Probabilistic earthquake-tsunami multi-hazard analysis:application to the Tohoku region, Japan

This study develops a novel simulation-based procedure for the estimation of the likelihood that seismic intensity (in terms of spectral acceleration) and tsunami inundation (in terms of wave height), at a particular location, will exceed given hazard levels. The procedure accounts for a common physical rupture process for shaking and tsunami. Numerous realizations of stochastic slip distributions of earthquakes having different magnitudes are generated using scaling relationships of source parameters for subduction zones and then using a stochastic synthesis method of earthquake slip distribution. Probabilistic characterization of earthquake and tsunami intensity parameters is carried out by evaluating spatially correlated strong motion intensity through the adoption of ground motion prediction equations as a function of magnitude and shortest distance from the rupture plane and by solving nonlinear shallow water equations for tsunami wave propagation and inundation. The minimum number of simulations required to obtain stable estimates of seismic and tsunami intensity measures is investigated through a statistical bootstrap analysis. The main output of the proposed procedure is the earthquake-tsunami hazard curves representing, for each mean annual rate of occurrence, the corresponding seismic and inundation tsunami intensity measures. This simulation-based procedure facilitates the earthquake-tsunami hazard deaggregation with respect to magnitude and distance. Results are particularly useful for multi-hazard mapping purposes and the developed framework can be further extended to probabilistic earthquake-tsunami risk assessment

Optimal rates of convergence for persistence diagrams in Topological Data Analysis

Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a statistical approach. We show that the use of persistent homology can be naturally considered in general statistical frameworks and persistence diagrams can be used as statistics with interesting convergence properties. Some numerical experiments are performed in various contexts to illustrate our results

Intra-industry trade and labour market adjustment: A reassessment using data on individual workers

We re-examine the relationship between intra-industry trade and labour reallocation, using individual-level data on manufacturing worker moves in the United Kingdom. The contribution of this analysis is twofold. First, we estimate the impact of intra-industry trade on worker moves between occupations as well as between industries. Second, we run individual-level regressions that allow us to control for worker heterogeneity. Our results suggest that intra-industry trade does have the stipulated attenuating effect on worker moves, both between occupations and between industries, but that this effect is relatively small compared to other determinants of labour reallocation

Minimax estimation of smooth optimal transport maps

Brenier's theorem is a cornerstone of optimal transport that guarantees the existence of an optimal transport map $T$ between two probability distributions $P$ and $Q$ over $\mathbb{R}^d$ under certain regularity conditions. The main goal of this work is to establish the minimax estimation rates for such a transport map from data sampled from $P$ and $Q$ under additional smoothness assumptions on $T$. To achieve this goal, we develop an estimator based on the minimization of an empirical version of the semi-dual optimal transport problem, restricted to truncated wavelet expansions. This estimator is shown to achieve near minimax optimality using new stability arguments for the semi-dual and a complementary minimax lower bound. Furthermore, we provide numerical experiments on synthetic data supporting our theoretical findings and highlighting the practical benefits of smoothness regularization. These are the first minimax estimation rates for transport maps in general dimension.Comment: 53 pages, 6 figure