A Bayesian regression approach to assess uncertainty in pollutant wash-off modelling

Due to knowledge gaps in relation to urban stormwater quality processes, an in-depth understanding of model uncertainty can enhance decision making. Uncertainty in stormwater quality models can originate from a range of sources such as the complexity of urban rainfall-runoff-stormwater pollutant processes and the paucity of observed data. Unfortunately, studies relating to epistemic uncertainty, which arises from the simplification of reality are limited and often deemed mostly unquantifiable. This paper presents a statistical modelling framework for ascertaining epistemic uncertainty associated with pollutant wash-off under a regression modelling paradigm using Ordinary Least Squares Regression (OLSR) and Weighted Least Squares Regression (WLSR) methods with a Bayesian/Gibbs sampling statistical approach. The study results confirmed that WLSR assuming probability distributed data provides more realistic uncertainty estimates of the observed and predicted wash-off values compared to OLSR modelling. It was also noted that the Bayesian/Gibbs sampling approach is superior compared to the most commonly adopted classical statistical and deterministic approaches commonly used in water quality modelling. The study outcomes confirmed that the predication error associated with wash-off replication is relatively higher due to limited data availability. The uncertainty analysis also highlighted the variability of the wash-off modelling coefficient k as a function of complex physical processes, which is primarily influenced by surface characteristics and rainfall intensity.

Do prediction markets produce well-calibrated probability forecasts?

This article presents new theoretical and empirical evidence on the forecasting ability of prediction markets. We develop a model that predicts that the time until expiration of a prediction market should negatively affect the accuracy of prices as a forecasting tool in the direction of a ‘favourite/longshot bias’. That is, high-likelihood events are underpriced, and low-likelihood events are over-priced. We confirm this result using a large data set of prediction market transaction prices. Prediction markets are reasonably well calibrated when time to expiration is relatively short, but prices are significantly biased for events farther in the future. When time value of money is considered, the miscalibration can be exploited to earn excess returns only when the trader has a relatively low discount rate.

Using the quantum probability ranking principle to rank interdependent documents

A known limitation of the Probability Ranking Principle (PRP) is that it does not cater for dependence between documents. Recently, the Quantum Probability Ranking Principle (QPRP) has been proposed, which implicitly captures dependencies between documents through “quantum interference”. This paper explores whether this new ranking principle leads to improved performance for subtopic retrieval, where novelty and diversity is required. In a thorough empirical investigation, models based on the PRP, as well as other recently proposed ranking strategies for subtopic retrieval (i.e. Maximal Marginal Relevance (MMR) and Portfolio Theory(PT)), are compared against the QPRP. On the given task, it is shown that the QPRP outperforms these other ranking strategies. And unlike MMR and PT, one of the main advantages of the QPRP is that no parameter estimation/tuning is required; making the QPRP both simple and effective. This research demonstrates that the application of quantum theory to problems within information retrieval can lead to significant improvements.

Developing the quantum probability ranking principle

In this work, we summarise the development of a ranking principle based on quantum probability theory, called the Quantum Probability Ranking Principle (QPRP), and we also provide an overview of the initial experiments performed employing the QPRP. The main difference between the QPRP and the classic Probability Ranking Principle, is that the QPRP implicitly captures the dependencies between documents by means of quantum interference". Subsequently, the optimal ranking of documents is not based solely on documents' probability of relevance but also on the interference with the previously ranked documents. Our research shows that the application of quantum theory to problems within information retrieval can lead to consistently better retrieval effectiveness, while still being simple, elegant and tractable.

Integrated approach for diagnostics and prognostics of HP LNG pump based on health state probability estimation

Effective machine fault prognostic technologies can lead to elimination of unscheduled downtime and increase machine useful life and consequently lead to reduction of maintenance costs as well as prevention of human casualties in real engineering asset management. This paper presents a technique for accurate assessment of the remnant life of machines based on health state probability estimation technique and historical failure knowledge embedded in the closed loop diagnostic and prognostic system. To estimate a discrete machine degradation state which can represent the complex nature of machine degradation effectively, the proposed prognostic model employed a classification algorithm which can use a number of damage sensitive features compared to conventional time series analysis techniques for accurate long-term prediction. To validate the feasibility of the proposed model, the five different level data of typical four faults from High Pressure Liquefied Natural Gas (HP-LNG) pumps were used for the comparison of intelligent diagnostic test using five different classification algorithms. In addition, two sets of impeller-rub data were analysed and employed to predict the remnant life of pump based on estimation of health state probability using the Support Vector Machine (SVM) classifier. The results obtained were very encouraging and showed that the proposed prognostics system has the potential to be used as an estimation tool for machine remnant life prediction in real life industrial applications.

Probability and story-telling : normative and descriptive models of juridical proof

The operation of the law rests on the selection of an account of the facts. Whether this involves prediction or postdiction, it is not possible to achieve certainty. Any attempt to model the operation of the law completely will therefore raise questions of how to model the process of proof. In the selection of a model a crucial question will be whether the model is to be used normatively or descriptively. Focussing on postdiction, this paper presents and contrasts the mathematical model with the story model. The former carries the normative stamp of scientific approval, whereas the latter has been developed by experimental psychologists to describe how humans reason. Neil Cohen's attempt to use a mathematical model descriptively provides an illustration of the dangers in not clearly setting this parameter of the modelling process. It should be kept in mind that the labels 'normative' and 'descriptive' are not eternal. The mathematical model has its normative limits, beyond which we may need to critically assess models with descriptive origins.

The Quantum Probability Ranking Principle for Information Retrieval

While the Probability Ranking Principle for Information Retrieval provides the basis for formal models, it makes a very strong assumption regarding the dependence between documents. However, it has been observed that in real situations this assumption does not always hold. In this paper we propose a reformulation of the Probability Ranking Principle based on quantum theory. Quantum probability theory naturally includes interference effects between events. We posit that this interference captures the dependency between the judgement of document relevance. The outcome is a more sophisticated principle, the Quantum Probability Ranking Principle, that provides a more sensitive ranking which caters for interference/dependence between documents’ relevance.

Error and variance bounds on sigmoidal neurons with weight and input errors

Bounds on the expectation and variance of errors at the output of a multilayer feedforward neural network with perturbed weights and inputs are derived. It is assumed that errors in weights and inputs to the network are statistically independent and small. The bounds obtained are applicable to both digital and analogue network implementations and are shown to be of practical value.

A novel ambiguity acceptance test threshold determination method with controllable failure rate

Ambiguity validation as an important procedure of integer ambiguity resolution is to test the correctness of the fixed integer ambiguity of phase measurements before being used for positioning computation. Most existing investigations on ambiguity validation focus on test statistic. How to determine the threshold more reasonably is less understood, although it is one of the most important topics in ambiguity validation. Currently, there are two threshold determination methods in the ambiguity validation procedure: the empirical approach and the fixed failure rate (FF-) approach. The empirical approach is simple but lacks of theoretical basis. The fixed failure rate approach has a rigorous probability theory basis, but it employs a more complicated procedure. This paper focuses on how to determine the threshold easily and reasonably. Both FF-ratio test and FF-difference test are investigated in this research and the extensive simulation results show that the FF-difference test can achieve comparable or even better performance than the well-known FF-ratio test. Another benefit of adopting the FF-difference test is that its threshold can be expressed as a function of integer least-squares (ILS) success rate with specified failure rate tolerance. Thus, a new threshold determination method named threshold function for the FF-difference test is proposed. The threshold function method preserves the fixed failure rate characteristic and is also easy-to-apply. The performance of the threshold function is validated with simulated data. The validation results show that with the threshold function method, the impact of the modelling error on the failure rate is less than 0.08%. Overall, the threshold function for the FF-difference test is a very promising threshold validation method and it makes the FF-approach applicable for the real-time GNSS positioning applications.

Development of fourth-grade students’ understanding of experimental and theoretical probability

Students explored variation and expectation in a probability activity at the end of the first year of a 3-year longitudinal study across grades 4-6. The activity involved experiments in tossing coins both manually and with simulation using the graphing software, TinkerPlots. Initial responses indicated that the students were aware of uncertainty, although an understanding of chance concepts appeared limited. Predicting outcomes of 10 tosses reflected an intuitive notion of equiprobability, with little awareness of variation. Understanding the relationship between experimental and theoretical probability did not emerge until multiple outcomes and representations were generated with the software.

Cost-effective suppression and eradication of invasive predators

Introduced predators can have pronounced effects on naïve prey species; thus, predator control is often essential for conservation of threatened native species. Complete eradication of the predator, although desirable, may be elusive in budget-limited situations, whereas predator suppression is more feasible and may still achieve conservation goals. We used a stochastic predator-prey model based on a Lotka-Volterra system to investigate the cost-effectiveness of predator control to achieve prey conservation. We compared five control strategies: immediate eradication, removal of a constant number of predators (fixed-number control), removal of a constant proportion of predators (fixed-rate control), removal of predators that exceed a predetermined threshold (upper-trigger harvest), and removal of predators whenever their population falls below a lower predetermined threshold (lower-trigger harvest). We looked at the performance of these strategies when managers could always remove the full number of predators targeted by each strategy, subject to budget availability. Under this assumption immediate eradication reduced the threat to the prey population the most. We then examined the effect of reduced management success in meeting removal targets, assuming removal is more difficult at low predator densities. In this case there was a pronounced reduction in performance of the immediate eradication, fixed-number, and lower-trigger strategies. Although immediate eradication still yielded the highest expected minimum prey population size, upper-trigger harvest yielded the lowest probability of prey extinction and the greatest return on investment (as measured by improvement in expected minimum population size per amount spent). Upper-trigger harvest was relatively successful because it operated when predator density was highest, which is when predator removal targets can be more easily met and the effect of predators on the prey is most damaging. This suggests that controlling predators only when they are most abundant is the "best" strategy when financial resources are limited and eradication is unlikely. © 2008 Society for Conservation Biology.

A survey: Error control methods used in bio-cryptography

Integration of biometrics is considered as an attractive solution for the issues associated with password based human authentication as well as for secure storage and release of cryptographic keys which is one of the critical issues associated with modern cryptography. However, the widespread popularity of bio-cryptographic solutions are somewhat restricted by the fuzziness associated with biometric measurements. Therefore, error control mechanisms must be adopted to make sure that fuzziness of biometric inputs can be sufficiently countered. In this paper, we have outlined such existing techniques used in bio-cryptography while explaining how they are deployed in different types of solutions. Finally, we have elaborated on the important facts to be considered when choosing appropriate error correction mechanisms for a particular biometric based solution.

Low probability differentials and the cryptanalysis of full-round CLEFIA-128

So far, low probability differentials for the key schedule of block ciphers have been used as a straightforward proof of security against related-key differential analysis. To achieve resistance, it is believed that for cipher with k-bit key it suffices the upper bound on the probability to be 2− k . Surprisingly, we show that this reasonable assumption is incorrect, and the probability should be (much) lower than 2− k . Our counter example is a related-key differential analysis of the well established block cipher CLEFIA-128. We show that although the key schedule of CLEFIA-128 prevents differentials with a probability higher than 2− 128, the linear part of the key schedule that produces the round keys, and the Feistel structure of the cipher, allow to exploit particularly chosen differentials with a probability as low as 2− 128. CLEFIA-128 has 214 such differentials, which translate to 214 pairs of weak keys. The probability of each differential is too low, but the weak keys have a special structure which allows with a divide-and-conquer approach to gain an advantage of 27 over generic analysis. We exploit the advantage and give a membership test for the weak-key class and provide analysis of the hashing modes. The proposed analysis has been tested with computer experiments on small-scale variants of CLEFIA-128. Our results do not threaten the practical use of CLEFIA.

In search of good probability assessors: An experimental comparison of elicitation rules for confidence judgments

In this paper, we use an experimental design to compare the performance of elicitation rules for subjective beliefs. Contrary to previous works in which elicited beliefs are compared to an objective benchmark, we consider a purely subjective belief framework (confidence in one’s own performance in a cognitive task and a perceptual task). The performance of different elicitation rules is assessed according to the accuracy of stated beliefs in predicting success. We measure this accuracy using two main factors: calibration and discrimination. For each of them, we propose two statistical indexes and we compare the rules’ performances for each measurement. The matching probability method provides more accurate beliefs in terms of discrimination, while the quadratic scoring rule reduces overconfidence and the free rule, a simple rule with no incentives, which succeeds in eliciting accurate beliefs. Nevertheless, the matching probability appears to be the best mechanism for eliciting beliefs due to its performances in terms of calibration and discrimination, but also its ability to elicit consistent beliefs across measures and across tasks, as well as its empirical and theoretical properties.