Optimal Probabilistic Forecasts for Counts

Optimal probabilistic forecasts of integer-valued random variables are derived. The optimality is achieved by estimating the forecast distribution nonparametrically over a given broad model class and proving asymptotic efficiency in that setting. The ideas are demonstrated within the context of the integer autoregressive class of models, which is a suitable class for any count data that can be interpreted as a queue, stock, birth and death process or branching process. The theoretical proofs of asymptotic optimality are supplemented by simulation results which demonstrate the overall superiority of the nonparametric method relative to a misspecified parametric maximum likelihood estimator, in large but .nite samples. The method is applied to counts of wage claim benefits, stock market iceberg orders and civilian deaths in Iraq, with bootstrap methods used to quantify sampling variation in the estimated forecast distributions.Nonparametric Inference; Asymptotic Efficiency; Count Time Series; INAR Model Class; Bootstrap Distributions; Iceberg Stock Market Orders.

Scoping biological indicators of soil quality Phase II. Defra Final Contract Report SP0534

This report presents results from a field assessment of a limited suite of potential biological indicators of soil quality to investigate their suitability for national-scale soil monitoring

Understanding service demand for mental health among Australians aged 16 to 64 years according to their possible need for treatment

Background: To inform decisions about mental health resource allocation, planners require reliable estimates of people who report service demand (i.e. people who use or want mental health services) according to their level of possible need. Methods: Using data on 6915 adults aged 16-64 years in Australia's 2007 National Survey of Mental Health and Wellbeing, we examined past-year service demand among respondents grouped into four levels of possible need: (a) 12-month mental disorder; (b) lifetime but no 12-month mental disorder; (c) any other indicator of possible need (12-month symptoms or reaction to stressful event, or lifetime hospitalisation); (d) no indicator of possible need. Multivariate logistic regression analyses examined correlates of service demand, separately for respondents in each of levels 1-3. Results: Sixteen per cent of Australian adults reported service demand, of whom one-third did not meet criteria for a 12-month mental disorder (equivalent to 5.7% of the adult population). Treatment patterns tended to follow a gradient defined by level of possible need. For example, service users with a 12-month disorder received, on average, 1.6-3.9 times more consultations than their counterparts in other levels of possible need, and had 1.9-2.2 times higher rates of psychologist consultation. Service users with a lifetime but not 12-month disorder or any other indicator of need consumed a similar average number of services to people with mild 12-month mental disorders, but received relatively fewer services involving the mental health sector. Service demand was associated with increased suicidality and psychological distress in all levels of possible need examined, and with poorer clinical and functional status for those with 12-month or lifetime disorders. Conclusions: Many Australians reporting service demand do not meet criteria for a current mental disorder, but may require services to maintain recovery following a past episode or because they are experiencing symptoms and significant psychological distress

Efficiency of the Incomplete Enumeration algorithm for Monte-Carlo simulation of linear and branched polymers

We study the efficiency of the incomplete enumeration algorithm for linear and branched polymers. There is a qualitative difference in the efficiency in these two cases. The average time to generate an independent sample of $n$ sites for large $n$ varies as $n^2$ for linear polymers, but as $exp(c n^{\alpha})$ for branched (undirected and directed) polymers, where $0<\alpha<1$. On the binary tree, our numerical studies for $n$ of order $10^4$ gives $\alpha = 0.333 \pm 0.005$. We argue that $\alpha=1/3$ exactly in this case.Comment: replaced with published versio

Universality Class of Thermally Diluted Ising Systems at Criticality

The universality class of thermally diluted Ising systems, in which the realization of the disposition of magnetic atoms and vacancies is taken from the local distribution of spins in the pure original Ising model at criticality, is investigated by finite size scaling techniques using the Monte Carlo method. We find that the critical temperature, the critical exponents and therefore the universality class of these thermally diluted Ising systems depart markedly from the ones of short range correlated disordered systems. Our results agree fairly well with theoretical predictions previously made by Weinrib and Halperin for systems with long range correlated disorder.Comment: 7 pages, 6 figures, RevTe

Anomalous tag diffusion in the asymmetric exclusion model with particles of arbitrary sizes

Anomalous behavior of correlation functions of tagged particles are studied in generalizations of the one dimensional asymmetric exclusion problem. In these generalized models the range of the hard-core interactions are changed and the restriction of relative ordering of the particles is partially brocken. The models probing these effects are those of biased diffusion of particles having size S=0,1,2,..., or an effective negative "size" S=-1,-2,..., in units of lattice space. Our numerical simulations show that irrespective of the range of the hard-core potential, as long some relative ordering of particles are kept, we find suitable sliding-tag correlation functions whose fluctuations growth with time anomalously slow ($t^{{1/3}}$), when compared with the normal diffusive behavior ($t^{{1/2}}$). These results indicate that the critical behavior of these stochastic models are in the Kardar-Parisi-Zhang (KPZ) universality class. Moreover a previous Bethe-ansatz calculation of the dynamical critical exponent $z$, for size $S \geq 0$ particles is extended to the case $S<0$ and the KPZ result $z=3/2$ is predicted for all values of $S \in {Z}$.Comment: 4 pages, 3 figure

An evaluation of automated GPD threshold selection methods for hydrological extremes across different scales

This study investigated core components of an extreme value methodology for the estimation of high-flow frequencies from agricultural surface water run-off. The Generalized Pareto distribution (GPD) was used to model excesses in time-series data that resulted from the ‘Peaks Over Threshold’ (POT) method. First, the performance of eight different GPD parameter estimators was evaluated through a Monte Carlo experiment. Second, building on the estimator comparison, two existing automated GPD threshold selection methods were evaluated against a proposed approach that automates the threshold stability plots. For this second experiment, methods were applied to discharge measured at a highly-instrumented agricultural research facility in the UK. By averaging fine-resolution 15-minute data to hourly, 6-hourly and daily scales, we were also able to determine the effect of scale on threshold selection, as well as the performance of each method. The results demonstrate the advantages of the proposed threshold selection method over two commonly applied methods, while at the same time providing useful insights into the effect of the choice of the scale of measurement on threshold selection. The results can be generalised to similar water monitoring schemes and are important for improved characterisations of flood events and the design of associated disaster management protocols

Normal tissue complication probability (NTCP) parameters for breast fibrosis: pooled results from two randomised trials

Introduction: the dose–volume effect of radiation therapy on breast tissue is poorly understood. We estimate NTCP parameters for breast fibrosis after external beam radiotherapy.Materials and methods: we pooled individual patient data of 5856 patients from 2 trials including whole breast irradiation followed with or without a boost. A two-compartment dose volume histogram model was used with boost volume as the first compartment and the remaining breast volume as second compartment. Results from START-pilot trial (n?=?1410) were used to test the predicted models.Results: 26.8% patients in the Cambridge trial (5?years) and 20.7% patients in the EORTC trial (10?years) developed moderate-severe breast fibrosis. The best fit NTCP parameters were BEUD3(50)?=?136.4?Gy, ?50?=?0.9 and n?=?0.011 for the Niemierko model and BEUD3(50)?=?132?Gy, m?=?0.35 and n?=?0.012 for the Lyman Kutcher Burman model. The observed rates of fibrosis in the START-pilot trial agreed well with the predicted rates.Conclusions: this large multi-centre pooled study suggests that the effect of volume parameter is small and the maximum RT dose is the most important parameter to influence breast fibrosis. A small value of volume parameter ‘n’ does not fit with the hypothesis that breast tissue is a parallel organ. However, this may reflect limitations in our current scoring system of fibrosi