Learning in neural networks and stochastic approximation methods with averaging

The problem of adjusting the weights (learning) in multilayer feedforward neural networks (NN) is known to be of a high importance when utilizing NN techniques in various practical applications. The learning procedure is to be performed as fast as possible and in a simple computational fashion, the two requirements which are usually not satisfied practically by the methods developed so far. Moreover, the presence of random inaccuracies are usually not taken into account. In view of these three issues, an alternative stochastic approximation approach discussed in the paper, seems to be very promising.

Integrating spatial dependence into stochastic frontier analysis

An approach to incorporate spatial dependence into stochastic frontier analysis is developed and applied to a sample of 215 dairy farms in England and Wales. A number of alternative specifications for the spatial weight matrix are used to analyse the effect of these on the estimation of spatial dependence. Estimation is conducted using a Bayesian approach and results indicate that spatial dependence is present when explaining technical inefficiency.

Provision of environmental output within a multi-output distance function approach

This paper redefines technical efficiency by incorporating provision of environmental goods as one of the outputs of the farm. The proportion of permanent and rough grassland to total agricultural land area is used as a proxy for the provision of environmental goods. Stochastic frontier analysis was conducted using a Bayesian procedure. The methodology is applied to panel data on 215 dairy farms in England and Wales. Results show that farm efficiency rankings change when provision of environmental outputs by farms is incorporated in the efficiency analysis, which may have important political implications.

Direct Computation of Stochastic Flow in Reservoirs with Uncertain Parameters

A direct method is presented for determining the uncertainty in reservoir pressure, flow, and net present value (NPV) using the time-dependent, one phase, two- or three-dimensional equations of flow through a porous medium. The uncertainty in the solution is modelled as a probability distribution function and is computed from given statistical data for input parameters such as permeability. The method generates an expansion for the mean of the pressure about a deterministic solution to the system equations using a perturbation to the mean of the input parameters. Hierarchical equations that define approximations to the mean solution at each point and to the field covariance of the pressure are developed and solved numerically. The procedure is then used to find the statistics of the flow and the risked value of the field, defined by the NPV, for a given development scenario. This method involves only one (albeit complicated) solution of the equations and contrasts with the more usual Monte-Carlo approach where many such solutions are required. The procedure is applied easily to other physical systems modelled by linear or nonlinear partial differential equations with uncertain data.

The stochastic component in choice and regression to the mean

In this article, we illustrate experimentally an important consequence of the stochastic component in choice behaviour which has not been acknowledged so far. Namely, its potential to produce ‘regression to the mean’ (RTM) effects. We employ a novel approach to individual choice under risk, based on repeated multiple-lottery choices (i.e. choices among many lotteries), to show how the high degree of stochastic variability present in individual decisions can distort crucially certain results through RTM effects. We demonstrate the point in the context of a social comparison experiment.

A unified approach to the recognition of complex actions from sequences of zone-crossings

We present a method for the recognition of complex actions. Our method combines automatic learning of simple actions and manual definition of complex actions in a single grammar. Contrary to the general trend in complex action recognition that consists in dividing recognition into two stages, our method performs recognition of simple and complex actions in a unified way. This is performed by encoding simple action HMMs within the stochastic grammar that models complex actions. This unified approach enables a more effective influence of the higher activity layers into the recognition of simple actions which leads to a substantial improvement in the classification of complex actions. We consider the recognition of complex actions based on person transits between areas in the scene. As input, our method receives crossings of tracks along a set of zones which are derived using unsupervised learning of the movement patterns of the objects in the scene. We evaluate our method on a large dataset showing normal, suspicious and threat behaviour on a parking lot. Experiments show an improvement of ~ 30% in the recognition of both high-level scenarios and their composing simple actions with respect to a two-stage approach. Experiments with synthetic noise simulating the most common tracking failures show that our method only experiences a limited decrease in performance when moderate amounts of noise are added.

Using stochastic volatility models to analyse weekly ozone averages in Mexico City

In this paper we make use of some stochastic volatility models to analyse the behaviour of a weekly ozone average measurements series. The models considered here have been used previously in problems related to financial time series. Two models are considered and their parameters are estimated using a Bayesian approach based on Markov chain Monte Carlo (MCMC) methods. Both models are applied to the data provided by the monitoring network of the Metropolitan Area of Mexico City. The selection of the best model for that specific data set is performed using the Deviance Information Criterion and the Conditional Predictive Ordinate method.

On the cutting stock problem under stochastic demand

This paper addresses the one-dimensional cutting stock problem when demand is a random variable. The problem is formulated as a two-stage stochastic nonlinear program with recourse. The first stage decision variables are the number of objects to be cut according to a cutting pattern. The second stage decision variables are the number of holding or backordering items due to the decisions made in the first stage. The problem`s objective is to minimize the total expected cost incurred in both stages, due to waste and holding or backordering penalties. A Simplex-based method with column generation is proposed for solving a linear relaxation of the resulting optimization problem. The proposed method is evaluated by using two well-known measures of uncertainty effects in stochastic programming: the value of stochastic solution-VSS-and the expected value of perfect information-EVPI. The optimal two-stage solution is shown to be more effective than the alternative wait-and-see and expected value approaches, even under small variations in the parameters of the problem.

Symmetry in biology: from genetic code to stochastic gene regulation

Mathematical models, as instruments for understanding the workings of nature, are a traditional tool of physics, but they also play an ever increasing role in biology - in the description of fundamental processes as well as that of complex systems. In this review, the authors discuss two examples of the application of group theoretical methods, which constitute the mathematical discipline for a quantitative description of the idea of symmetry, to genetics. The first one appears, in the form of a pseudo-orthogonal (Lorentz like) symmetry, in the stochastic modelling of what may be regarded as the simplest possible example of a genetic network and, hopefully, a building block for more complicated ones: a single self-interacting or externally regulated gene with only two possible states: ` on` and ` off`. The second is the algebraic approach to the evolution of the genetic code, according to which the current code results from a dynamical symmetry breaking process, starting out from an initial state of complete symmetry and ending in the presently observed final state of low symmetry. In both cases, symmetry plays a decisive role: in the first, it is a characteristic feature of the dynamics of the gene switch and its decay to equilibrium, whereas in the second, it provides the guidelines for the evolution of the coding rules.

A Spatial-Temporal Downscaling Approach To Construction Of Rainfall Intensity-Duration-Frequency Relations In The Context Of Climate Change

This paper proposes a spatial-temporal downscaling approach to construction of the intensity-duration-frequency (IDF) relations at a local site in the context of climate change and variability. More specifically, the proposed approach is based on a combination of a spatial downscaling method to link large-scale climate variables given by General Circulation Model (GCM) simulations with daily extreme precipitations at a site and a temporal downscaling procedure to describe the relationships between daily and sub-daily extreme precipitations based on the scaling General Extreme Value (GEV) distribution. The feasibility and accuracy of the suggested method were assessed using rainfall data available at eight stations in Quebec (Canada) for the 1961-2000 period and climate simulations under four different climate change scenarios provided by the Canadian (CGCM3) and UK (HadCM3) GCM models. Results of this application have indicated that it is feasible to link sub-daily extreme rainfalls at a local site with large-scale GCM-based daily climate predictors for the construction of the IDF relations for present (1961-1990) and future (2020s, 2050s, and 2080s) periods at a given site under different climate change scenarios. In addition, it was found that annual maximum rainfalls downscaled from the HadCM3 displayed a smaller change in the future, while those values estimated from the CGCM3 indicated a large increasing trend for future periods. This result has demonstrated the presence of high uncertainty in climate simulations provided by different GCMs. In summary, the proposed spatial-temporal downscaling method provided an essential tool for the estimation of extreme rainfalls that are required for various climate-related impact assessment studies for a given region.

A risk management approach to emerging market's sovereign debt sustainability with an application to Brazilian data

In this paper we study the question of debt sustainability from a risk management perspective. The debt accumulation equation for any country involves variables that are stochastic and closely intertwined. When these aspects are taken into consideration the notion of debt sustainability is expanded to studying the stochastic properties of the debt dynamics. We illustrate the methodology by studying the Brazilian case. We find that even though the debt could be sustainable in the absence of risk, there are paths in which it is clearly unsustainable. Furthermore, we show that properties of the debt dynamics are closely related to the spreads on sovereign dollar denominated debt.

A Numerical method for the semilinear stochastic transport equation

Trabalho apresentado no XXXV CNMAC, Natal-RN, 2014.

Computer simulation of the stochastic transport equation

Trabalho apresentado no 37th Conference on Stochastic Processes and their Applications - July 28 - August 01, 2014 -Universidad de Buenos Aires

Non-asymptotic confidence bounds for the optimal value of a stochastic program

We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds for the optimal value of the problem which are essentially better than the quality of the corresponding optimal solutions. At the same time, such bounds are more reliable than “standard” confidence bounds obtained through the asymptotic approach. We also discuss bounding the optimal value of MinMax Stochastic Optimization and stochastically constrained problems. We conclude with a small simulation study illustrating the numerical behavior of the proposed bounds.

Stochastic discount factor bounds and rare events: a review

We aim to provide a review of the stochastic discount factor bounds usually applied to diagnose asset pricing models. In particular, we mainly discuss the bounds used to analyze the disaster model of Barro (2006). Our attention is focused in this disaster model since the stochastic discount factor bounds that are applied to study the performance of disaster models usually consider the approach of Barro (2006). We first present the entropy bounds that provide a diagnosis of the analyzed disaster model which are the methods of Almeida and Garcia (2012, 2016); Ghosh et al. (2016). Then, we discuss how their results according to the disaster model are related to each other and also present the findings of other methodologies that are similar to these bounds but provide different evidence about the performance of the framework developed by Barro (2006).