Stochastic Set Research Articles

LPM Density Functions for the Computation of the SD Efficient Set

The equivalence between partial moments and stochastic dominance dates back to Bawa [1] and Fishburn [2]. We present a test for first, second, and third degree stochastic dominance between two variables using Lower Partial Moments. The results uphold Hadar and Russell’s [3] original conclusions about the odd moments of preferred prospects. We recall Nawrocki’s [4] research comparing Mean/Variance portfolios against the continuum of risk-averse investors using Lower Partial Moments. The excess skewness of the LPM portfolios clearly demonstrates the preference of positive skewness for risk-averse investors. Finally, we provide an algorithm for efficiently determining stochastic dominance efficient sets among large numbers of variables.

Capturing rogue waves by multi-point statistics

As an example of a complex system with extreme events, we investigate ocean wave states exhibiting rogue waves. We present a statistical method of data analysis based on multi-point statistics which for the first time allows the grasping of extreme rogue wave events in a highly satisfactory statistical manner. The key to the success of the approach is mapping the complexity of multi-point data onto the statistics of hierarchically ordered height increments for different time scales, for which we can show that a stochastic cascade process with Markov properties is governed by a Fokker–Planck equation. Conditional probabilities as well as the Fokker–Planck equation itself can be estimated directly from the available observational data. With this stochastic description surrogate data sets can in turn be generated, which makes it possible to work out arbitrary statistical features of the complex sea state in general, and extreme rogue wave events in particular. The results also open up new perspectives for forecasting the occurrence probability of extreme rogue wave events, and even for forecasting the occurrence of individual rogue waves based on precursory dynamics.

A mean-reverting stochastic model for the political business cycle

In this article, we look at the political business cycle problem through the lens of uncertainty. The feedback control used by us is the famous NKPC with stochasticity and wage rigidities. We extend the New Keynesian Phillips Curve model to the continuous time stochastic set up with an Ornstein–Uhlenbeck process. We minimize relevant expected quadratic cost by solving the corresponding Hamilton–Jacobi–Bellman equation. The basic intuition of the classical model is qualitatively carried forward in our set up but uncertainty also plays an important role in determining the optimal trajectory of the voter support function. The internal variability of the system acts as a base shifter for the support function in the risk neutral case. The role of uncertainty is even more prominent in the risk averse case where all the shape parameters are directly dependent on variability. Thus, in this case variability controls both the rates of change as well as the base shift parameters. To gain more insight we have also studied the model when the coefficients are time invariant and studied numerical solutions. The close relationship between the unemployment rate and the support function for the incumbent party is highlighted. The role of uncertainty in creating sampling fluctuation in this set up, possibly towards apparently anomalous results, is also explored.

ELM Regime Classification by Conformal Prediction on an Information Manifold

Characterization and control of plasma instabilities known as edge-localized modes (ELMs) is crucial for the operation of fusion reactors. Recently, machine learning methods have demonstrated good potential in making useful inferences from stochastic fusion data sets. However, traditional classification methods do not offer an inherent estimate of the goodness of their prediction. In this paper, a distance-based conformal predictor classifier integrated with a geometric-probabilistic framework is presented. The first benefit of the approach lies in its comprehensive treatment of highly stochastic fusion data sets, by modeling the measurements with probability distributions in a metric space. This enables calculation of a natural distance measure between probability distributions: the Rao geodesic distance. Second, the predictions are accompanied by estimates of their accuracy and reliability. The method is applied to the classification of regimes characterized by different types of ELMs based on the measurements of global parameters and their error bars. This yields promising success rates and outperforms state-of-the-art automatic techniques for recognizing ELM signatures. The estimates of goodness of the predictions increase the confidence of classification by ELM experts, while allowing more reliable decisions regarding plasma control and at the same time increasing the robustness of the control system.

Coupling mode-destination accessibility with seismic risk assessment to identify at-risk communities

In this paper, we develop a framework for coupling mode-destination accessibility with quantitative seismic risk assessment to identify communities at high risk for travel disruptions after an earthquake. Mode-destination accessibility measures the ability of people to reach destinations they desire. We use a probabilistic seismic risk assessment procedure, including a stochastic set of earthquake events, ground-motion intensity maps, damage maps, and realizations of traffic and accessibility impacts. For a case study of the San Francisco Bay Area, we couple our seismic risk framework with a practical activity-based traffic model. As a result, we quantify accessibility risk probabilistically by community and household type. We find that accessibility varies more strongly as a function of travelers׳ geographic location than as a function of their income class, and we identify particularly at-risk communities. We also observe that communities more conducive to local trips by foot or bike are predicted to be less impacted by losses in accessibility. This work shows the potential to link quantitative risk assessment methodologies with high-resolution travel models used by transportation planners. Quantitative risk metrics of this type should have great utility for planners working to reduce risk to a region׳s infrastructure systems.

Stochastic particle level set simulations of buoyancy-driven droplets in non-Newtonian fluids

The aim of this paper is to present stochastic, micro–macro simulations of droplets rising in non-Newtonian fluids by means of a particle level set method implemented using the Finite Element Method (FEM) and semi-Lagrangian schemes. A set of dumbbells scattered throughout the domain conveys the molecular information from the microscopic scale to the macroscopic scale, first by integrating the stochastic-equivalent of the Fokker–Planck equations, then by taking second moments from the internal configurations to produce the polymer stress tensor to be incorporated into the macroscopic momentum equation. The kinetic models considered in this work are the simpler Hooke (Oldroyd-B constitutive) model, and the more realistic ‘Finitely Extensible Nonlinear Elastic’ (FENE) model. First, we carry out microscopic and macroscopic convergence analyses to validate the numerical calculations of 2D rising droplets, obtaining satisfactory results for grids of size 1/h={40,80,160},and a number of particles ranging from Nd=105up to 1.75 · 108, making use of both kinetic models along with mildly viscoelastic effects in solutions with relatively low polymeric concentrations and relaxation times (De=1,c=1). We then perform a series of increasingly elastic simulations that ends up with the arrival of two purely non-Newtonian features: the onset of a cusp-like tail and the appearance of downward velocities at a certain distance of the droplet (negative wake).

Evolution through the stochastic dyadic Cantor Set: the uniqueness of mankind in the Universe

AbstractThe search for intelligent life or any type of life involves processes with nonlinear chaotic behaviours throughout the Universe. Through the sensitive dependence condition, chaotic dynamics are also difficult or impossible to duplicate, forecast and predict. Similar evolution patterns will result in completely different outcomes. Even, the intelligent life evolution pattern, based on carbon, DNA–RNA–protein, will differ from all possible sequences. In the present paper, the stochastic dyadic Cantor set models the many possible variations of such chaotic behaviours in the Universe, yielding to a tendency to zero, for any scenario of intelligent life evolution. The probability of the development of the exact microscopic and macroscopic scenario that is capable of supporting intelligent life or any other type of life in any planet is vanishingly small. Thus, the present analysis suggests that mankind, as an extremely statistically uncommon occurrence, is unique and alone in the Universe.

A new approach to probabilistic earthquake-induced tsunami risk assessment

A new approach is proposed for the probabilistic financial risk assessment of earthquake-induced tsunami. The risk is evaluated in a probabilistic framework for a full set of hazard events including all uncertainties. The hazard is defined as a stochastic and historic set of events, collectively exhaustive and mutually exclusive, that describes the spatial distribution, the annual frequency and the randomness of the hazard intensity. The risk is expressed as losses in different terms: the average annual loss and the loss exceedance curve. These metrics are of particular importance for risk financing schemes and risk transfer instruments. As an illustrative example, this approach is applied to the probabilistic tsunami risk assessment for public schools in southern Mexico.

Application of a synthetic cyclone method for assessment of tropical cyclone storm tides in Samoa

Tropical cyclone-induced storm surges cause damaging impacts in coastal regions. The present study uses a stochastic cyclone modelling approach to evaluate the likelihoods of storm tides, the combination of storm surges and astronomical tides, for Samoa. Cyclones that occurred in the vicinity of Samoa from 1969 to 2009 are used to build a stochastic tropical cyclone data set, and an analytic cyclone model and hydrodynamic model are used to model storm tides under average, La Nina and El Nino cyclone and sea level conditions for present climate conditions as well as cyclone and sea level conditions relevant for 2055, and storm tide return periods are estimated. We find that extreme storm tides exhibit relatively modest variation around the coastline of Samoa owing to the uniform width of the shelf surrounding the coastlines of two main islands of Savai’i and Upolu. The frequency of cyclones and hence storm tides during El Nino conditions is similar to the frequency for all seasons, but is considerably lower in La Nina conditions. For the future, tropical cyclones are assumed to undergo decreased frequency and increased intensity. This is found to lower the storm tide height for return periods <100 years and increase it for return periods greater than about 200 years. Sea level rise is shown to have a larger influence on storm tides than future changes to tropical cyclones. Considering the aggregated probabilities of storm tides occurring at the national scale, we find that the likelihood of a storm tide occurring that locally exceeds a 1-in-100-year level (i.e. an event with a 1 % annual exceedance probability) has a 6 % probability of occurring somewhere along the entire coastline of Samoa. Such information may be useful for those involved in coastal management and disaster response for which there may be a need to consider the overall likelihood that a nation may have to respond to such a disaster.

The effect of choice set misspecification on welfare measures in random utility models

Random utility models have been widely employed in environmental valuation. But stochastic choice set formation models in the random utility framework are rarely applied in this literature, although previous research has shown that ignoring choice set formation (when it exists) leads to biased parameter estimates and welfare measures. This paper conducts Monte Carlo (MC) experiments to investigate the directionality and magnitude of welfare measure bias arising from ignoring or misspecifying choice set formation. We find that when attribute cutoff-based choice set formation exists in the data generation process, typical RUM models ignoring or misspecifying choice set formation underestimate welfare measures by 30–50%. Models that approximate choice set formation may produce unbiased welfare measures, but constitute a promising area for future research. This paper illustrates the importance of applying choice set formation in environmental valuation and provides practical guidance about the usage of stochastic choice set formation models.

Learning daily activity patterns with probabilistic grammars

Daily activity pattern is the reflection and abstraction of actual individual activity participation on daily basis. It carries information on activity type, frequency and sequence. Preference of daily activity patterns varies among population, and thus can be interpreted as personal life styles. This paper advances studies on human daily activity patterns by providing new perspective and methodology in the modeling and learning of daily activity patterns using probabilistic context-free grammars. In this paper, similarities between daily activity pattern—which is defined as activity sequence—and language are explored. We developed context-free grammars to parse and generate daily activity patterns. To replicate people’s heterogeneity in selecting daily activity patterns, we introduced probabilistic context-free grammars and proposed several formulations to estimate the probability of a context-free grammar with daily activity patterns observed in household travel survey. We conducted experiments on the proposed formulations, finding that under proper context-free grammar and problem formulation, the estimated probabilistic context-free grammar is able to reproduce the observed pattern distribution in household travel survey with satisfactory precision. Practically, the proposed methodology sheds light on the issue of generating stochastic and accessibility-dependent choice sets for daily activity pattern models in certain activity-based modeling frameworks.

A Mean-Reverting Stochastic Model for the Political Business Cycle

In this paper we look at the PBC problem through the lens of uncertainty. The feedback control used by us is the famous NKPC with stochasticity and wage rigidities. We extend the NKPC model to the continuous time stochastic set up with an Ornstein-Uhlenbeck process. We minimize relevant expected quadratic cost by solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation. The basic intuition of the classical model is qualitatively carried forward in our set up but uncertainty also plays an important role in determining the optimal trajectory of the voter support function. The internal variability of the system acts as a base shifter for the support function in the risk neutral case. The role of uncertainty is even more prominent in the risk averse case where all the shape parameters are directly dependent on variability. Thus, in this case variability controls both the rates of change as well as the base shift parameters. To gain more insight we have also studied the model when the coefficients are time invariant and studied numerical solutions. The close relationship between the unemployment rate and the support function for the incumbent party is highlighted. The role of uncertainty in creating sampling fluctuation in this set up, possibly towards apparently anomalous results, is also explored.

A Fast and Robust Framework for Semiautomatic and Automatic Registration of Photographs to 3D Geometry

We present a simple, fast, and robust complete framework for 2D/3D registration capable to align in a semiautomatic or completely automatic manner a large set of unordered images to a massive point cloud. Our method converts the hard to solve image-to-geometry registration task in a Structure-from-Motion (SfM) plus a 3D/3D alignment problem. We exploit a SfM framework that, starting just from an unordered image collection, computes an estimate of the camera parameters and a sparse 3D geometry deriving from matched image features. We then coarsely register this model to the given 3D geometry by estimating a global scale and absolute orientation using two solutions: a minimal user intervention or a stochastic global point set registration approach. A specialized sparse bundle adjustment (SBA) step, that exploits the correspondence between the sparse geometry and the fine input 3D model, is then used to refine intrinsic and extrinsic parameters of each camera. Output data is suitable for photo blending frameworks to produce seamless colored models. The effectiveness of the method is demonstrated on a series of synthetic and real-world 2D/3D Cultural Heritage datasets.

Event-based approach for probabilistic agricultural drought risk assessment under rainfed conditions

An event-based approach for the probabilistic risk assessment of agricultural drought under rainfed conditions to estimate the economic impact is proposed. The risk parameters are evaluated in an event-based probabilistic framework for a set of hazard events; these results are probabilistically integrated including, in a formal way, all uncertainties related to every part of the process. The hazard is defined as a stochastic or historic set of events, collectively exhaustive and mutually exclusive, that describes the spatial distribution, the annual frequency, and the randomness of the hazard intensity. The risk is expressed in different economic terms: the average annual loss (or pure risk premium) and the loss exceedance curve; these metrics are of particular importance for risk retention (financing) schemes or risk transfer instruments. As an illustrative example, this approach is applied to probabilistic drought risk assessment of maize under rainfed conditions in Mexico. These results are the base of further studies in defining strategies for financial protection against agricultural losses and disasters.

MODELLING NEARSHORE WAVES AND OVERTOPPING USING A STOCHASTIC TYPHOON SET

Typhoons and the storm surges and large waves generated by them have caused severe coastal damage in Japan such as during typhoon Vera in 1959. This event struck the Ise Bay region of Japan and caused wide spread devastation where coastal sea walls were destroyed and storm surges caused significant flooding destroying thousands of buildings and contaminating drinking water. This event caused approximately $1.9 billion worth of damage in today’s money (RMS report). Whilst Japan is well defended against surge and waves caused by typhoons some areas of defence could be liable to overtopping by very large waves acting on increased sea level due to surge and wave-setup. Breaching by powerful wave action may also occur exacerbating the situation and leaving low lying land susceptible to flooding. For example, during typhoon Vera earthen levees were either overtopped or breached and only defences constructed since 1953 along one side of Ise Bay after a previous typhoon could withstand the increased water levels and force of the waves (JWF, 2005). In this respect defences are constructed to design levels based on previous experience including a small tolerance level and may not cope with a storm that occurs in the tail end of the severity distribution. Were the 1959 Vera event to occur today, damage due to waves and storm surge could add up to $6 billion to total value of loss to residential properties including the wind loss despite improved flood defences (RMS report). It is important to try and quantify the possibility of flooding by all probable typhoons now and in the future. To estimate the potential loss due to certain events stochastic sets of typhoons can be statistically generated to create thousands of scenarios to drive surge and wave models and predict the magnitude of the surge and wave height at the coast (e.g. Yasuda et al., 2011). Modelling waves is very computationally expensive. Therefore, to create an event set based on thousands of typhoons a simplification of the modeling approach for waves at the coastal defences is required before simulating any subsequent overtopping. In this work a modeling system is developed to propagate the most severe typhoons (in terms of wave generation) in a stochastic set through a wave model to calculate any subsequent overtopping that is computationally viable and has a high degree of flexibility to explore uncertainties and investigate a range of scenarios.

A pseudo-optimal inexact stochastic interval T2 fuzzy sets approach for energy and environmental systems planning under uncertainty: A case study for Xiamen City of China

In this study, a new Pseudo-optimal Inexact Stochastic Interval Type-2 Fuzzy Sets Linear Programming (PIS-IT2FSLP) energy model is developed to support energy system planning and environment requirements under uncertainties for Xiamen City. The PIS-IT2FSLP model is based on an integration of interval Type 2 (T2) Fuzzy Sets (FS) boundary programming and stochastic linear programming techniques, enables it to have robust abilities to the tackle uncertainties expressed as T2 FS intervals and probabilistic distributions within a general optimization framework. This new model can sophisticatedly facilitate system analysis of energy supply and energy conversion processes, and environmental requirements as well as provide capacity expansion options with multiple periods. The PIS-IT2FSLP model was applied to a real case study of Xiamen energy systems. Based on a robust two-step solution algorithm, reasonable solutions have been obtained, which reflect tradeoffs between economic and environmental requirements, and among seasonal volatility energy demands of the right hand side constraints of Xiamen energy system. Thus, the lower and upper solutions of PIS-IT2FSLP would then help local energy authorities adjust current energy patterns, and discover an optimal energy strategy for the development of Xiamen City.

Reliability optimization in stochastic domain via genetic algorithm

Purpose– The purpose of this paper is to formulate the reliability optimization problem in stochastic and interval domain and also to solve the same under different stochastic set up.Design/methodology/approach– Stochastic programming technique has been used to convert the chance constraints into deterministic form and the corresponding problem is transformed to mixed-integer constrained optimization problem with interval objective. Then the reduced problem has been converted to unconstrained optimization problem with interval objective by Big-M penalty technique. The resulting problem has been solved by advanced real coded genetic algorithm with interval fitness, tournament selection, intermediate crossover and one-neighbourhood mutation.Findings– A new optimization technique has been developed in stochastic domain and the concept of interval valued parameters has been integrated with the stochastic setup so as to increase the applicability of the resultant solution to the interval valued nonlinear optimization problems.Practical implications– The concept of probability distribution with interval valued parameters has been introduced. This concept will motivate the researchers to carry out the research in this new direction.Originality/value– The application of genetic algorithm is extended to solve the reliability optimization problem in stochastic and interval domain.

Thumbnail galleries for procedural models

AbstractProcedural modeling allows for the generation of innumerable variations of models from a parameterized, conditional or stochastic rule set. Due to the abstractness, complexity and stochastic nature of rule sets, it is often very difficult to have an understanding of the diversity of models that a given rule set defines. We address this problem by presenting a novel system to automatically generate, cluster, rank, and select a series of representative thumbnail images out of a rule set. We introduce a set of ‘view attributes’ that can be used to measure the suitability of an image to represent a model, and allow for comparison of different models derived from the same rule set. To find the best thumbnails, we exploit these view attributes on images of models obtained by stochastically sampling the parameter space of the rule set. The resulting thumbnail gallery gives a representative visual impression of the procedural modeling potential of the rule set. Performance is discussed by means of a number of distinct examples and compared to state‐of‐the‐art approaches.

A framework for variable amplitude corrosion fatigue materials tests for offshore wind steel support structures

ABSTRACTClimate change and sustainability have driven enormous development programmes for offshore wind. These large structures are mainly fabricated of welded steel tubular and plate sections not dissimilar to structural details commonly encountered in the ship, and offshore oil and gas sectors, but design requirements differ significantly due to environmental aspects, loading regime and low capital expenditure and operational expenditure requirements. There is therefore a requirement to quickly update corrosion fatigue knowledge and data bases in order to assist operations and designers to optimise structures with respect to fatigue strength and cost. This paper reviews seawater corrosion fatigue and potential approaches to developing appropriate test procedures and analysis methods to produce reliable and meaningful corrosion‐fatigue behaviour under stochastic loading conditions and sets out some fundamental principles for any such testing programme.

Properties of Solutions to Stochastic Set Differential Equations under Non-Lipschitzian Coefficients

A class of stochastic set differential equations (SSDEs) with non-Lipschitzian coefficients is investigated. We first give the preliminaries on the stochastic set differential equations. Then the nonexplosion of solutions to the SSDEs is discussed. Moreover, the existence and uniqueness of the solutions to SSDEs are proven. Finally, the continuous dependence of the solutions to SSDEs is studied.