Unified landslide hazard assessment using hurdle models: a case study in the Island of Dominica

Climatically-induced natural hazards are a threat to communities. They can cause life losses and heavy damage to infrastructure, and due to climate change, they have become increasingly frequent. This is especially in tropical regions, where major hurricanes have consistently appeared in recent history. Such events induce damage due to the high wind speed they carry, and the high intensity/duration rainfall they discharge can further induce a chain of hydro-morphological hazards in the form of widespread debris slides/flows. The way the scientific community has developed preparatory steps to mitigate the potential damage of these hydro-morphological threats includes assessing where they are likely to manifest across a given landscape. This concept is referred to as susceptibility, and it is commonly achieved by implementing binary classifiers to estimate probabilities of landslide occurrences. However, predicting where landslides can occur may not be sufficient information, for it fails to convey how large landslides may be. This work proposes using a flexible Bernoulli-log-Gaussian hurdle model to simultaneously model landslide occurrence and size per areal unit. Covariate and spatial information are introduced using a generalised additive modelling framework. To cope with the high spatial resolution of the data, our model uses a Markovian representation of the Matérn covariance function based on the stochastic partial differential equation (SPDE) approach. Assuming Gaussian priors, our model can be integrated into the class of latent Gaussian models, for which inference is conveniently performed based on the integrated nested Laplace approximation method. We use our modelling approach in Dominica, where Hurricane Maria (September 2017) induced thousands of shallow flow-like landslides passing over the island. Our results show that we can not only estimate where landslides may occur and how large they may be, but we can also combine this information in a unified landslide hazard model, which is the first of its kind.

Conversion Among Arma Models And State-Space Representation

We present the ARMA models (or Non-Markovian) and state-space (or Markovian) representation relationship. Then we break the problem into three different cases to discuss how one form could be converted to another form. In case A, we assume that we know the state-space representation then we convert it into the ARMA model. In case B, we reverse the situation, given the ARMA model we convert into state-space representation. In Case C, we combine the first two cases, conversion the two forms in either directions.

The Limit of Stationary Distributions of Many-Server Queues in the Halfin–Whitt Regime

We consider the so-called GI/GI/N queue, in which a stream of jobs with independent and identically distributed service times arrive as a renewal process to a common queue that is served by [Formula: see text] identical parallel servers in a first-come, first-served manner. We introduce a new representation for the state of the system and, under suitable conditions on the service and interarrival distributions, establish convergence of the corresponding sequence of centered and scaled stationary distributions in the so-called Halfin–Whitt asymptotic regime. In particular, this resolves an open question posed by Halfin and Whitt in 1981. We also characterize the limit as the stationary distribution of an infinite-dimensional, two-component Markov process that is the unique solution to a certain stochastic partial differential equation. Previous results were essentially restricted to exponential service distributions or service distributions with finite support, for which the corresponding limit process admits a reduced finite-dimensional Markovian representation. We develop a different approach to deal with the general case when the Markovian representation of the limit is truly infinite dimensional. This approach is more broadly applicable to a larger class of networks.

Performance Guarantees for Homomorphisms beyond Markov Decision Processes

Most real-world problems have huge state and/or action spaces. Therefore, a naive application of existing tabular solution methods is not tractable on such problems. Nonetheless, these solution methods are quite useful if an agent has access to a relatively small state-action space homomorphism of the true environment and near-optimal performance is guaranteed by the map. A plethora of research is focused on the case when the homomorphism is a Markovian representation of the underlying process. However, we show that nearoptimal performance is sometimes guaranteed even if the homomorphism is non-Markovian.

On the Applicability of the Ho-Kalman Minimal Realization Theory

The reduced-order model of a time-invariant linear dynamical system, excited by a force of an impulsive type, may be readily obtained using the Ho-Kalman minimal-realization algorithm [1]. The method is based upon a particular factorization of the Hankel matrix in the Markovian representation of the discrete-time process. For stochastic systems, the applicability of the theory has been demonstrated by Akaike [2] on the assumption that the excitation is a zero-mean white noise of a gaussian type. Some of the most widely known output-only identification methods, such as Eigensystem Realization Algorithm (ERA), Canonical Variate Analysis (CVA), and Balanced Realization (BR)) are based upon the above-mentioned work, with the aid of a robust factorization technique, such as Singular-Value Decomposition (SVD). Notwithstanding the growing popularity of the above methods, some aspects of their applicability are not yet understood. Two points are of particular interest: the first regards the applicability of the theory in highly damped systems; and the second regards its applicability to systems driven by excitations different from the one hypothesized. The aim of the present work is to define a reliable test on the hypotheses. Some numerical and experimental results are presented.