive power of these models lets us categorize human actions very soon after the beginning of the action. Because of the generic nature of the typical behaviors of each of the implemented systems there is a reason to believe that this approach to modeling human behavior would generalize to other dynamic human-machine systems. This would allow us to recognize automatically people's intended action, and thus build control systems that dynamically adapt to suit the human's purposes better.by Nuria M. Oliver.Ph.D

Homeostatic epistemology : reliability, coherence and coordination in a Bayesian virtue epistemology

How do agents with limited cognitive capacities flourish in informationally impoverished or unexpected circumstances? Aristotle argued that human flourishing emerged from knowing about the world and our place within it. If he is right, then the virtuous processes that produce knowledge, best explain flourishing. Influenced by Aristotle, virtue epistemology defends an analysis of knowledge where beliefs are evaluated for their truth and the intellectual virtue or competences relied on in their creation. However, human flourishing may emerge from how degrees of ignorance are managed in an uncertain world. Perhaps decision-making in the shadow of knowledge best explains human wellbeing—a Bayesian approach? In this dissertation I argue that a hybrid of virtue and Bayesian epistemologies explains human flourishing—what I term homeostatic epistemology. \ud \ud Homeostatic epistemology supposes that an agent has a rational credence p when p is the product of reliable processes aligned with the norms of probability theory; whereas an agent knows that p when a rational credence p is the product of reliable processes such that: 1) p meets some relevant threshold for belief (such that the agent acts as though p were true and indeed p is true), 2) p coheres with a satisficing set of relevant beliefs and, 3) the relevant set of beliefs is coordinated appropriately to meet the integrated aims of the agent. \ud \ud Homeostatic epistemology recognizes that justificatory relationships between beliefs are constantly changing to combat uncertainties and to take advantage of predictable circumstances. Contrary to holism, justification is built up and broken down across limited sets like the anabolic and catabolic processes that maintain homeostasis in the cells, organs and systems of the body. It is the coordination of choristic sets of reliably produced beliefs that create the greatest flourishing given the limitations inherent in the situated agent. \u

Risk as a tool in water resource management

Please read the abstract in the section 00front of this documentThesis (PhD (Water Utilisation))--University of Pretoria, 2005.Civil Engineeringunrestricte

On the use of 'improved' estimators in econometrics

This thesis carries a title that might appear to be too extensive as a topic. However, those familiar with the literature on biased estimators may agree that there is a well defined class of estimation procedures of interest to both mathematical statisticians and econometricians. Efforts to introduce ideas which deviate from the traditional classical notion of unbiasedness have encountered enormous resistance. Admittedly, results relating to biased estimators are not as wellestablished as those relating to unbiased estimators, but unbiasedness is an arbitrary and unnecessarily stringent criterion. One should not therefore neglect the usefulness of biased estimators. With this background in mind, the thesis was written to synthesize the many differently motivated contributions which aim at improved estimation of unknown economic linear relationships. Apart from highlighting the author’s own contributions in the area, the author has also attempted to make the thesis a self-contained one. Chapter 1 motivates the study and defines the framework in which new estimators are developed. The fundamentals of Bayesian inference are discussed and the relation between formal and empirical Bayes procedures is examined. Chapter 2 provides a synthesis of different attempts to improve upon the traditional unbiased estimator. This chapter is necessary because it is not generally acknowledged that the differently motivated efforts can lead to the same result - namely, some sort of shrinkage must be introduced to improve estimation and that all the improved estimators are basically generalised Bayes rules. Chapter 3 introduces the controversial ridge estimator and provides a comprehensive survey. A new contribution made in this chapter is the introduction of a recursive algorithm for generating the ridge trace. Chapter 4, 5 and 6 form the core of the thesis where new ideas are developed. Specifically, Chapter 4 attempts theoretical and Monte Carlo studies of the potential and realised reduction in risk of the biased estimators. A number of good adaptive ridge estimators are identified. As an illustration these are applied to re-estimating an investment function. Significantly more accurate predictions are achieved by the biased estimators than by conventional ordinary least squares estimator and the preliminary test estimators. Two new contributions are made in Chapter 5. Firstly, an analysis of seasonal variability in the distributed lag model sets the stage for the introduction of various estimators which can incorporate bi-dimensional prior information in the form of exchangeability and smoothness. Secondly, estimation of distributed lag model in the frequency domain is justified and the Spectral Ridge Estimator is introduced as an extension of Hannan’s Efficient Estimator. The estimator’s performance is compared to other well-known estimators using Almon’s data. Chapter 6 works out the small sample bias and mean square error of a Generalised Ridge Instrumental Variable estimator for a structural equation in the context of a simultaneous equation system. The problem of undersized sample is tackled and the traditional optimism about 2SPC questioned. A new estimator which involves the application of ridge regression instead of the traditional least square regression at both stages of a 2SLS procedure is proposed and its statistical properties analysed (both asymptotically and in finite sample). Some further results concerning ridge regression are presented in the last chapter, i.e. 7. The robustness of ridge regression under misspecification is analysed. Problems of testing stochastic hypotheses and the construction of confidence sets are also discussed. Some of the criticisms of the technique are reviewed and a personal view is expressed

Bayesian spatio-temporal modelling of rainfall through non-homogenous hidden Markov models

Multi-site statistical models for daily rainfall should account for spatial and temporal dependence amongst measurements and also allow for the event of no rain. Recent research into climate change and variability has sparked interest in the relationship between rainfall and climate, stimulating the development of statistical models that relate large-scale atmospheric variables to local precipitation. Although modelling daily rainfall presents a challenging and topical problem, there have been few attempts taking a subjective Bayesian approach. This thesis is concerned with developing hidden Markov models (HMMs) for the spatio-temporal analysis of rainfall data, within a Bayesian framework. In these models, daily rainfall patterns are driven by a finite number of unobserved states, interpreted as weather states, that evolve in time as a first order Markov chain. The weather states explain space time structure in the data so that reasonably simple models can be adopted within states. Throughout this thesis, the models and procedures are illustrated using data from a small dense network of six sites situated in Yorkshire, UK. First we study a simple (homogeneous) HMM in which rainfall occurrences and amounts, given occurrences, are conditionally independent in space and time, given the weather state, and have Bernoulli and gamma distributions, respectively. We compare methods for approximating the posterior distribution for the number of weather states. This simple model does not incorporate atmospheric information and appears not to capture the observed spatio-temporal structure. We therefore investigate two non-homogeneous hidden Markov models (NHMMs) in which we allow the transition probabilities between weather states to depend on time-varying atmospheric variables and successively relax the conditional independence assumptions. The first NHMM retains the simple conditional model for non-zero rainfall amounts but allows occurrences to form a Markov chain of autologistic models, given the weather state. The second introduces latent multivariate normal random variables to form a hierarchical NHMM in which neither rainfall occurrences nor non-zero amounts are conditionally spatially or temporally independent, given the weather state. Throughout this thesis, we emphasise the elicitation of prior distributions that convey genuine initial beliefs. For each hidden Markov model studied we demonstrate techniques to assist in this task.EThOS - Electronic Theses Online ServiceEngineering and Physical Sciences Research CouncilGBUnited Kingdo