IFSM representation of Brownian motion with applications to simulation

Several methods are currently available to simulate paths of the Brownian motion. In particular, paths of the BM can be simulated using the properties of the increments of the process like in the Euler scheme, or as the limit of a random walk or via L2 decomposition like the Kac-Siegert/Karnounen-Loeve series. In this paper we first propose a IFSM (Iterated Function Systems with Maps) operator whose fixed point is the trajectory of the BM. We then use this representation of the process to simulate its trajectories. The resulting simulated trajectories are self-affine, continuous and fractal by construction. This fact produces more realistic trajectories than other schemes in the sense that their geometry is closer to the one of the true BM's trajectories. The IFSM trajectory of the BM can then be used to generate more realistic solutions of stochastic differential equations

Least squares volatility change point estimation for partially observed diffusion processes

A one dimensional diffusion process $X=\{X_t, 0\leq t \leq T\}$, with drift $b(x)$ and diffusion coefficient $\sigma(\theta, x)=\sqrt{\theta} \sigma(x)$ known up to $\theta>0$, is supposed to switch volatility regime at some point $t^*\in (0,T)$. On the basis of discrete time observations from $X$, the problem is the one of estimating the instant of change in the volatility structure $t^*$ as well as the two values of $\theta$, say $\theta_1$ and $\theta_2$, before and after the change point. It is assumed that the sampling occurs at regularly spaced times intervals of length $\Delta_n$ with $n\Delta_n=T$. To work out our statistical problem we use a least squares approach. Consistency, rates of convergence and distributional results of the estimators are presented under an high frequency scheme. We also study the case of a diffusion process with unknown drift and unknown volatility but constant

Measuring Social Well Being in The Big Data Era : Asking or Listening?

The literature on well being measurement seems to suggest that "asking" for a self-evaluation is the only way to estimate a complete and reliable measure of well being. At the same time "not asking" is the only way to avoid biased evaluations due to self-reporting. Here we propose a method for estimating the welfare perception of a community simply "listening" to the conversations on Social Network Sites. The Social Well Being Index (SWBI) and its components are proposed through to an innovative technique of supervised sentiment analysis called iSA which scales to any language and big data. As main methodological advantages, this approach can estimate several aspects of social well being directly from self-declared perceptions, instead of approximating it through objective (but partial) quantitative variables like GDP; moreover self-perceptions of welfare are spontaneous and not obtained as answers to explicit questions that are proved to bias the result. As an application we evaluate the SWBI in Italy through the period 2012-2015 through the analysis of more than 143 millions of tweets

The Langevin diffusion as a continuous-time model of animal movement and habitat selection

TM was supported by the Centre for Advanced Biological Modelling at the University of Sheffield, funded by the Leverhulme Trust, award number DS-2014-081.1. The utilisation distribution of an animal describes the relative probability of space use. It is natural to think of it as the long-term consequence of the animal's short-term movement decisions: it is the accumulation of small displacements which, over time, gives rise to global patterns of space use. However, many estimation methods for the utilisation distribution either assume the independence of observed locations and ignore the underlying movement (e.g. kernel density estimation), or are based on simple Brownian motion movement rules (e.g. Brownian bridges). 2. We introduce a new continuous-time model of animal movement, based on the Langevin diffusion. This stochastic process has an explicit stationary distribution, conceptually analogous to the idea of the utilisation distribution, and thus provides an intuitive framework to integrate movement and space use. We model the stationary (utilisation) distribution with a resource selection function to link the movement to spatial covariates, and allow inference about habitat preferences of animals. 3. Standard approximation techniques can be used to derive the pseudo-likelihood of the Langevin diffusion movement model, and to estimate habitat preference and movement parameters from tracking data. We investigate the performance of the method on simulated data, and discuss its sensitivity to the time scale of the sampling. We present an example of its application to tracking data of Steller sea lions (Eumetopias jubatus). 4. Due to its continuous-time formulation, this method can be applied to irregular telemetry data. The movement model is specified using a habitat-dependent utilisation distribution, and it provides a rigorous framework to estimate long-term habitat selection from correlated movement data. The Langevin movement model can be approximated by linear model, which allows for very fast inference. Standard tools such as residuals can be used for model checking.PostprintPeer reviewe

Data-driven coarse graining in action: Modeling and prediction of complex systems

In many physical, technological, social, and economic applications, one is commonly faced with the task of estimating statistical properties, such as mean first passage times of a temporal continuous process, from empirical data (experimental observations). Typically, however, an accurate and reliable estimation of such properties directly from the data alone is not possible as the time series is often too short, or the particular phenomenon of interest is only rarely observed. We propose here a theoretical-computational framework which provides us with a systematic and rational estimation of statistical quantities of a given temporal process, such as waiting times between subsequent bursts of activity in intermittent signals. Our framework is illustrated with applications from real-world data sets, ranging from marine biology to paleoclimatic data

A counterfactual approach to measure the impact of wet grassland conservation on UK breeding bird populations

Wet grassland wader populations in the United Kingdom have experienced severe declines over the last three decades. To help mitigate these declines, the Royal Society for the Protection of Birds (RSPB) has restored and managed lowland wet grassland nature reserves to benefit these and other species. However, the impact that these reserves have on bird population trends has not been experimentally evaluated, as appropriate control populations do not readily exist. In this study, we compare population trends from 1994 ‐ 2018 for five bird species of conservation concern that breed on these nature reserves with counterfactual trends using matched breeding bird survey observations. Our results showed positive effects of conservation interventions for all four wader species that these reserves aim to benefit: Lapwing (Vanellus vanellus), Redshank (Tringa totanus), Curlew (Numenius arquata) and Snipe (Gallinago gallinago). There was no positive effect of conservation interventions on reserves for the passerine, Yellow Wagtail (Motacilla flava). We compared reserve trends with three different counterfactuals, based on different scenarios of how reserve populations could have developed in the absence of conservation, and found that reserve trends performed better regardless of the counterfactual used. Our approach using monitoring data to produce valid counterfactual controls is a broadly applicable method allowing large‐scale evaluation of conservation impact

Coping with the economic burden of Diabetes, TB and co-prevalence - Evidence from Bishkek, Kyrgyzstan

Background: The increasing number of patients co-affected with Diabetes and TB may place individuals with low socio-economic status at particular risk of persistent poverty. Kyrgyz health sector reforms aim at reducing this burden, with the provision of essential health services free at the point of use through a State-Guaranteed Benefit Package (SGBP). However, despite a declining trend in out-of-pocket expenditure, there is still a considerable funding gap in the SGBP. Using data from Bishkek, Kyrgyzstan, this study aims to explore how households cope with the economic burden of Diabetes, TB and co-prevalence. Methods: This study uses cross-sectional data collected in 2010 from Diabetes and TB patients in Bishkek, Kyrgyzstan. Quantitative questionnaires were administered to 309 individuals capturing information on patients' socioeconomic status and a range of coping strategies. Coarsened exact matching (CEM) is used to generate socio-economically balanced patient groups. Descriptive statistics and logistic regression are used for data analysis. Results: TB patients are much younger than Diabetes and co-affected patients. Old age affects not only the health of the patients, but also the patient's socio-economic context. TB patients are more likely to be employed and to have higher incomes while Diabetes patients are more likely to be retired. Co-affected patients, despite being in the same age group as Diabetes patients, are less likely to receive pensions but often earn income in informal arrangements. Out-of-pocket (OOP) payments are higher for Diabetes care than for TB care. Diabetes patients cope with the economic burden by using social welfare support. TB patients are most often in a position to draw on income or savings. Co-affected patients are less likely to receive social welfare support than Diabetes patients. Catastrophic health spending is more likely in Diabetes and co-affected patients than in TB patients. Conclusions: This study shows that while OOP are moderate for TB affected patients, there are severe consequences for Diabetes affected patients. As a result of the underfunding of the SGBP, Diabetes and co-affected patients are challenged by OOP. Especially those who belong to lower socio-economic groups are challenged in coping with the economic burden

The impact of ADHD on the health and well-being of ADHD children and their siblings

Childhood attention-deficit/hyperactivity disorder (ADHD) has been associated with reduced health and well-being of patients and their families. The authors undertook a large UK survey-based observational study of the burden associated with childhood ADHD. The impact of ADHD on both the patient (N = 476) and their siblings (N = 337) on health-related quality of life (HRQoL) and happiness was quantified using multiple standard measures [e.g. child health utility-9D (CHU-9D), EuroQol-5D-Youth]. In the analysis, careful statistical adjustments were made to ensure a like-for-like comparison of ADHD families with two different control groups. We controlled for carers' ADHD symptoms, their employment and relationship status and siblings' ADHD symptoms. ADHD was associated with a significant deficit in the patient's HRQoL (with a CHU-9D score of around 6 % lower). Children with ADHD also have less sleep and were less happy with their family and their lives overall. No consistent decrement to the HRQoL of the siblings was identified across the models, except that related to their own conduct problems. The siblings do, however, report lower happiness with life overall and with their family, even when controlling for the siblings own ADHD symptoms. We also find evidence of elevated bullying between siblings in families with a child with ADHD. Overall, the current results suggest that the reduction in quality of life caused by ADHD is experienced both by the child with ADHD and their siblings