On the probability density function of the product of Rayleigh distributed random variables

In this paper we investigate the distribution of the product of Rayleigh distributed random variables. Considering the Mellin-Barnes inversion formula and using the saddle point approach we obtain an upper bound for the product distribution. The accuracy of this tail-approximation increases as the number of random variables in the product increase.

The probability archive : from essence to uncertainty in the mediation of knowledge

This volume puts together the works of a group of distinguished scholars and active researchers in the field of media and communication studies to reflect upon the past, present, and future of new media research. The chapters examine the implications of new media technologies on everyday life, existing social institutions, and the society at large at various levels of analysis. Macro-level analyses of changing techno-social formation – such as discussions of the rise of surveillance society and the "fifth estate" – are combined with studies on concrete and specific new media phenomena, such as the rise of Pro-Am collaboration and "fan labor" online. In the process, prominent concepts in the field of new media studies, such as social capital, displacement, and convergence, are critically examined, while new theoretical perspectives are proposed and explicated. Reflecting the inter-disciplinary nature of the field of new media studies and communication research in general, the chapters interrogate into the problematic through a range of theoretical and methodological approaches. The book should offer students and researchers who are interested in the social impact of new media both critical reviews of the existing literature and inspirations for developing new research questions.

Bearing fault prognosis based on health state probability estimation

In condition-based maintenance (CBM), effective diagnostic and prognostic tools are essential for maintenance engineers to identify imminent fault and predict the remaining useful life before the components finally fail. This enables remedial actions to be taken in advance and reschedule of production if necessary. All machine components are subjected to degradation processes in real environments and they have certain failure characteristics which can be related to the operating conditions. This paper describes a technique for accurate assessment of the remnant life of bearings based on health state probability estimation and historical knowledge embedded in the closed loop diagnostics and prognostics system. The technique uses the Support Vector Machine (SVM) classifier as a tool for estimating health state probability of machine degradation process to provide long term prediction. To validate the feasibility of the proposed model, real life fault historical data from bearings of High Pressure-Liquefied Natural Gas (HP-LNG) pumps were analysed and used to obtain the optimal prediction of remaining useful life (RUL). The results obtained were very encouraging and showed that the proposed prognosis system based on health state probability estimation has the potential to be used as an estimation tool for remnant life prediction in industrial machinery.

The Large Allen Cognitive Level Screen as an indicator for medication adherence among adults accessing community mental health services

Background: Medication remains the cornerstone treatment for mental illness. Cognition is one of the strongest predictors of non-adherence. The aim of this preliminary investigation was to examine the association between the Large Allen Cognitive Level Screen (LACLS) and medication adherence among a small sample of mental health service users to determine whether the LACLS has potential as a screening tool for capacity to manage medication regimens. Method: Demographic and clinical information was collected from a small sample of people who had recently accessed community mental health services. Participants then completed the LACLS and the Medication Adherence Rating Scale (MARS) at a single time point. The strength of association between the LACLS and MARS was examined using Spearman rank-order correlation. Results: A strong positive correlation between the LACLS and medication adherence (r = 0.71, p = 0.01) was evident. No participants reported the use of medication aids despite evidence of impaired cognitive functioning. Conclusion: This investigation has provided the first empirical evidence indicating that the LACLS may have utility as a screening instrument for capacity to manage medication adherence among this population. While promising, this finding should be interpreted with caveats given its preliminary nature.

Sampling stored-product insect pests : a comparison of four statistical sampling models for probability of pest detection

Background: Developing sampling strategies to target biological pests such as insects in stored grain is inherently difficult owing to species biology and behavioural characteristics. The design of robust sampling programmes should be based on an underlying statistical distribution that is sufficiently flexible to capture variations in the spatial distribution of the target species. Results: Comparisons are made of the accuracy of four probability-of-detection sampling models - the negative binomial model,1 the Poisson model,1 the double logarithmic model2 and the compound model3 - for detection of insects over a broad range of insect densities. Although the double log and negative binomial models performed well under specific conditions, it is shown that, of the four models examined, the compound model performed the best over a broad range of insect spatial distributions and densities. In particular, this model predicted well the number of samples required when insect density was high and clumped within experimental storages. Conclusions: This paper reinforces the need for effective sampling programs designed to detect insects over a broad range of spatial distributions. The compound model is robust over a broad range of insect densities and leads to substantial improvement in detection probabilities within highly variable systems such as grain storage.

Training-free probability models for whole-image based place recognition

Whole-image descriptors such as GIST have been used successfully for persistent place recognition when combined with temporal filtering or sequential filtering techniques. However, whole-image descriptor localization systems often apply a heuristic rather than a probabilistic approach to place recognition, requiring substantial environmental-specific tuning prior to deployment. In this paper we present a novel online solution that uses statistical approaches to calculate place recognition likelihoods for whole-image descriptors, without requiring either environmental tuning or pre-training. Using a real world benchmark dataset, we show that this method creates distributions appropriate to a specific environment in an online manner. Our method performs comparably to FAB-MAP in raw place recognition performance, and integrates into a state of the art probabilistic mapping system to provide superior performance to whole-image methods that are not based on true probability distributions. The method provides a principled means for combining the powerful change-invariant properties of whole-image descriptors with probabilistic back-end mapping systems without the need for prior training or system tuning.

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.

The impact of a congestion charging exemption on the demand for new low‐emission vehicles

Numerous initiatives have been employed around the world in order to address rising greenhouse gas (GHG) emissions originating from the transport sector. These measures include: travel demand management (congestion‐charging), increased fuel taxes, alternative fuel subsidies and low‐emission vehicle (LEV) rebates. Incentivizing the purchase of LEVs has been one of the more prevalent approaches in attempting to tackle this global issue. LEVs, whilst having the advantage of lower emissions and, in some cases, more efficient fuel consumption, also bring the downsides of increased purchase cost, reduced convenience of vehicle fuelling, and operational uncertainty. To stimulate demand in the face of these challenges, various incentive‐based policies, such as toll exemptions, have been used by national and local governments to encourage the purchase of these types of vehicles. In order to address rising GHG emissions in Stockholm, and in line with the Swedish Government’s ambition to operate a fossil free fleet by 2030, a number of policies were implemented targeting the transport sector. Foremost amongst these was the combination of a congestion charge – initiated to discourage emissions‐intensive travel – and an exemption from this charge for some LEVs, established to encourage a transition towards a ‘green’ vehicle fleet. Although both policies shared the aim of reducing GHG emissions, the exemption for LEVs carried the risk of diminishing the effectiveness of the congestion charging scheme. As the number of vehicle owners choosing to transition to an eligible LEV increased, the congestion‐reduction effectiveness of the charging scheme weakened. In fact, policy makers quickly recognized this potential issue and consequently phased out the LEV exemption less than 18 months after its introduction (1). Several studies have investigated the demand for LEVs through stated‐preference (SP) surveys across multiple countries, including: Denmark (2), Germany (3, 4), UK (5), Canada (6), USA (7, 8) and Australia (9). Although each of these studies differed in approach, all involved SP surveys where differing characteristics between various types of vehicles, including LEVs, were presented to respondents and these respondents in turn made hypothetical decisions about which vehicle they would be most likely to purchase. Although these studies revealed a number of interesting findings in regards to the potential demand for LEVs, they relied on SP data. In contrast, this paper employs an approach where LEV choice is modelled by taking a retrospective view and by using revealed preference (RP) data. By examining the revealed preferences of vehicle owners in Stockholm, this study overcomes one of the principal limitations of SP data, namely that stated preferences may not in fact reflect individuals’ actual choices, such as when cost, time, and inconvenience factors are real rather than hypothetical. This paper’s RP approach involves modelling the characteristics of individuals who purchased new LEVs, whilst estimating the effect of the congestion charging exemption upon choice probabilities and subsequent aggregate demand. The paper contributes to the current literature by examining the effectiveness of a toll exemption under revealed preference conditions, and by assessing the total effect of the policy based on key indicators for policy makers, including: vehicle owner home location, commuting patterns, number of children, age, gender and income. Extended Abstract Submission for Kuhmo Nectar Conference 2014 2 The two main research questions motivating this study were:  Which individuals chose to purchase a new LEV in Stockholm in 2008?; and,  How did the congestion charging exemption affect the aggregate demand for new LEVs in Stockholm in 2008? In order to answer these research questions the analysis was split into two stages. Firstly, a multinomial logit (MNL) model was used to identify which demographic characteristics were most significantly related to the purchase of an LEV over a conventional vehicle. The three most significant variables were found to be: intra‐cordon residency (positive); commuting across the cordon (positive); and distance of residence from the cordon (negative). In order to estimate the effect of the exemption policy on vehicle purchase choice, the model included variables to control for geographic differences in preferences, based on the location of the vehicle owners’ homes and workplaces in relation to the congestion‐charging cordon boundary. These variables included one indicator representing commutes across the cordon and another indicator representing intra‐cordon residency. The effect of the exemption policy on the probability of purchasing LEVs was estimated in the second stage of the analysis by focusing on the groups of vehicle owners that were most likely to have been affected by the policy i.e. those commuting across the cordon boundary (in both directions). Given the inclusion of the indicator variable representing commutes across the cordon, it is assumed that the estimated coefficient of this variable captures the effect of the exemption policy on the utility of choosing to purchase an exempt LEV for these two groups of vehicle owners. The intra‐cordon residency indicator variable also controls for differences between the two groups, based upon direction of travel across the cordon boundary. A counter‐hypothesis to this assumption is that the coefficient of the variable representing commuting across the cordon boundary instead only captures geo‐demographic differences that lead to variations in LEV ownership across the different groups of vehicle owners in relation to the cordon boundary. In order to address this counter‐hypothesis, an additional analysis was performed on data from a city with a similar geodemographic pattern to Stockholm, Gothenburg ‐ Sweden’s second largest city. The results of this analysis provided evidence to support the argument that the coefficient of the variable representing commutes across the cordon was capturing the effect of the exemption policy. Based upon this framework, the predicted vehicle type shares were calculated using the estimated coefficients of the MNL model and compared with predicted vehicle type shares from a simulated scenario where the exemption policy was inactive. This simulated scenario was constructed by setting the coefficient for the variable representing commutes across the cordon boundary to zero for all observations to remove the utility benefit of the exemption policy. Overall, the procedure of this second stage of the analysis led to results showing that the exemption had a substantial effect upon the probability of purchasing and aggregate demand for exempt LEVs in Stockholm during 2008. By making use of unique evidence of revealed preferences of LEV owners, this study identifies the common characteristics of new LEV owners and estimates the effect of Stockholm's congestion charging exemption upon the demand for new LEVs during 2008. It was found that the variables that had the greatest effect upon the choice of purchasing an exempt LEV included intra‐cordon residency (positive), distance of home from the cordon (negative), and commuting across the cordon (positive). It was also determined that owners under the age of 30 years preferred non‐exempt LEVs (low CO2 LEVs), whilst those over the age of 30 years preferred electric vehicles. In terms of electric vehicles, it was apparent that those individuals living within the city had the highest propensity towards purchasing this vehicle type. A negative relationship between choosing an electric vehicle and the distance of an individuals’ residency from the cordon was also evident. Overall, the congestion charging exemption was found to have increased the share of exempt LEVs in Stockholm by 1.9%, with, as expected, a much stronger effect on those commuting across the boundary, with those living inside the cordon having a 13.1% increase, and those owners living outside the cordon having a 5.0% increase. This increase in demand corresponded to an additional 538 (+/‐ 93; 95% C.I.) new exempt LEVs purchased in Stockholm during 2008 (out of a total of 5 427; 9.9%). Policy makers can take note that an incentive‐based policy can increase the demand for LEVs and appears to be an appropriate approach to adopt when attempting to reduce transport emissions through encouraging a transition towards a ‘green’ vehicle fleet.

Water Quality Indices from Unbalanced Spatio-Temporal Monitoring Designs

This chapter investigates a variety of water quality assessment tools for reservoirs with balanced/unbalanced monitoring designs and focuses on providing informative water quality assessments to ensure decision-makers are able to make risk-informed management decisions about reservoir health. In particular, two water quality assessment methods are described: non-compliance (probability of the number of times the indicator exceeds the recommended guideline) and amplitude (degree of departure from the guideline). Strengths and weaknesses of current and alternative water quality methods will be discussed. The proposed methodology is particularly applicable to unbalanced designs with/without missing values and reflects the general conditions and is not swayed too heavily by the occasional extreme value (very high or very low quality). To investigate the issues in greater detail, we use as a case study, a reservoir within South-East Queensland (SEQ), Australia. The purpose here is to obtain an annual score that reflected the overall water quality, temporally, spatially and across water quality indicators for each reservoir.

Benthic metabolism as an indicator of stream ecosystem health

We tested direct and indirect measures of benthic metabolism as indicators of stream ecosystem health across a known agricultural land-use disturbance gradient in southeast Queensland, Australia. Gross primary production (GPP) and respiration (R24) in benthic chambers in cobble and sediment habitats, algal biomass (as chlorophyll a) from cobbles and sediment cores, algal biomass accrual on artificial substrates and stable carbon isotope ratios of aquatic plants and benthic sediments were measured at 53 stream sites, ranging from undisturbed subtropical rainforest to catchments where improved pasture and intensive cropping are major land-uses. Rates of benthic GPP and R24 varied by more than two orders of magnitude across the study gradient. Generalised linear regression modelling explained 80% or more of the variation in these two indicators when sediment and cobble substrate dominated sites were considered separately, and both catchment and reach scale descriptors of the disturbance gradient were important in explaining this variation. Model fits were poor for net daily benthic metabolism (NDM) and production to respiration ratio (P/R). Algal biomass accrual on artificial substrate and stable carbon isotope ratios of aquatic plants and benthic sediment were the best of the indirect indicators, with regression model R2 values of 50% or greater. Model fits were poor for algal biomass on natural substrates for cobble sites and all sites. None of these indirect measures of benthic metabolism was a good surrogate for measured GPP. Direct measures of benthic metabolism, GPP and R24, and several indirect measures were good indicators of stream ecosystem health and are recommended in assessing process-related responses to riparian and catchment land use change and the success of ecosystem rehabilitation actions.