Parametric inference for discretely observed multidimensional diffusions with small diffusion coefficient

We consider a multidimensional diffusion X with drift coefficient b({\alpha},X(t)) and diffusion coefficient {\epsilon}{\sigma}({\beta},X(t)). The diffusion is discretely observed at times t_k=k{\Delta} for k=1..n on a fixed interval [0,T]. We study minimum contrast estimators derived from the Gaussian process approximating X for small {\epsilon}. We obtain consistent and asymptotically normal estimators of {\alpha} for fixed {\Delta} and {\epsilon}\rightarrow0 and of ({\alpha},{\beta}) for {\Delta}\rightarrow0 and {\epsilon}\rightarrow0. We compare the estimators obtained with various methods and for various magnitudes of {\Delta} and {\epsilon} based on simulation studies. Finally, we investigate the interest of using such methods in an epidemiological framework.Comment: 31 pages, 2 figures, 2 table

Approximation of epidemic models by diffusion processes and their statistical inference

Multidimensional continuous-time Markov jump processes $(Z(t))$ on $\mathbb{Z}^p$ form a usual set-up for modeling $SIR$-like epidemics. However, when facing incomplete epidemic data, inference based on $(Z(t))$ is not easy to be achieved. Here, we start building a new framework for the estimation of key parameters of epidemic models based on statistics of diffusion processes approximating $(Z(t))$. First, \previous results on the approximation of density-dependent $SIR$-like models by diffusion processes with small diffusion coefficient $\frac{1}{\sqrt{N}}$, where $N$ is the population size, are generalized to non-autonomous systems. Second, our previous inference results on discretely observed diffusion processes with small diffusion coefficient are extended to time-dependent diffusions. Consistent and asymptotically Gaussian estimates are obtained for a fixed number $n$ of observations, which corresponds to the epidemic context, and for $N\rightarrow \infty$. A correction term, which yields better estimates non asymptotically, is also included. Finally, performances and robustness of our estimators with respect to various parameters such as $R_0$ (the basic reproduction number), $N$, $n$ are investigated on simulations. Two models, $SIR$ and $SIRS$, corresponding to single and recurrent outbreaks, respectively, are used to simulate data. The findings indicate that our estimators have good asymptotic properties and behave noticeably well for realistic numbers of observations and population sizes. This study lays the foundations of a generic inference method currently under extension to incompletely observed epidemic data. Indeed, contrary to the majority of current inference techniques for partially observed processes, which necessitates computer intensive simulations, our method being mostly an analytical approach requires only the classical optimization steps.Comment: 30 pages, 10 figure

Closing the gap? Overcoming limitations in sociomaterial accounts of early literacy

This article uses a sociomaterial perspective to explore how deficit views of young children’s language and literacy are sustained and can be challenged. Foregrounding the notion of multiplicity, it considers how diverse sociomaterial relations work to uphold particular kinds of practice and particular arrangements of bodies and things over others. These relations may interfere with and interface with each other in different ways, sometimes sustaining but also potentially disrupting deficit discourses and practices. Our sociomaterial perspective is illustrated with a short vignette from a study of children and touchscreen tablets in an early years setting. An initial analysis is followed by a series of alternate and tentative tracings of other kinds of relations that play through those moments. The article contributes to debates about social inequality by troubling the certainties generated though deficit models of children’s literacy, whilst working proactively to envision and produce alternate possibilities that foreground the potentialities generated as people and other materials assemble together

Opening the Web of Learning: Students, Professors, and Community Partners Co-Creating Real-Life Learning Experiences

This article documents an example of a successful learning partnership for an activity called the Leadership Challenge (LC), an experiential learning design used by Royal Roads University (RRU) in its Master of Arts in Leadership Program. The LC is based on a co-learning model in which professors create the conditions for students’ learning; community-based organizations bring an authentic challenge as a scenario for learning to the students; and organizations, professors, and students all learn from one another throughout the process. We believe this experience is an example of how genuine partnerships between universities and community organizations can be created in which community partners are squarely placed in the center of the academic experience, rather than being treated as peripheral. Written from the perspective of representatives from both the university and the community service organization, this article also documents the limitations of this activity based on the short time frame allowed

Empirical Support for the HCR‐20: A Critical Analysis of the Violence Literature

Summary: The purpose of this project was to conduct a comprehensive search of the empirical literature published in peer-reviewed journals between 1997 and 2005 to identify studies that presented support for variables included on the HCR-20. This report includes a separate section for each of the measure’s 20 items, with one exception. Empirical support for Items C5 (Unresponsive to Treatment) and R4 (Noncompliance with Remediation Attempts) are presented together under a single heading because studies that were relevant to one item also tended to apply to the other item. Moreover, these studies could not be differentiated on the basis of having a present (clinical) or future (risk management) focus. Under each section, the most significant and methodologically sound studies identified in the search are summarized; abstracts of additional studies of relevance to the item are reproduced (with separate headings for studies that presented data on violent or non-vonviolent outcomes). Each section also lists narrative/qualitative literature reviews relevant to the item, as well as studies that offer “contradictory” empirical evidence. A table is presented at the beginning of the report that indicates whether, for each reference, a summary is provided, the abstract only is reprinted, or if it is a narrative review. Bookmark links are provided for each section of this report

Capacity Investment under Demand Uncertainty: The Role of Imports in the U.S. Cement Industry

Demand uncertainty is thought to in uence irreversible capacity decisions. Suppose local demand can be sourced from domestic (rigid) production or from (fl exible) imports. This paper shows that the optimal domestic capacity is either increasing or decreasing with demand uncertainty depending on the relative level of the costs of domestic production and imports. This relationship is tested with data on the U.S. cement industry, where, because cement is costly to transport over land, the diff erence in marginal cost between domestic production and imports varies across local U.S. markets. Industry data for 1999 to 2010 are consistent with the predictions of the model. The introduction of two technologies to the production set one rigid and one exible is crucial in understanding the relationship between capacity choice and uncertainty in this industry because there is no relationship at the aggregated U.S. data. The analysis presented in the paper reveals that the relationship is negative for coastal districts, and signi cantly more positive in landlocked districts