A Stochastic View of Optimal Regret through Minimax Duality

We study the regret of optimal strategies for online convex optimization games. Using von Neumann's minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical minimization algorithm in a stochastic process setting: it is equal to the maximum, over joint distributions of the adversary's action sequence, of the difference between a sum of minimal expected losses and the minimal empirical loss. We show that the optimal regret has a natural geometric interpretation, since it can be viewed as the gap in Jensen's inequality for a concave functional--the minimizer over the player's actions of expected loss--defined on a set of probability distributions. We use this expression to obtain upper and lower bounds on the regret of an optimal strategy for a variety of online learning problems. Our method provides upper bounds without the need to construct a learning algorithm; the lower bounds provide explicit optimal strategies for the adversary. Peter L. Bartlett, Alexander Rakhlin

Making coups history

International support is capable of making the difference between the successful defense of democracy and its ignominious defeat. Indeed, the perceived probability of both support for democratically chosen leaders and opposition to their attackers can fundamentally shift the balance in the domestic struggle between them. Nevertheless, although changes to international law and international relations justify a greater international role in preventing and deterring coups and erosions, not all responsibility for protecting democracy should be assigned to the international community. Indeed, the first line of defense should be a democracy’s own domestic initiatives, with the main role of the international community being to support a domestic response to threats to democracy.

How can soil monitoring networks be used to improve predictions of organic carbon pool dynamics and CO2 fluxes in agricultural soils?

Abstract As regional and continental carbon balances of terrestrial ecosystems become available, it becomes clear that the soils are the largest source of uncertainty. Repeated inventories of soil organic carbon (SOC) organized in soil monitoring networks (SMN) are being implemented in a number of countries. This paper reviews the concepts and design of SMNs in ten countries, and discusses the contribution of such networks to reducing the uncertainty of soil carbon balances. Some SMNs are designed to estimate country-specific land use or management effects on SOC stocks, while others collect soil carbon and ancillary data to provide a nationally consistent assessment of soil carbon condition across the major land-use/soil type combinations. The former use a single sampling campaign of paired sites, while for the latter both systematic (usually grid based) and stratified repeated sampling campaigns (5–10 years interval) are used with densities of one site per 10–1,040 km². For paired sites, multiple samples at each site are taken in order to allow statistical analysis, while for the single sites, composite samples are taken. In both cases, fixed depth increments together with samples for bulk density and stone content are recommended. Samples should be archived to allow for re-measurement purposes using updated techniques. Information on land management, and where possible, land use history should be systematically recorded for each site. A case study of the agricultural frontier in Brazil is presented in which land use effect factors are calculated in order to quantify the CO2 fluxes from national land use/management conversion matrices. Process-based SOC models can be run for the individual points of the SMN, provided detailed land management records are available. These studies are still rare, as most SMNs have been implemented recently or are in progress. Examples from the USA and Belgium show that uncertainties in SOC change range from 1.6–6.5 Mg C ha−1 for the prediction of SOC stock changes on individual sites to 11.72 Mg C ha−1 or 34% of the median SOC change for soil/land use/climate units. For national SOC monitoring, stratified sampling sites appears to be the most straightforward attribution of SOC values to units with similar soil/land use/climate conditions (i.e. a spatially implicit upscaling approach). Keywords Soil monitoring networks - Soil organic carbon - Modeling - Sampling design

Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations

Maximum-likelihood estimates of the parameters of stochastic differential equations are consistent and asymptotically efficient, but unfortunately difficult to obtain if a closed-form expression for the transitional probability density function of the process is not available. As a result, a large number of competing estimation procedures have been proposed. This article provides a critical evaluation of the various estimation techniques. Special attention is given to the ease of implementation and comparative performance of the procedures when estimating the parameters of the Cox–Ingersoll–Ross and Ornstein–Uhlenbeck equations respectively.

Hierarchical Bayesian modelling of early detection surveillance for plant pest invasions

Early detection surveillance programs aim to find invasions of exotic plant pests and diseases before they are too widespread to eradicate. However, the value of these programs can be difficult to justify when no positive detections are made. To demonstrate the value of pest absence information provided by these programs, we use a hierarchical Bayesian framework to model estimates of incursion extent with and without surveillance. A model for the latent invasion process provides the baseline against which surveillance data are assessed. Ecological knowledge and pest management criteria are introduced into the model using informative priors for invasion parameters. Observation models assimilate information from spatio-temporal presence/absence data to accommodate imperfect detection and generate posterior estimates of pest extent. When applied to an early detection program operating in Queensland, Australia, the framework demonstrates that this typical surveillance regime provides a modest reduction in the estimate that a surveyed district is infested. More importantly, the model suggests that early detection surveillance programs can provide a dramatic reduction in the putative area of incursion and therefore offer a substantial benefit to incursion management. By mapping spatial estimates of the point probability of infestation, the model identifies where future surveillance resources can be most effectively deployed.

Statistical analyses of weigh-in-motion data for bridge live load development

This paper discusses the statistical analyses used to derive bridge live loads models for Hong Kong from a 10-year weigh-in-motion (WIM) data. The statistical concepts required and the terminologies adopted in the development of bridge live load models are introduced. This paper includes studies for representative vehicles from the large amount of WIM data in Hong Kong. Different load affecting parameters such as gross vehicle weights, axle weights, axle spacings, average daily number of trucks etc are first analyzed by various stochastic processes in order to obtain the mathematical distributions of these parameters. As a prerequisite to determine accurate bridge design loadings in Hong Kong, this study not only takes advantages of code formulation methods used internationally but also presents a new method for modelling collected WIM data using a statistical approach.