Spatio-Temporal Modeling of Southern Pine Beetle Outbreaks with a Block Bootstrapping Approach

Our study focuses on modeling southern pine beetle (SPB) outbreaks in the southern area. The approach is to evaluate SPB outbreak frequency in a spatio-temporal framework. A block bootstrapping method with zero-inflated estimation has been proposed to construct a statistical model accounting for explanatory variables while adjusting for spatial and temporal autocorrelation. Although the bootstrap (Efron 1979) method can handle independent observations well, the strong autocorrelation of SPB outbreaks brings about a major challenge. Motivated by bootstrapping overlapping blocks method in autoregressive time series scenario (Kunsch 1989) and block bootstrapping method of dependent data from a spatial map (Hall 1985), we have developed a method to bootstrap overlapping spatio-temporal blocks. By selecting an appropriate block size, the spatial-temporal correlation can be eliminated. The second challenge arises from the fact that the SPB spots distribution has a heavy weight on 0. To accommodate this issue, the zero-inflated models are adopted in the estimation stage. With our saptio-temporal block bootstrapping approach, impacts of environmental factors on SPB outbreaks and implications of pine forest management are assessed. Almost all the explanatory variables, including drought, temperature, forest ecosystem and hurricane, have been detected to have significant impacts. Forestland size and government share of forestland would positively contribute to SPB outbreaks significantly. Meanwhile, our method offers a way to forecast the frequency of future SPB outbreaks, given the current environmental information of a county.Southern Pinebeetle, Block Bootstrapping, Risk and Uncertainty,

Price of Anarchy for Non-atomic Congestion Games with Stochastic Demands

We generalize the notions of user equilibrium and system optimum to non-atomic congestion games with stochastic demands. We establish upper bounds on the price of anarchy for three different settings of link cost functions and demand distributions, namely, (a) affine cost functions and general distributions, (b) polynomial cost functions and general positive-valued distributions, and (c) polynomial cost functions and the normal distributions. All the upper bounds are tight in some special cases, including the case of deterministic demands.Comment: 31 page