Uniform convergence of Vapnik--Chervonenkis classes under ergodic sampling

We show that if $\mathcal{X}$ is a complete separable metric space and $\mathcal{C}$ is a countable family of Borel subsets of $\mathcal{X}$ with finite VC dimension, then, for every stationary ergodic process with values in $\mathcal{X}$, the relative frequencies of sets $C\in\mathcal{C}$ converge uniformly to their limiting probabilities. Beyond ergodicity, no assumptions are imposed on the sampling process, and no regularity conditions are imposed on the elements of $\mathcal{C}$. The result extends existing work of Vapnik and Chervonenkis, among others, who have studied uniform convergence for i.i.d. and strongly mixing processes. Our method of proof is new and direct: it does not rely on symmetrization techniques, probability inequalities or mixing conditions. The uniform convergence of relative frequencies for VC-major and VC-graph classes of functions under ergodic sampling is established as a corollary of the basic result for sets.Comment: Published in at http://dx.doi.org/10.1214/09-AOP511 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Valuing Catastrophic Citrus Losses

Courts are often required to estimate changes in welfare to agricultural operations from catastrophic events. For example, courts must assign damages in lawsuits, such as with pesticide drift cases, or determine "just compensation" when the government takes private land for public use, as with the removal of dairy farms from environmentally sensitive land or destruction of canker-contaminated citrus trees. In economics, the traditional method of quantifying producer losses is estimating changes in producer welfare, but courts rarely use this method. Instead, they turn to substitute valuation methods that may not fully capture welfare changes, such as changes in land value, tree replacement value, and total revenue. This study examines various measures for valuing the back-to-back catastrophic freezes that occurred in the Florida citrus industry in the 1980s. We first use the traditional method to determine the welfare change due to a freeze (1) for a citrus grove that loses one crop and is able to return to full production the next year, and (2) the lower measure of welfare loss due to a citrus grove that loses all of its trees and is abandoned or is replanted. The lower measure is used to simulate the legal doctrine of avoidable consequences. These measures are then compared to substitute valuation measures that have been used by courts to determine welfare changes. For case 1, total revenue overestimates losses by 35.6%. For case 2, total revenue overestimates losses by 55.3%, tree replacement value underestimates losses by 93.6%, and changes in land value underestimates losses by 13.2%.citrus, perennial crops, catastrophic loss, damages, freeze, Crop Production/Industries,

Valuing Catastrophic Losses for Perennial Agricultural Crops

Courts are often required to estimate changes in welfare to agricultural operations from catastrophic events. For example, courts must assign damages in lawsuits, such as with pesticide drift cases, or determine 'just compensation' when the government takes private land for public use, as with the removal of dairy farms from environmentally sensitive land or destruction of canker-contaminated citrus trees. In economics, the traditional method of estimating changes in producer welfare is the computation of lost producer surplus, but courts rarely use this method. Instead, they turn to substitute valuation methods that may not fully capture welfare change, such as changes in land value, tree replacement value, and total revenue. This study examines various measures for valuing the back-to-back catastrophic freezes that occurred in the Florida citrus industry in the 1980s. We first use the traditional method to determine the welfare change due to a freeze (1) for a citrus grove that loses one crop and is able to return to full production the next year (simulating destruction of annual crops), and (2)the lower measure of welfare loss due to a citrus grove that loses all of its trees and is abandoned or is replanted. The lower measure is used to simulate the legal doctrine of avoidable consequences. These measures are then compared to substitute valuation measures that have been used by courts to determine welfare changes. For case 1, total revenue overestimated losses by 35.6%. For case 2, total revenue overestimates losses by 55.3%, tree replacement value underestimates losses by 93.6%, and changes in land value underestimates losses by 13.2%.citrus, perennial crops, catastrophic loss, damages, freeze, Crop Production/Industries,

Effects of a Severe Cold Event on the Subtropical, Estuarine-Dependent Common Snook, Centropomus undecimalis

The effects of infrequent disturbance events on marine fishes are often difficult to determine, due largely to lack of sufficient pre- and post-disturbance event data. In January 2010, subtropical southwestern Florida (USA) experienced extreme cold for 13 days, which caused extensive mortality of many fish species. The effect of this severe cold event on common snook (Centropomus undecimalis), an economically important gamefish, was assessed using three years (2007-2009) of pre-event and one year (2010) of post-event data from a tag-recapture program conducted over 28 km of Gulf of Mexico barrier islands of Florida. All metrics pointed to a significant effect of the severe cold event: post-disturbance apparent survival of marked fish was 96-97% lower than pre-disturbance, and post-disturbance common snook abundance was 75.57% and 41.88% less than in 2008 and 2009, the two years immediately pre-event. Although severe cold events have impacted subtropical Florida in the past, these events are infrequent (the previous recorded event was \u3e30 years prior), and documentation of the impacts on common snook have not previously been published

Political economics, collective action and wicked socio-ecological problems: A practice story from the field

Empowering integrative, sustainable and equitable approaches to wicked socio-ecological problems requires multiple disciplines and ways of knowing. Following calls for greater attention to political economics in this transdisciplinary work, we offer a practitioner perspective on political economy and collective action and their influences on our community engagement practice and public policy. Our perspective is grounded in a pervasive wicked problem in Australia, invasive rabbits, and the emergence of the Victorian Rabbit Action Network. The network grew out of a publically funded research project to support community-led action in rabbit management. Victorian residents and workers affected by rabbits – public and private land managers, scientists, government officers and others – were invited to engage in a participatory planning process to generate sustainable strategies to address the rabbit problem. Each stage in the process, which involved interviews, a workshop and consultations, was designed to nurture the critical enquiry, listening and learning skills of participants, advance understandings of the problem from multiple perspectives, generate collective options to guide decision-making, and encourage community-led collective action. We reflect on our understanding of these processes using the language and lens of political economics and, in particular, the context of democratic professionalism. In so doing, we define terms and refer to information resources that have enabled us to bring a practical working knowledge of political economics to our professional practice. Our intent is to motivate academics, community members, government officials, and scientists alike, to draw on their knowledge and field experiences and to share practice stories through the lens of political economics and collective action. This is an opportunity to engage each other in small ‘p’ politics of how we understand and act on wicked problems, to negotiate and connect across disciplines, practical experiences and human difference, so that people may work more creatively and effectively together to address the challenging issues of our time. &nbsp

Uniform approximation of Vapnik–Chervonenkis classes

For any family of measurable sets in a probability space, we show that either (i) the family has infinite Vapnik–Chervonenkis (VC) dimension or (ii) for every $\varepsilon >0$ there is a finite partition $\pi$ such the essential $\pi$-boundary of each set has measure at most $\varepsilon$. Immediate corollaries include the fact that a separable family with finite VC dimension has finite bracketing numbers, and satisfies uniform laws of large numbers for every ergodic process. From these corollaries, we derive analogous results for VC major and VC graph families of functions