A model for compressing probabilities in belief networks

Probabilistic reasoning with belief (Bayesian) networks is based on conditional probability matrices. Thus it suffers from NP-hard implementations. In particular, the amount of probabilistic information necessary for the computations is often overwhelming. So, compressing the conditional probability table is one of the most important issues faced by the probabilistic reasoning community. Santos suggested an approach (called linear potential functions) for compressing the information from a combinatorial amount to roughly linear in the number of random variable assignments. However, much of the information in Bayesian networks, in which there are no linear potential functions, would be fitted by polynomial approximating functions rather than by reluctantly linear functions. For this reason, we construct a polynomial method to compress the conditional probability table in this paper. We evaluated the proposed technique, and our experimental results demonstrate that the approach is efficient and promising.

Activities between activities of focus-Relevant when assessing DNA transfer probabilities

Consideration of the indirect transfer of 'touch DNA' is increasingly becoming part of criminal investigations. Focus is often concentrated on the actions relating to the pick-up of the relevant DNA and key actions associated with transfer to the exhibit from which the sample in question was collected. There is often a time lapse between such actions. As any contact can influence the gain and/or loss of DNA, it is relevant to have an awareness of what hands touch during everyday activities in order to assist consideration of what may be occurring during potential time lapses within contemplated scenarios. To gain an appreciation of the manner and frequency of hands contacting various surfaces during everyday activities, we analysed several videos of individuals performing a variety of general activities. The findings indicate that several items are touched over a relatively short period of time. Appreciation and consideration of general activities that may have occurred between key focus activities are necessary to assess any impact these may have on what is deposited at the final collection site. The information this provides is imperative when weighting alternative transfer scenario propositions.

Stability analysis of two-dimensional Markovian jump state-delayed systems in the Roesser model with uncertain transition probabilities

This paper is concerned with the problem of stochastic stability analysis of discrete-time two-dimensional (2-D) Markovian jump systems (MJSs) described by the Roesser model with interval time-varying delays. The transition probabilities of the jumping process/Markov chain are assumed to be uncertain, that is, they are not exactly known but can be estimated. A Lyapunov-like scheme is first extended to 2-D MJSs with delays. Based on some novel 2-D summation inequalities proposed in this paper, delay-dependent stochastic stability conditions are derived in terms of linear matrix inequalities (LMIs) which can be computationally solved by various convex optimization algorithms. Finally, two numerical examples are given to illustrate the effectiveness of the obtained results.

Predicting the distribution of discrete spatial events using artificial neural networks

Although the development of geographic information system (GIS) technology and digital data manipulation techniques has enabled practitioners in the geographical and geophysical sciences to make more efficient use of resource information, many of the methods used in forming spatial prediction models are still inherently based on traditional techniques of map stacking in which layers of data are combined under the guidance of a theoretical domain model. This paper describes a data-driven approach by which Artificial Neural Networks (ANNs) can be trained to represent a function characterising the probability that an instance of a discrete event, such as the presence of a mineral deposit or the sighting of an endangered animal species, will occur over some grid element of the spatial area under consideration. A case study describes the application of the technique to the task of mineral prospectivity mapping in the Castlemaine region of Victoria using a range of geological, geophysical and geochemical input variables. Comparison of the maps produced using neural networks with maps produced using a density estimation-based technique demonstrates that the maps can reliably be interpreted as representing probabilities. However, while the neural network model and the density estimation-based model yield similar results under an appropriate choice of values for the respective parameters, the neural network approach has several advantages, especially in high dimensional input spaces.

Comparison of MLP and Bayesian approaches on mineral prospectivity mapping tasks

Mineral Prospectivity Mapping is the process of combining maps containing different geoscientific data sets to produce a single map depicting areas ranked according to their potential to host mineral deposits of a particular type. This paper outlines two approaches for deriving a function which can be used to assign to each cell in the study area a value representing the posterior probability that the cell contains a deposit of the sought-after mineral. One approach is based on estimating probability density functions (pdfs); the second uses multilayer perceptrons (MLPs). Results are provided from applying these approaches to geoscientific datasets covering a region in North Western Victoria, Australia. The results demonstrate that while both the Bayesian approach and the MLP approach yield similar results when the number of input dimensions is small, the Bayesian approach rapidly becomes unstable as the number of input dimensions increases, with the resulting maps displaying high sensitivity to the number of mixtures used to model the distributions. However, despite the fact that Bayesian assigned values cannot be interpreted as posterior probabilities in high dimensional input spaces, the pixel favorability rankings produced by the two methods is similar.

Bayesian clustering with AutoClass explicitly recognises uncertainties in landscape classification

Clustering of multivariate data is a commonly used technique in ecology, and many approaches to clustering are available. The results from a clustering algorithm are uncertain, but few clustering approaches explicitly acknowledge this uncertainty. One exception is Bayesian mixture modelling, which treats all results probabilistically, and allows comparison of multiple plausible classifications of the same data set. We used this method, implemented in the AutoClass program, to classify catchments (watersheds) in the Murray Darling Basin (MDB), Australia, based on their physiographic characteristics (e.g. slope, rainfall, lithology). The most likely classification found nine classes of catchments. Members of each class were aggregated geographically within the MDB. Rainfall and slope were the two most important variables that defined classes. The second-most likely classification was very similar to the first, but had one fewer class. Increasing the nominal uncertainty of continuous data resulted in a most likely classification with five classes, which were again aggregated geographically. Membership probabilities suggested that a small number of cases could be members of either of two classes. Such cases were located on the edges of groups of catchments that belonged to one class, with a group belonging to the second-most likely class adjacent. A comparison of the Bayesian approach to a distance-based deterministic method showed that the Bayesian mixture model produced solutions that were more spatially cohesive and intuitively appealing. The probabilistic presentation of results from the Bayesian classification allows richer interpretation, including decisions on how to treat cases that are intermediate between two or more classes, and whether to consider more than one classification. The explicit consideration and presentation of uncertainty makes this approach useful for ecological investigations, where both data and expectations are often highly uncertain.

Minimising risks in IT outsourcing: choosing target services

This paper provides a risk-based framework for deciding on which IT services to outsource and which to keep in-house. This framework considers the probabilities both of negative outcomes, and of failing to achieve positive outcomes. The authors examine the major components of outsourcing risk and their drivers, and from this derive a series of questions decision-makers can ask when deciding what sourcing options to adopt for different services. The framework was developed on the basis of five years of qualitative and quantitative research into the experiences of organizations involved in outsourcing IT.

Dynamic reconfiguration of multi-agent systems based on autonomy oriented computing

Dynamic reconfiguration has been listed as one of the key challenges in support of agent adaptation to environments, which has attracted much attention of researchers world wide. To tackle this tough problem, an agent-based dynamic reconfiguration model (ADRM) is proposed from the autonomy-oriented computing (AOC) point of view. The ERA (environment-reactive rules-agents) algorithm used in AOC is improved to support the organization formation behavior, which is essential in dynamic reconfiguration. To test the efficiency of this model and the effectiveness of different reactive behaviors, the performance of this model was investigated under different selection probabilities.

Bayesian classification of catchments using spatial data: a first step to improved modelling of catchment effects on stream ecological condition

A major challenge facing freshwater ecologists and managers is the development of models that link stream ecological condition to catchment scale effects, such as land use. Previous attempts to make such models have followed two general approaches. The bottom-up approach employs mechanistic models, which can quickly become too complex to be useful. The top-down approach employs empirical models derived from large data sets, and has often suffered from large amounts of unexplained variation in stream condition.

We believe that the lack of success of both modelling approaches may be at least partly explained by scientists considering too wide a breadth of catchment type. Thus, we believe that by stratifying large sets of catchments into groups of similar types prior to modelling, both types of models may be improved. This paper describes preliminary work using a Bayesian classification software package, ‘Autoclass’ (Cheeseman and Stutz 1996) to create classes of catchments within the Murray Darling Basin based on physiographic data.

Autoclass uses a model-based classification method that employs finite mixture modelling and trades off model fit versus complexity, leading to a parsimonious solution. The software provides information on the posterior probability that the classification is ‘correct’ and also probabilities for alternative classifications. The importance of each attribute in defining the individual classes is calculated and presented, assisting description of the classes. Each case is ‘assigned’ to a class based on membership probability, but the probability of membership of other classes is also provided. This feature deals very well with cases that do not fit neatly into a larger class. Lastly, Autoclass requires the user to specify the measurement error of continuous variables.

Catchments were derived from the Australian digital elevation model. Physiographic data werederived from national spatial data sets. There was very little information on measurement errors for the spatial data, and so a conservative error of 5% of data range was adopted for all continuous attributes. The incorporation of uncertainty into spatial data sets remains a research challenge.

The results of the classification were very encouraging. The software found nine classes of catchments in the Murray Darling Basin. The classes grouped together geographically, and followed altitude and latitude gradients, despite the fact that these variables were not included in the classification. Descriptions of the classes reveal very different physiographic environments, ranging from dry and flat catchments (i.e. lowlands), through to wet and hilly catchments (i.e. mountainous areas). Rainfall and slope were two important discriminators between classes. These two attributes, in particular, will affect the ways in which the stream interacts with the catchment, and can thus be expected to modify the effects of land use change on ecological condition. Thus, realistic models of the effects of land use change on streams would differ between the different types of catchments, and sound management practices will differ.

A small number of catchments were assigned to their primary class with relatively low probability. These catchments lie on the boundaries of groups of catchments, with the second most likely class being an adjacent group. The locations of these ‘uncertain’ catchments show that the Bayesian classification dealt well with cases that do not fit neatly into larger classes.

Although the results are intuitive, we cannot yet assess whether the classifications described in this paper would assist the modelling of catchment scale effects on stream ecological condition. It is most likely that catchment classification and modelling will be an iterative process, where the needs of the model are used to guide classification, and the results of classifications used to suggest further refinements to models.

Nurses' critical event risk assessments : a judgement analysis

Aims. To explore and explain nurses' use of readily available clinical information when deciding whether a patient is at risk of a critical event.

Background. Half of inpatients who suffer a cardiac arrest have documented but unacted upon clinical signs of deterioration in the 24 hours prior to the event. Nurses appear to be both misinterpreting and mismanaging the nursing-knowledge 'basics' such as heart rate, respiratory rate and oxygenation. Whilst many medical interventions originate from nurses, up to 26% of nurses' responses to abnormal signs result in delays of between one and three hours.

Methods. A double system judgement analysis using Brunswik's lens model of cognition was undertaken with 245 Dutch, UK, Canadian and Australian acute care nurses. Nurses were asked to judge the likelihood of a critical event, 'at-risk' status, and whether they would intervene in response to 50 computer-presented clinical scenarios in which data on heart rate, systolic blood pressure, urine output, oxygen saturation, conscious level and oxygenation support were varied. Nurses were also presented with a protocol recommendation and also placed under time pressure for some of the scenarios. The ecological criterion was the predicted level of risk from the Modified Early Warning Score assessments of 232 UK acute care inpatients.

Results. Despite receiving identical information, nurses varied considerably in their risk assessments. The differences can be partly explained by variability in weightings given to information. Time and protocol recommendations were given more weighting than clinical information for key dichotomous choices such as classifying a patient as 'at risk' and deciding to intervene. Nurses' weighting of cues did not mirror the same information's contribution to risk in real patients. Nurses synthesized information in non-linear ways that contributed little to decisional accuracy. The low-moderate achievement (Ra) statistics suggests that nurses' assessments of risk were largely inaccurate; these assessments were applied consistently among 'patients' (scenarios). Critical care experience was statistically associated with estimates of risk, but not with the decision to intervene.

Conclusion. Nurses overestimated the risk and the need to intervene in simulated paper patients at risk of a critical event. This average response masked considerable variation in risk predictions, the need for action and the weighting afforded to the information they had available to them. Nurses did not make use of the linear reasoning required for accurate risk predictions in this task. They also failed to employ any unique knowledge that could be shown to make them more accurate. The influence of time pressure and protocol recommendations depended on the kind of judgement faced suggesting then that knowing more about the types of decisions nurses face may influence information use.

Relevance to clinical practice. Practice developers and educators need to pay attention to the quality of nurses' clinical experience as well as the quantity when developing judgement expertise in nurses. Intuitive unaided decision making in the assessment of risk may not be as accurate as supported decision making. Practice developers and educators should consider teaching nurses normative rules for revising probabilities (even subjective ones) such as Bayes' rule for diagnostic or assessment judgements and also that linear ways of thinking, in which decision support may help, may be useful for many choices that nurses face. Nursing needs to separate the rhetoric of 'holism' and 'expertise' from the science of predictive validity, accuracy and competence in judgement and decision making.

Modelling the public health consequences of cannabis use in Australia

Aims: To detail and validate a simulation model that describes the dynamics of cannabis use, including its probable causal relationships with schizophrenia, road traffic accidents (RTA) and heroin/poly-drug use (HPU).

Methods: A Markov model with 17 health-states was constructed. Annual cycles were used to simulate the initiation of cannabis use, progression in use, reduction and complete remission. The probabilities of transition between health-states were derived from observational data. Following 10-year-old Australian children for 90 years, the model estimated age-specific prevalence for cannabis use. By applying the relative risks according to the extent of cannabis use, the age-specific prevalence of schizophrenia and HPU, and the annual RTA incidence and fatality rate were also estimated. Predictive validity of the model was tested by comparing modelled outputs with data from other credible sources. Sensitivity and scenario analyses were conducted to evaluate technical validity and face validity.

Results: The estimated cannabis use prevalence in individuals aged 10-65 years was 12.2% which comprised 27.4% weekly and 18.0% daily users. The modelled prevalence and age profile were comparable to the reported cross-sectional data. The model also provided good approximations to the prevalence of schizophrenia (Modelled: 4.75/1,000 persons vs Observed: 4.6/1,000 persons), HPU (3.2/1,000 vs 3.1/1,000) and the RTA fatality rate (8.1 per 100,000 vs 8.2 per 100,000). Sensitivity analyses and scenario analysis provided expected and explainable trends.

Conclusions: The validated model provides a valuable tool to assess the likely effectiveness and cost-effectiveness of interventions designed to affect patterns of cannabis use. It can be updated as new data becomes available and/or applied to other countries.

The exact distribution of the maximum, minimum and the range of multinomial/dirichlet and multivariate hypergeometric frequencies

The exact distribution of the maximum and minimum frequencies of Multinomial/Dirichlet and Multivariate Hypergeometric distributions of n balls in m urns is compactly represented as a product of stochastic matrices. This representation does not require equal urn probabilities, is invariant to urn order, and permits rapid calculation of exact probabilities. The exact distribution of the range is also obtained. These algorithms satisfy a long-standing need for routines to compute exact Multinomial/Dirichlet and Multivariate Hypergeometric maximum, minimum, and range probabilities in statistical computation libraries and software packages.

The projected impact of population and high-risk strategies for risk-factor control on coronary heart disease and stroke events

Objective: To model the impact of both population and high-risk strategies on cardiovascular disease (CVD) outcomes.

Design, setting and participants: A CVD risk-factor survey was carried out in rural south-eastern Australia from 2004 to 2006. Using a stratified random sample, data for 1116 participants aged 35–74 years were analysed. Applying the Framingham risk equations to risk-factor data, 5-year probabilities of a coronary heart disease event, stroke and cardiovascular event were calculated. The effect of different changes in risk factors were modelled to assess the extent to which cardiovascular diseases can be prevented by changing the risk factors at a population level (population strategy), among the high-risk individuals (high-risk strategy) or both.

Results: Among men, a population strategy could reduce cardiovascular events by 19.3% (193 per 1000 per 5 years), the high-risk strategy by 12.6% (126 per 1000) and a combined strategy by 24.1% (241 per 1000); and among women, by 21.9% (219 per 1000), 19.0% (190 per 1000) and 28.7% (287 per 1000), respectively.

Conclusions: For prevention of CVD in Australia, it is important both to treat high-risk individuals and to reduce the mean risk-factor levels in the population. We show how risk-factor survey data can be used to set targets for prevention and to monitor progress in line with the recommendations of the National Preventative Health Taskforce.

Does migration of hybrids contribute to post-zygotic isolation in flycatchers?

In the face of hybridization, species integrity can only be maintained through post-zygotic isolating barriers (PIBs). PIBs need not only be intrinsic (i.e. hybrid inviability and sterility caused by developmental incompatibilities), but also can be extrinsic due to the hybrid's intermediate phenotype falling between the parental niches. For example, in migratory species, hybrid fitness might be reduced as a result of intermediate migration pathways and reaching suboptimal wintering grounds. Here, we test this idea by comparing the juvenile to adult survival probabilities as well as the wintering grounds of pied flycatchers (Ficedula hypoleuca), collared flycatchers (Ficedula albicollis) and their hybrids using stable isotope ratios of carbon (δ13C) and nitrogen (δ15N) in feathers developed at the wintering site. Our result supports earlier observations of largely segregated wintering grounds of the two parental species. The isotope signature of hybrids clustered with that of pied flycatchers. We argue that this pattern can explain the high annual survival of hybrid flycatchers. Hence, dominant expression of the traits of one of the parental species in hybrids may substantially reduce the ecological costs of hybridization.