Local Exchangeability

Exchangeability---in which the distribution of an infinite sequence is invariant to reorderings of its elements---implies the existence of a simple conditional independence structure that may be leveraged in the design of probabilistic models, efficient inference algorithms, and randomization-based testing procedures. In practice, however, this assumption is too strong an idealization; the distribution typically fails to be exactly invariant to permutations and de Finetti's representation theory does not apply. Thus there is the need for a distributional assumption that is both weak enough to hold in practice, and strong enough to guarantee a useful underlying representation. We introduce a relaxed notion of local exchangeability---where swapping data associated with nearby covariates causes a bounded change in the distribution. We prove that locally exchangeable processes correspond to independent observations from an underlying measure-valued stochastic process. We thereby show that de Finetti's theorem is robust to perturbation and provide further justification for the Bayesian modelling approach. Using this probabilistic result, we develop three novel statistical procedures for (1) estimating the underlying process via local empirical measures, (2) testing via local randomization, and (3) estimating the canonical premetric of local exchangeability. These three procedures extend the applicability of previous exchangeability-based methods without sacrificing rigorous statistical guarantees. The paper concludes with examples of popular statistical models that exhibit local exchangeability

Weighted Goal Programming and Penalty Functions: Whole-farm Planning Approach Under Risk

The paper presents multiple criteria approach to deal with risk in farmer’s decisions. Decision making process is organised in a framework of spreadsheet tool. It is supported by deterministic and stochastic mathematical programming techniques applying optimisation concept. Decision making process is conceptually divided into seven autonomous modules that are mutually linked up. Beside the common maximisation of expected income through linear programming it enables also reconstruction of current production practice. Income risk modelling is based on portfolio theory resting on expected value, variance (E,V) paradigm. Modules dealing with risk are therefore supported with quadratic and constrained quadratic programming. Non-parametric approach is utilised to estimate decision maker’s risk attitude. It is measured with coefficient of risk aversion, needed to maximise certainty equivalent for analysed farms. Multiple criteria paradigm is based on goal programming approach. In contribution focus is put on benefits and possible drawbacks of supporting weighted goal programming with penalty functions. Application of the tool is illustrated with three dairy farm cases. Obtained results confirm advantage of utilizing penalty function system. Beside greater positiveness it proves as useful approach for fine tuning of the model enabling imitation of farmer’s behaviour, which is due to his/her conservative nature not perfect or rational. Results confirm hypothesis that single criteria decision making, based on maximisation of expected income, might be biased and does not necessary lead to the best - achievable option for analysed farm.goal programming, risk modelling, risk aversion, production planning, Risk and Uncertainty,

CEST and MEST: Tools for the simulation of radio frequency electric discharges in waveguides

This is the author’s version of a work that was accepted for publication in Simulation Modelling Practice and Theory. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Simulation Modelling Practice and Theory, 16, 9, (2008) http://dx.doi.org/10.1016/j.simpat.2008.08.002In this paper we present two software tools for the simulation of electron multiplication processes in radio frequency (RF) waveguides. The electric discharges are caused by the multiplication of a small initial number of electrons. These are accelerated by the RF field and produce new electrons either by collisions with the walls of the waveguide (ripping new electrons from them), or by ionization of the neutral atoms of a gas inside the device. MEST allows simulating the Multipactor effect, a discharge produced in vacuum and generated by the collision of the electrons with the walls. CEST simulates the discharge when in addition a neutral gas is present in the waveguide, at pressures lower than ground levels (often denominated Corona discharge). The main characteristic of both tools is that they implement individual-based, microscopic models, where every electron is individually represented and tracked. In the case of MEST, the simulation is discrete-event, as the trajectory of each electron can be computed analytically. In CEST we use a hybrid simulation approach. The trajectory of each electron is governed by the Langevin stochastic differential equations that take into account a deterministic RF electric force and the random interaction with the neutral atom background. In addition, wall and ionizing collisions are modelled as discrete events. The tools allow performing batches of simulations with different wall coating materials and gases, and have produced results in good agreement with experimental and theoretical data. The different output forms generated at run-time have proven to be very useful in order to analyze the different discharge processes. The tools are valuable for the selection of the most promising coating materials for the construction of the waveguide, as well as for the identification of safe operating parameters.Work sponsored by the ESA, TRP activity program 17025/03/NL/EC: Surface Treatment and Coating

Industry views on water resources planning methods – prospects for change in England and Wales

This paper describes a qualitative study of practitioner perspectives on regulated water resources planning practice in England and Wales. The study focuses on strengths and weaknesses of existing practice and the case for change towards a risk-based approach informed by stochastic modelling assessments. In-depth, structured interviews were conducted to capture the views of planners, regulators and consultants closely involved in the planning process. We found broad agreement that the existing water availability assessment methods are fallible; they lack transparency, are often highly subjective and may fail to adequately expose problems of resilience. While most practitioners believe these issues warrant a more detailed examination of risk in the planning process, few believe there is a strong case for a fundamental shift towards risk-based planning informed by stochastic modelling assessments. The study identifies perceived business risks associated with change and exposes widespread scepticism of stochastic methods

Modelling and feedback control design for quantum state preparation

The goal of this article is to provide a largely self-contained introduction to the modelling of controlled quantum systems under continuous observation, and to the design of feedback controls that prepare particular quantum states. We describe a bottom-up approach, where a field-theoretic model is subjected to statistical inference and is ultimately controlled. As an example, the formalism is applied to a highly idealized interaction of an atomic ensemble with an optical field. Our aim is to provide a unified outline for the modelling, from first principles, of realistic experiments in quantum control

Linear State Models for Volatility Estimation and Prediction

This report covers the important topic of stochastic volatility modelling with an emphasis on linear state models. The approach taken focuses on comparing models based on their ability to fit the data and their forecasting performance. To this end several parsimonious stochastic volatility models are estimated using realised volatility, a volatility proxy from high frequency stock price data. The results indicate that a hidden state space model performs the best among the realised volatility-based models under consideration. For the state space model different sampling intervals are compared based on in-sample prediction performance. The comparisons are partly based on the multi-period prediction results that are derived in this report

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

Modelling FX smile : from stochastic volatility to skewness

Imperial Users onl

A modular hybrid simulation framework for complex manufacturing system design

For complex manufacturing systems, the current hybrid Agent-Based Modelling and Discrete Event Simulation (ABM–DES) frameworks are limited to component and system levels of representation and present a degree of static complexity to study optimal resource planning. To address these limitations, a modular hybrid simulation framework for complex manufacturing system design is presented. A manufacturing system with highly regulated and manual handling processes, composed of multiple repeating modules, is considered. In this framework, the concept of modular hybrid ABM–DES technique is introduced to demonstrate a novel simulation method using a dynamic system of parallel multi-agent discrete events. In this context, to create a modular model, the stochastic finite dynamical system is extended to allow the description of discrete event states inside the agent for manufacturing repeating modules (meso level). Moreover, dynamic complexity regarding uncertain processing time and resources is considered. This framework guides the user step-by-step through the system design and modular hybrid model. A real case study in the cell and gene therapy industry is conducted to test the validity of the framework. The simulation results are compared against the data from the studied case; excellent agreement with 1.038% error margin is found in terms of the company performance. The optimal resource planning and the uncertainty of the processing time for manufacturing phases (exo level), in the presence of dynamic complexity is calculated