Gaussian approximations in high dimensional estimation

Several estimation techniques assume validity of Gaussian approximations for estimation purposes. Interestingly, these ensemble methods have proven to work very well for high-dimensional data even when the distributions involved are not necessarily Gaussian. We attempt to bridge the gap between this oft-used computational assumption and the theoretical understanding of why this works, by employing some recent results on random projections on low dimensional subspaces and concentration inequalities.     

Algorithmic estimation of risk factors in financial markets with stochastic drift

We assume a financial market governed by a diffusion process reverting to a stochastic mean which is itself governed by an unobservable ergodic diffusion, similar to those observed in electricity and other energy markets. We develop a moment method algorithm for the estimation of the parameters of both the observable process and the unobservable stochastic mean. Our approach is contrasted with other methods for parameter estimation of partially observed diffusions, and applications to the modelling of interest rates and commodity prices are discussed.     

Characterising economic trends by Bayesian stochastic model specification search

A recently proposed Bayesian model selection technique, stochastic model specification search, is carried out to discriminate between two trend generation hypotheses. The first is the trend-stationary hypothesis, for which the trend is a deterministic function of time and the short run dynamics are represented by a stationary autoregressive process. The second is the difference-stationary hypothesis, according to which the trend results from the cumulation of the effects of random disturbances. A difference-stationary process may originate in two ways: from an unobserved components process adding up an integrated trend and an orthogonal transitory component, or implicitly from an autoregressive process with roots on the unit circle. The different trend generation hypotheses are nested within an encompassing linear state space model. After a reparameterisation in non-centred form, the empirical evidence supporting a particular hypothesis is obtained by performing variable selection on the model components, using a suitably designed Gibbs sampling scheme. The methodology is illustrated with reference to a set of US macroeconomic time series which includes the traditional Nelson and Plosser dataset. The conclusion is that most series are better represented by autoregressive models with time-invariant intercept and slope and coefficients that are close to boundary of the stationarity region. The posterior distribution of the autoregressive parameters provides useful insight on quasi-integrated nature of the specifications selected.     

Optimization of cost and service level in the presence of supply chain disruption risks: Single vs. multiple sourcing

The coordinated supplier selection and customer order scheduling in the presence of supply chain disruption risks is studied for single and multiple sourcing strategies. Given a set of customer orders for products, the decision maker needs to select a single supplier or a subset of suppliers for purchasing parts required to complete the customer orders, and schedule the orders over the planning horizon, to mitigate the impact of disruption risks. The suppliers are located in different geographic regions and the supplies are subject to different types of disruptions: to random local disruptions of each supplier individually, to random regional disruptions of all suppliers in the same region simultaneously and to random global disruptions of all suppliers simultaneously. For any combination of suppliers hit by different types of disruptions, a formula for calculating the corresponding disruption probability is developed. The obtained combinatorial stochastic optimization problem is formulated as a mixed integer program with conditional value-at-risk as a risk measure. The problem objective is either to minimize expected worst-case cost or to maximize expected worst-case customer service level, i.e., the expected worst-case fraction of customer orders filled on or before their due dates. The risk-averse solutions that optimize worst-case performance of a supply chain under disruptions risks are compared for the two sourcing strategies and the two objective functions. Numerical examples and computational results are presented and some managerial insights on the choice between the two sourcing strategies are reported.     

Bidding strategy of wind-thermal energy producers

This paper presents a stochastic mixed-integer linear programming approach for solving the self-scheduling problem of a price-taker thermal and wind power producer taking part in a pool-based electricity market. Uncertainty on electricity price and wind power is considered through a set of scenarios. Thermal units are modelled by variable costs, start-up costs and technical operating constraints, such as: forbidden operating zones, ramp up/down limits and minimum up/down time limits. An efficient mixed-integer linear program is presented to develop the offering strategies of the coordinated production of thermal and wind energy generation, having as a goal the maximization of profit. A case study with data from the Iberian Electricity Market is presented and results are discussed to show the effectiveness of the proposed approach.     

A study of equivalent electrical circuit fitting to electrochemical impedance using a stochastic method

Modeling electrochemical impedance spectroscopy is usually done using equivalent electrical circuits. These circuits have parameters that need to be estimated properly in order to make possible the simulation of impedance data. Despite the fitting procedure is an optimization problem solved recurrently in the literature, rarely statistical significance of the estimated parameters is evaluated. In this work, the optimization process for the equivalent electrical circuit fitting to the impedance data is detailed. First, a mathematical development regarding the minimization of residual least squares is presented in order to obtain a statistically valid objective function of the complex nonlinear regression problem. Then, the optimization method used in this work is presented, the Differential Evolution, a global search stochastic method. Furthermore, it is shown how a population-based stochastic method like this can be used directly to obtain confidence regions to the estimated parameters. A sensitivity analysis was also conducted. Finally, the equivalent circuit fitting is done to model synthetic experimental data, in order to demonstrate the adopted procedure.     

Concentrator utilisation under geological uncertainty

Mineral concentrators are designed from preliminary geological data, and are therefore subject to geological uncertainty. This uncertainty has a demonstrable impact on the mining lifecycle, and has motivated stochastic strategic mine planning algorithms. The current paper describes how these algorithms may be extended to consider mineral processing operations in conjunction with open-pit mining operations. In particular, the paper describes an effective way to incorporate variable concentrator feed grade into these algorithms, which is the first step toward more elaborate representations of mineral concentrators. The resulting framework will be able to connect geological data to alternate configurations of the downstream resources, hence comparing the benefit of each configuration, and the corresponding capital investments. Sample computations are presented, comparing the net present value and utilisation for several different mineral processing capacities.     

Function projective synchronization between integer-order and stochastic fractional-order nonlinear systems

In this paper, the function projective synchronization between integer-order and stochastic fractional-order nonlinear systems is investigated. Firstly, according to the stability theory of fractional-order systems and tracking control, a controller is designed. At the same time, based on the orthogonal polynomial approximation, the method of transforming stochastic error system into an equivalent deterministic system is given. Thus, the stability of the stochastic error system can be analyzed through its equivalent deterministic one. Finally, to demonstrate the effectiveness of the proposed scheme, the function projective synchronization between integer-order Lorenz system and stochastic fractional-order Chen system is studied.     

Optimization of multi-product economic production quantity model with partial backordering and physical constraints: SQP,SFS, SA,and WCA

A multi-product economic production quantity model with several real-world technical and physical constraints is developed in this paper. The cost function includes ordering, holding, backordering, lost sale, and the cost caused by unused space in the warehouse. The goal is to minimize the total inventory cost, where shortages are allowed and partially backordered with fixed and linear costs. The aim is to determine the length of the inventory cycle, the length of positive inventory period, and the backordering rates of the products during the shortage period in order to minimize the total inventory costs while satisfying all constraints. Due to complexity and non-linearity of the proposed model, sequential quadratic programming (SQP), stochastic fractal search (SFS), simulated annealing (SA), and water cycle algorithm (WCA) are utilized for solution. Ninety numerical examples in small, medium, and large sizes are solved to evaluate the efficiency of the solution methods. The performances of the solution methods are compared statistically. Besides, sensitivity analysis is performed to determine the effect of change in the main parameters of the problem on the objective function value and decision variables.     

Approximately bisimilar symbolic models for randomly switched stochastic systems

In the past few years there has been a growing interest in the use of symbolic models for control systems. The main reason is the possibility to leverage algorithmic techniques over symbolic models to synthesize controllers that are valid for the concrete control systems. Such controllers can enforce complex logical specifications that are otherwise hard (if not impossible) to establish on the concrete models with classical control techniques. Examples of such specifications include those expressible via linear temporal logic or as automata on infinite strings. A relevant goal in this research line is in the identification of classes of systems that admit symbolic models: in particular, continuous-time systems with stochastic or hybrid dynamics have been only recently considered, due to their rather general and complex dynamics. In this work we make progress in this direction by enlarging the class of stochastic hybrid systems admitting finite, symbolic models: specifically, we show that randomly switched stochastic systems, satisfying some incremental stability assumption, admit such models.