Reasoning algebraically about probabilistic loops

Back and von Wright have developed algebraic laws for reasoning about loops in the refinement calculus. We extend their work to reasoning about probabilistic loops in the probabilistic refinement calculus. We apply our algebraic reasoning to derive transformation rules for probabilistic action systems. In particular we focus on developing data refinement rules for probabilistic action systems. Our extension is interesting since some well known transformation rules that are applicable to standard programs are not applicable to probabilistic ones: we identify some of these important differences and we develop alternative rules where possible. In particular, our probabilistic action system data refinement rules are new.

Defining civilization utilizing anthropic reasoning

We utilize anthropic reasoning to demonstrate that we are typical observers of our reference class under a self-sampling assumption by investigating the definition of what a civilization is. With reference to the conflict between such reasoning and the observational lack of extra-terrestrial intelligent life, we conclude that a part of our theoretical understanding of the Universe will be at fault.

Use of a probabilistic neural network to reduce costs of selecting construction rock

Rocks used as construction aggregate in temperate climates deteriorate to differing degrees because of repeated freezing and thawing. The magnitude of the deterioration depends on the rock's properties. Aggregate, including crushed carbonate rock, is required to have minimum geotechnical qualities before it can be used in asphalt and concrete. In order to reduce chances of premature and expensive repairs, extensive freeze-thaw tests are conducted on potential construction rocks. These tests typically involve 300 freeze-thaw cycles and can take four to five months to complete. Less time consuming tests that (1) predict durability as well as the extended freeze-thaw test or that (2) reduce the number of rocks subject to the extended test, could save considerable amounts of money. Here we use a probabilistic neural network to try and predict durability as determined by the freeze-thaw test using four rock properties measured on 843 limestone samples from the Kansas Department of Transportation. Modified freeze-thaw tests and less time consuming specific gravity (dry), specific gravity (saturated), and modified absorption tests were conducted on each sample. Durability factors of 95 or more as determined from the extensive freeze-thaw tests are viewed as acceptable—rocks with values below 95 are rejected. If only the modified freeze-thaw test is used to predict which rocks are acceptable, about 45% are misclassified. When 421 randomly selected samples and all four standardized and scaled variables were used to train aprobabilistic neural network, the rate of misclassification of 422 independent validation samples dropped to 28%. The network was trained so that each class (group) and each variable had its own coefficient (sigma). In an attempt to reduce errors further, an additional class was added to the training data to predict durability values greater than 84 and less than 98, resulting in only 11% of the samples misclassified. About 43% of the test data was classed by the neural net into the middle group—these rocks should be subject to full freeze-thaw tests. Thus, use of the probabilistic neural network would meanthat the extended test would only need be applied to 43% of the samples, and 11% of the rocks classed as acceptable would fail early.

Precautionary principles: a jurisdiction-free framework for decision-making under risk

Fundamental principles of precaution are legal maxims that ask for preventive actions, perhaps as contingent interim measures while relevant information about causality and harm remains unavailable, to minimize the societal impact of potentially severe or irreversible outcomes. Such principles do not explain how to make choices or how to identify what is protective when incomplete and inconsistent scientific evidence of causation characterizes the potential hazards. Rather, they entrust lower jurisdictions, such as agencies or authorities, to make current decisions while recognizing that future information can contradict the scientific basis that supported the initial decision. After reviewing and synthesizing national and international legal aspects of precautionary principles, this paper addresses the key question: How can society manage potentially severe, irreversible or serious environmental outcomes when variability, uncertainty, and limited causal knowledge characterize their decision-making? A decision-analytic solution is outlined that focuses on risky decisions and accounts for prior states of information and scientific beliefs that can be updated as subsequent information becomes available. As a practical and established approach to causal reasoning and decision-making under risk, inherent to precautionary decision-making, these (Bayesian) methods help decision-makers and stakeholders because they formally account for probabilistic outcomes, new information, and are consistent and replicable. Rational choice of an action from among various alternatives-defined as a choice that makes preferred consequences more likely-requires accounting for costs, benefits and the change in risks associated with each candidate action. Decisions under any form of the precautionary principle reviewed must account for the contingent nature of scientific information, creating a link to the decision-analytic principle of expected value of information (VOI), to show the relevance of new information, relative to the initial ( and smaller) set of data on which the decision was based. We exemplify this seemingly simple situation using risk management of BSE. As an integral aspect of causal analysis under risk, the methods developed in this paper permit the addition of non-linear, hormetic dose-response models to the current set of regulatory defaults such as the linear, non-threshold models. This increase in the number of defaults is an important improvement because most of the variants of the precautionary principle require cost-benefit balancing. Specifically, increasing the set of causal defaults accounts for beneficial effects at very low doses. We also show and conclude that quantitative risk assessment dominates qualitative risk assessment, supporting the extension of the set of default causal models.

A probabilistic switch model of information flow in social networks: Application for virtual circuits to organizational design

Network building and exchange of information by people within networks is crucial to the innovation process. Contrary to older models, in social networks the flow of information is noncontinuous and nonlinear. There are critical barriers to information flow that operate in a problematic manner. New models and new analytic tools are needed for these systems. This paper introduces the concept of virtual circuits and draws on recent concepts of network modelling and design to introduce a probabilistic switch theory that can be described using matrices. It can be used to model multistep information flow between people within organisational networks, to provide formal definitions of efficient and balanced networks and to describe distortion of information as it passes along human communication channels. The concept of multi-dimensional information space arises naturally from the use of matrices. The theory and the use of serial diagonal matrices have applications to organisational design and to the modelling of other systems. It is hypothesised that opinion leaders or creative individuals are more likely to emerge at information-rich nodes in networks. A mathematical definition of such nodes is developed and it does not invariably correspond with centrality as defined by early work on networks.

Population-based continuous optimization, probabilistic modelling and mean shift

Evolutionary algorithms perform optimization using a population of sample solution points. An interesting development has been to view population-based optimization as the process of evolving an explicit, probabilistic model of the search space. This paper investigates a formal basis for continuous, population-based optimization in terms of a stochastic gradient descent on the Kullback-Leibler divergence between the model probability density and the objective function, represented as an unknown density of assumed form. This leads to an update rule that is related and compared with previous theoretical work, a continuous version of the population-based incremental learning algorithm, and the generalized mean shift clustering framework. Experimental results are presented that demonstrate the dynamics of the new algorithm on a set of simple test problems.

Power system sensitivity analysis for probabilistic small signal stability assessment in a deregulated environment

Deregulations and market practices in power industry have brought great challenges to the system planning area. In particular, they introduce a variety of uncertainties to system planning. New techniques are required to cope with such uncertainties. As a promising approach, probabilistic methods are attracting more and more attentions by system planners. In small signal stability analysis, generation control parameters play an important role in determining the stability margin. The objective of this paper is to investigate power system state matrix sensitivity characteristics with respect to system parameter uncertainties with analytical and numerical approaches and to identify those parameters have great impact on system eigenvalues, therefore, the system stability properties. Those identified parameter variations need to be investigated with priority. The results can be used to help Regional Transmission Organizations (RTOs) and Independent System Operators (ISOs) perform planning studies under the open access environment.

Matching of catalogues by probabilistic pattern classification

We consider the statistical problem of catalogue matching from a machine learning perspective with the goal of producing probabilistic outputs, and using all available information. A framework is provided that unifies two existing approaches to producing probabilistic outputs in the literature, one based on combining distribution estimates and the other based on combining probabilistic classifiers. We apply both of these to the problem of matching the HI Parkes All Sky Survey radio catalogue with large positional uncertainties to the much denser SuperCOSMOS catalogue with much smaller positional uncertainties. We demonstrate the utility of probabilistic outputs by a controllable completeness and efficiency trade-off and by identifying objects that have high probability of being rare. Finally, possible biasing effects in the output of these classifiers are also highlighted and discussed.

Prediction of protein continuum secondary structure with probabilistic models based on NMR solved structures

Background: The structure of proteins may change as a result of the inherent flexibility of some protein regions. We develop and explore probabilistic machine learning methods for predicting a continuum secondary structure, i.e. assigning probabilities to the conformational states of a residue. We train our methods using data derived from high-quality NMR models. Results: Several probabilistic models not only successfully estimate the continuum secondary structure, but also provide a categorical output on par with models directly trained on categorical data. Importantly, models trained on the continuum secondary structure are also better than their categorical counterparts at identifying the conformational state for structurally ambivalent residues. Conclusion: Cascaded probabilistic neural networks trained on the continuum secondary structure exhibit better accuracy in structurally ambivalent regions of proteins, while sustaining an overall classification accuracy on par with standard, categorical prediction methods.

Science-policy in environmental and health risk assessment: if we cannot do without, can we do better?

How can empirical evidence of adverse effects from exposure to noxious agents, which is often incomplete and uncertain, be used most appropriately to protect human health? We examine several important questions on the best uses of empirical evidence in regulatory risk management decision-making raised by the US Environmental Protection Agency (EPA)'s science-policy concerning uncertainty and variability in human health risk assessment. In our view, the US EPA (and other agencies that have adopted similar views of risk management) can often improve decision-making by decreasing reliance on default values and assumptions, particularly when causation is uncertain. This can be achieved by more fully exploiting decision-theoretic methods and criteria that explicitly account for uncertain, possibly conflicting scientific beliefs and that can be fully studied by advocates and adversaries of a policy choice, in administrative decision-making involving risk assessment. The substitution of decision-theoretic frameworks for default assumption-driven policies also allows stakeholder attitudes toward risk to be incorporated into policy debates, so that the public and risk managers can more explicitly identify the roles of risk-aversion or other attitudes toward risk and uncertainty in policy recommendations. Decision theory provides a sound scientific way explicitly to account for new knowledge and its effects on eventual policy choices. Although these improvements can complicate regulatory analyses, simplifying default assumptions can create substantial costs to society and can prematurely cut off consideration of new scientific insights (e.g., possible beneficial health effects from exposure to sufficiently low 'hormetic' doses of some agents). In many cases, the administrative burden of applying decision-analytic methods is likely to be more than offset by improved effectiveness of regulations in achieving desired goals. Because many foreign jurisdictions adopt US EPA reasoning and methods of risk analysis, it may be especially valuable to incorporate decision-theoretic principles that transcend local differences among jurisdictions.

Logic of Violations: A gentzen systems for reasoning with contrary-to-duty obligations

In this paper we present a Gentzen system for reasoning with contrary-to-duty obligations. The intuition behind the system is that a contrary-to-duty is a special kind of normative exception. The logical machinery to formalise this idea is taken from substructural logics and it is based on the definition of a new non-classical connective capturing the notion of reparational obligation. Then the system is tested against well-known contrary-to-duty paradoxes.

Probabilistic world modelling for distributed team planning

This paper describes an application of decoupled probabilistic world modeling to achieve team planning. The research is based on the principle that tbe action selection mechanism of a member in a robot team cm select am effective action if a global world model is available to all team members. In the real world, the sensors are imprecise, and are individual to each robot, hence providing each robot a partial and unique view about the environment. We address this problem by creating a probabilistic global view on each agent by combining the perceptual information from each robot. This probsbilistie view forms the basis for selecting actions to achieve the team goal in a dynamic environment. Experiments have been carried ont to investigate the effectiveness of this principle using custom-built robots for real world performance, in addition, to extensive simulation results. The results show an improvement in team effectiveness when using probabilistic world modeling based on perception sharing for team planning.