Nonstationary Hazards Research Articles

Time-varying copula and average annual reliability-based nonstationary hazard assessment of extreme rainfall events

Due to global climate change and urbanization, more attention has been paid to decipher the nonstationary multivariate risk analysis from the perspective of probability distribution establishment. In this study, a multivariate nonstationary hazard assessment of annual extreme rainfall events, extracted from daily precipitation data observed at eight meteorological stations in Haihe River basin, China, was done in three phases: (1) Several statistical tests, such as nonparametric trend tests, log likelihood ratio (LR) tests and Change-point (CP) tests were applied to both the marginal distributions and the dependence structures to decipher different forms of nonstationarity; (2) estimation of the time-varying parameter for the marginal and joint probability distributions by maximum likelihood method; and (3) calculation of hydrologic design quantiles at different average annual reliability levels (ARR) during a certain design life period in terms of hazard assessment. According to the results, the attributes and their dependence structure belonging to several stations show nonstationarity because of existed trend in model parameter or change point. In the process of hazard assessment, the nonstationarity of dependence structure would produce less impact on ARR-based designed quantile estimation than the nonstationarity of marginal distribution on the one hand. On the other hand, it would add more uncertainty of quantile estimation for hydrologic design.

Higher-order analysis of probabilistic long-term loss under nonstationary hazards

Quantification of hazard-induced losses plays a significant role in risk assessment and management of civil infrastructure subjected to hazards in a life-cycle context. A rational approach to assess long-term loss is of vital importance. The loss assessment associated with stationary hazard models and low-order moments (i.e., expectation and variance) has been widely investigated in previous studies. This paper proposes a novel approach for the higher-order analysis of long-term loss under both stationary and nonstationary hazards. An analytical approach based on the moment generating function is developed to assess the first four statistical moments of long-term loss under different stochastic models (e.g., homogeneous Poisson process, non-homogeneous Poisson process, renewal process). Based on the law of total expectation, the developed approach expands the application scope of the moment generating function to nonstationary models and higher-order moments (i.e., skewness and kurtosis). Furthermore, by employing the convolution technique, the proposed approach effectively addresses the difficulty of assessing higher-order moments in a renewal process. Besides the loss analysis, the mixed Poisson process, a relatively new stochastic model, is introduced to consider uncertainty springing from the stochastic occurrence rate. Two illustrative examples are presented to demonstrate practical implementations of the developed approach. Ultimately, the proposed framework could aid the decision-maker to select the optimal option by incorporating higher-order moments of long-term loss within the decision-making process.

Extreme events and predictability of catastrophic failure in composite materials and in the Earth

Despite all attempts to isolate and predict extreme earthquakes, these nearly always occur without obvious warning in real time: fully deterministic earthquake prediction is very much a ‘black swan’. On the other hand engineering-scale samples of rocks and other composite materials often show clear precursors to dynamic failure under controlled conditions in the laboratory, and successful evacuations have occurred before several volcanic eruptions. This may be because extreme earthquakes are not statistically special, being an emergent property of the process of dynamic rupture. Nevertheless, probabilistic forecasting of event rate above a given size, based on the tendency of earthquakes to cluster in space and time, can have significant skill compared to say random failure, even in real-time mode. We address several questions in this debate, using examples from the Earth (earthquakes, volcanoes) and the laboratory, including the following. How can we identify ‘characteristic’ events, i.e. beyond the power law, in model selection (do dragon-kings exist)? How do we discriminate quantitatively between stationary and non-stationary hazard models (is a dragon likely to come soon)? Does the system size (the size of the dragon’s domain) matter? Are there localising signals of imminent catastrophic failure we may not be able to access (is the dragon effectively invisible on approach)? We focus on the effect of sampling effects and statistical uncertainty in the identification of extreme events and their predictability, and highlight the strong influence of scaling in space and time as an outstanding issue to be addressed by quantitative studies, experimentation and models.

A non-stationary hazard function of leaving unemployment for employment

This paper introduces a non-stationary hazard of exiting unemployment for employment. The source of the non-stationarity is the duration dependent intensity of offer arrivals subject to a Poisson process. Based on these non-stationary offer arrivals and simplifying assumptions, a closed form non-stationary hazard of exiting unemployment is derived using a sequential search model.