Managing uncertainty in complex stochastic models: design and emulation of a Rabies model

In this paper we present a novel method for emulating a stochastic, or random output, computer model and show its application to a complex rabies model. The method is evaluated both in terms of accuracy and computational efficiency on synthetic data and the rabies model. We address the issue of experimental design and provide empirical evidence on the effectiveness of utilizing replicate model evaluations compared to a space-filling design. We employ the Mahalanobis error measure to validate the heteroscedastic Gaussian process based emulator predictions for both the mean and (co)variance. The emulator allows efficient screening to identify important model inputs and better understanding of the complex behaviour of the rabies model.

Variational inference for diffusion processes

Diffusion processes are a family of continuous-time continuous-state stochastic processes that are in general only partially observed. The joint estimation of the forcing parameters and the system noise (volatility) in these dynamical systems is a crucial, but non-trivial task, especially when the system is nonlinear and multimodal. We propose a variational treatment of diffusion processes, which allows us to compute type II maximum likelihood estimates of the parameters by simple gradient techniques and which is computationally less demanding than most MCMC approaches. We also show how a cheap estimate of the posterior over the parameters can be constructed based on the variational free energy.

Modelling nonlinear stochastic dynamics in financial time series

For analysing financial time series two main opposing viewpoints exist, either capital markets are completely stochastic and therefore prices follow a random walk, or they are deterministic and consequently predictable. For each of these views a great variety of tools exist with which it can be tried to confirm the hypotheses. Unfortunately, these methods are not well suited for dealing with data characterised in part by both paradigms. This thesis investigates these two approaches in order to model the behaviour of financial time series. In the deterministic framework methods are used to characterise the dimensionality of embedded financial data. The stochastic approach includes here an estimation of the unconditioned and conditional return distributions using parametric, non- and semi-parametric density estimation techniques. Finally, it will be shown how elements from these two approaches could be combined to achieve a more realistic model for financial time series.

Exploiting uncertainty in nonlinear stochastic control problem

This work introduces a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. Convergence of the output error for the proposed control method is verified by using a Lyapunov function. Several simulation examples are provided to demonstrate the efficiency of the developed control method. The manner in which such a method is extended to nonlinear multi-variable systems with different delays between the input-output pairs is considered and demonstrated through simulation examples.

A Bayesian perspective on stochastic neurocontrol

Control design for stochastic uncertain nonlinear systems is traditionally based on minimizing the expected value of a suitably chosen loss function. Moreover, most control methods usually assume the certainty equivalence principle to simplify the problem and make it computationally tractable. We offer an improved probabilistic framework which is not constrained by these previous assumptions, and provides a more natural framework for incorporating and dealing with uncertainty. The focus of this paper is on developing this framework to obtain an optimal control law strategy using a fully probabilistic approach for information extraction from process data, which does not require detailed knowledge of system dynamics. Moreover, the proposed control method framework allows handling the problem of input-dependent noise. A basic paradigm is proposed and the resulting algorithm is discussed. The proposed probabilistic control method is for the general nonlinear class of discrete-time systems. It is demonstrated theoretically on the affine class. A nonlinear simulation example is also provided to validate theoretical development.

Stochastic beamforming for cochlear implant coding

Cochlear implants are prosthetic devices used to provide hearing to people who would otherwise be profoundly deaf. The deliberate addition of noise to the electrode signals could increase the amount of information transmitted, but standard cochlear implants do not replicate the noise characteristic of normal hearing because if noise is added in an uncontrolled manner with a limited number of electrodes then it will almost certainly lead to worse performance. Only if partially independent stochastic activity can be achieved in each nerve fibre can mechanisms like suprathreshold stochastic resonance be effective. We are investigating the use of stochastic beamforming to achieve greater independence. The strategy involves presenting each electrode with a linear combination of independent Gaussian noise sources. Because the cochlea is filled with conductive salt solutions, the noise currents from the electrodes interact and the effective stimulus for each nerve fibre will therefore be a different weighted sum of the noise sources. To some extent therefore, the effective stimulus for a nerve fibre will be independent of the effective stimulus of neighbouring fibres. For a particular patient, the electrode position and the amount of current spread are fixed. The objective is therefore to find the linear combination of noise sources that leads to the greatest independence between nerve discharges. In this theoretical study we show that it is possible to get one independent point of excitation (one null) for each electrode and that stochastic beamforming can greatly decrease the correlation between the noise exciting different regions of the cochlea. © 2007 Copyright SPIE - The International Society for Optical Engineering.

Financial liberalization and stock market volatility:the case of Indonesia

This article examines the relationship between financial liberalization and stock market volatility in Indonesia. By looking at the time series properties of the Jakarta Composite Index (JCI) we identify breaks in stock market volatility which coincide with the timing of major policy events. Our main findings are (i) a significant decrease in volatility after the 'official' opening of the stock market to foreign participation; (ii) a significant increase in volatility in the year before market opening following reforms that eased entry requirements and the issuance of brokerage licenses and (iii) a significant increase in volatility at the time of the Asian crisis followed by a significant decrease in the second and sixth years after the crisis.

Stock market efficiency before and after a financial liberalisation reform:do breaks in volatility dynamics matter?

This article focuses on the deviations from normality of stock returns before and after a financial liberalisation reform, and shows the extent to which inference based on statistical measures of stock market efficiency can be affected by not controlling for breaks. Drawing from recent advances in the econometrics of structural change, it compares the distribution of the returns of five East Asian emerging markets when breaks in the mean and variance are either (i) imposed using certain official liberalisation dates or (ii) detected non-parametrically using a data-driven procedure. The results suggest that measuring deviations from normality of stock returns with no provision for potentially existing breaks incorporates substantial bias. This is likely to severely affect any inference based on the corresponding descriptive or test statistics.

State-owned enterprises, exporting and productivity in China:a stochastic dominance approach

A popular explanation for China's rapid economic growth in recent years has been the dramatic increase in the number of private domestic and foreign-owned firms and a decline in the state-owned sector. However, recent evidence suggest that China's state-owned enterprise (SOEs) are in fact stronger than ever. In this paper we examine over 78,000 manufacturing firms between 2002 and 2006 to investigate the relationship between ownership structure and the degree of firm-level exposure to export markets and firm-level productivity. Using a conditional stochastic dominance approach we reveal that although our results largely adhere to prior expectations, the performance of state-owned enterprises differs markedly between those that export and those that supply the domestic market only. It appears that China's internationally focused SOEs have become formidable global competitors.

Productivity change using growth accounting and frontier-based approaches:evidence from a Monte Carlo analysis

This study presents some quantitative evidence from a number of simulation experiments on the accuracy of the productivitygrowth estimates derived from growthaccounting (GA) and frontier-based methods (namely data envelopment analysis-, corrected ordinary least squares-, and stochastic frontier analysis-based malmquist indices) under various conditions. These include the presence of technical inefficiency, measurement error, misspecification of the production function (for the GA and parametric approaches) and increased input and price volatility from one period to the next. The study finds that the frontier-based methods usually outperform GA, but the overall performance varies by experiment. Parametric approaches generally perform best when there is no functional form misspecification, but their accuracy greatly diminishes otherwise. The results also show that the deterministic approaches perform adequately even under conditions of (modest) measurement error and when measurement error becomes larger, the accuracy of all approaches (including stochastic approaches) deteriorates rapidly, to the point that their estimates could be considered unreliable for policy purposes.

Accommodating energy price volatility in life cycle cost analysis of asphalt pavements

Energy price is related to more than half of the total life cycle cost of asphalt pavements. Furthermore, the fluctuation related to price of energy has been much higher than the general inflation and interest rate. This makes the energy price inflation an important variable that should be addressed when performing life cycle cost (LCC) studies re- garding asphalt pavements. The present value of future costs is highly sensitive to the selected discount rate. Therefore, the choice of the discount rate is the most critical element in LCC analysis during the life time of a project. The objective of the paper is to present a discount rate for asphalt pavement projects as a function of interest rate, general inflation and energy price inflation. The discount rate is defined based on the portion of the energy related costs during the life time of the pavement. Consequently, it can reflect the financial risks related to the energy price in asphalt pavement projects. It is suggested that a discount rate sensitivity analysis for asphalt pavements in Sweden should range between –20 and 30%.

A procedure for the reconstruction of a stochastic stationary temperature field

An iterative procedure is proposed for the reconstruction of a temperature field from a linear stationary heat equation with stochastic coefficients, and stochastic Cauchy data given on a part of the boundary of a bounded domain. In each step, a series of mixed well-posed boundary-value problems are solved for the stochastic heat operator and its adjoint. Well-posedness of these problems is shown to hold and convergence in the mean of the procedure is proved. A discretized version of this procedure, based on a Monte Carlo Galerkin finite-element method, suitable for numerical implementation is discussed. It is demonstrated that the solution to the discretized problem converges to the continuous as the mesh size tends to zero.

A stochastic frontier approach to modelling financial constraints in firms:an application to India

We propose the use of stochastic frontier approach to modelling financial constraints of firms. The main advantage of the stochastic frontier approach over the stylised approaches that use pooled OLS or fixed effects panel regression models is that we can not only decide whether or not the average firm is financially constrained, but also estimate a measure of the degree of the constraint for each firm and for each time period, and also the marginal impact of firm characteristics on this measure. We then apply the stochastic frontier approach to a panel of Indian manufacturing firms, for the 1997–2006 period. In our application, we highlight and discuss the aforementioned advantages, while also demonstrating that the stochastic frontier approach generates regression estimates that are consistent with the stylised intuition found in the literature on financial constraint and the wider literature on the Indian credit/capital market.