Point process modeling of wildfire hazard in Los Angeles County, California

The Burning Index (BI) produced daily by the United States government's National Fire Danger Rating System is commonly used in forecasting the hazard of wildfire activity in the United States. However, recent evaluations have shown the BI to be less effective at predicting wildfires in Los Angeles County, compared to simple point process models incorporating similar meteorological information. Here, we explore the forecasting power of a suite of more complex point process models that use seasonal wildfire trends, daily and lagged weather variables, and historical spatial burn patterns as covariates, and that interpolate the records from different weather stations. Results are compared with models using only the BI. The performance of each model is compared by Akaike Information Criterion (AIC), as well as by the power in predicting wildfires in the historical data set and residual analysis. We find that multiplicative models that directly use weather variables offer substantial improvement in fit compared to models using only the BI, and, in particular, models where a distinct spatial bandwidth parameter is estimated for each weather station appear to offer substantially improved fit.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS401 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotic expansions and fast computation of oscillatory Hilbert transforms

In this paper, we study the asymptotics and fast computation of the one-sided oscillatory Hilbert transforms of the form $$H^{+}(f(t)e^{i\omega t})(x)=-int_{0}^{\infty}e^{i\omega t}\frac{f(t)}{t-x}dt,\qquad \omega>0,\qquad x\geq 0,$$ where the bar indicates the Cauchy principal value and $f$ is a real-valued function with analytic continuation in the first quadrant, except possibly a branch point of algebraic type at the origin. When $x=0$, the integral is interpreted as a Hadamard finite-part integral, provided it is divergent. Asymptotic expansions in inverse powers of $\omega$ are derived for each fixed $x\geq 0$, which clarify the large $\omega$ behavior of this transform. We then present efficient and affordable approaches for numerical evaluation of such oscillatory transforms. Depending on the position of $x$, we classify our discussion into three regimes, namely, $x=\mathcal{O}(1)$ or $x\gg1$, $0<x\ll 1$ and $x=0$. Numerical experiments show that the convergence of the proposed methods greatly improve when the frequency $\omega$ increases. Some extensions to oscillatory Hilbert transforms with Bessel oscillators are briefly discussed as well.Comment: 32 pages, 6 figures, 4 table

Housing over time and over the life cycle: a structural estimation

We estimate a structural model of optimal life-cycle housing and consumption in the presence of realistic labor income and house price uncertainties. The model postulates constant elasticity of substitution between housing service and nonhousing consumption, and explicitly incorporates a house adjustment cost. Our estimation fits the cross-sectional and time-series household wealth and housing profiles from the Panel Study of Income Dynamics quite well, and suggests an intra-temporal elasticity of substitution between housing and nonhousing consumption of 0.33 and a housing adjustment cost that amounts to about 15 percent of house value. Policy experiments with estimated preference parameters imply that households respond nonlinearly to house price changes with large house price declines leading to sizable decreases in both the aggregate homeownership rate and aggregate non-housing consumption. The average marginal propensity to consume out of housing wealth changes ranges from 0.4 percent to 6 percent. When lending conditions are tightened in the form of a higher down payment requirement, interestingly, large house price declines result in more severe drops in the aggregate homeownership rate but milder decreases in nonhousing consumption.