An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.

A Reliable Basis for Approximate Association Rules

For most of the work done in developing association rule mining, the primary focus has been on the efficiency of the approach and to a lesser extent the quality of the derived rules has been emphasized. Often for a dataset, a huge number of rules can be derived, but many of them can be redundant to other rules and thus are useless in practice. The extremely large number of rules makes it difficult for the end users to comprehend and therefore effectively use the discovered rules and thus significantly reduces the effectiveness of rule mining algorithms. If the extracted knowledge can’t be effectively used in solving real world problems, the effort of extracting the knowledge is worth little. This is a serious problem but not yet solved satisfactorily. In this paper, we propose a concise representation called Reliable Approximate basis for representing non-redundant approximate association rules. We prove that the redundancy elimination based on the proposed basis does not reduce the belief to the extracted rules. We also prove that all approximate association rules can be deduced from the Reliable Approximate basis. Therefore the basis is a lossless representation of approximate association rules.

Estimation of parameters for macroparasite population evolution using approximate Bayesian computation

We estimate the parameters of a stochastic process model for a macroparasite population within a host using approximate Bayesian computation (ABC). The immunity of the host is an unobserved model variable and only mature macroparasites at sacrifice of the host are counted. With very limited data, process rates are inferred reasonably precisely. Modeling involves a three variable Markov process for which the observed data likelihood is computationally intractable. ABC methods are particularly useful when the likelihood is analytically or computationally intractable. The ABC algorithm we present is based on sequential Monte Carlo, is adaptive in nature, and overcomes some drawbacks of previous approaches to ABC. The algorithm is validated on a test example involving simulated data from an autologistic model before being used to infer parameters of the Markov process model for experimental data. The fitted model explains the observed extra-binomial variation in terms of a zero-one immunity variable, which has a short-lived presence in the host.

Approximate Bayesian computation using indirect inference

We present a novel approach for developing summary statistics for use in approximate Bayesian computation (ABC) algorithms by using indirect inference. ABC methods are useful for posterior inference in the presence of an intractable likelihood function. In the indirect inference approach to ABC the parameters of an auxiliary model fitted to the data become the summary statistics. Although applicable to any ABC technique, we embed this approach within a sequential Monte Carlo algorithm that is completely adaptive and requires very little tuning. This methodological development was motivated by an application involving data on macroparasite population evolution modelled by a trivariate stochastic process for which there is no tractable likelihood function. The auxiliary model here is based on a beta–binomial distribution. The main objective of the analysis is to determine which parameters of the stochastic model are estimable from the observed data on mature parasite worms.

Practical stability with respect to model mismatch of approximate discrete-time output feedback control

This paper establishes a practical stability result for discrete-time output feedback control involving mismatch between the exact system to be stabilised and the approximating system used to design the controller. The practical stability is in the sense of an asymptotic bound on the amount of error bias introduced by the model approximation, and is established using local consistency properties of the systems. Importantly, the practical stability established here does not require the approximating system to be of the same model type as the exact system. Examples are presented to illustrate the nature of our practical stability result.

Approximate Membership Localization within a Web-Based Join Framework

In this paper, we propose a search-based approach to join two tables in the absence of clean join attributes. Non-structured documents from the web are used to express the correlations between a given query and a reference list. To implement this approach, a major challenge we meet is how to efficiently determine the number of times and the locations of each clean reference from the reference list that is approximately mentioned in the retrieved documents. We formalize the Approximate Membership Localization (AML) problem and propose an efficient partial pruning algorithm to solve it. A study using real-word data sets demonstrates the effectiveness of our search-based approach, and the efficiency of our AML algorithm.

An approximate Bayesian computation approach for estimating parameters of complex environmental processes in a cellular automata

Modelling an environmental process involves creating a model structure and parameterising the model with appropriate values to accurately represent the process. Determining accurate parameter values for environmental systems can be challenging. Existing methods for parameter estimation typically make assumptions regarding the form of the Likelihood, and will often ignore any uncertainty around estimated values. This can be problematic, however, particularly in complex problems where Likelihoods may be intractable. In this paper we demonstrate an Approximate Bayesian Computational method for the estimation of parameters of a stochastic CA. We use as an example a CA constructed to simulate a range expansion such as might occur after a biological invasion, making parameter estimates using only count data such as could be gathered from field observations. We demonstrate ABC is a highly useful method for parameter estimation, with accurate estimates of parameters that are important for the management of invasive species such as the intrinsic rate of increase and the point in a landscape where a species has invaded. We also show that the method is capable of estimating the probability of long distance dispersal, a characteristic of biological invasions that is very influential in determining spread rates but has until now proved difficult to estimate accurately.

Approximate clone detection in repositories of business process models

Evidence exists that repositories of business process models used in industrial practice contain significant amounts of duplication. This duplication may stem from the fact that the repository describes variants of the same pro- cesses and/or because of copy/pasting activity throughout the lifetime of the repository. Previous work has put forward techniques for identifying duplicate fragments (clones) that can be refactored into shared subprocesses. However, these techniques are limited to finding exact clones. This paper analyzes the prob- lem of approximate clone detection and puts forward two techniques for detecting clusters of approximate clones. Experiments show that the proposed techniques are able to accurately retrieve clusters of approximate clones that originate from copy/pasting followed by independent modifications to the copied fragments.

Using approximate Bayesian computation to estimate transmission rates of nosocomial pathogens

In this paper, we apply a simulation based approach for estimating transmission rates of nosocomial pathogens. In particular, the objective is to infer the transmission rate between colonised health-care practitioners and uncolonised patients (and vice versa) solely from routinely collected incidence data. The method, using approximate Bayesian computation, is substantially less computer intensive and easier to implement than likelihood-based approaches we refer to here. We find through replacing the likelihood with a comparison of an efficient summary statistic between observed and simulated data that little is lost in the precision of estimated transmission rates. Furthermore, we investigate the impact of incorporating uncertainty in previously fixed parameters on the precision of the estimated transmission rates.

Sufficiently informative measurements for stability of approximate conditional mean estimates

This paper establishes sufficient conditions to bound the error in perturbed conditional mean estimates derived from a perturbed model (only the scalar case is shown in this paper but a similar result is expected to hold for the vector case). The results established here extend recent stability results on approximating information state filter recursions to stability results on the approximate conditional mean estimates. The presented filter stability results provide bounds for a wide variety of model error situations.

Detecting approximate clones in process model repositories with Apromore

Approximate clone detection is the process of identifying similar process fragments in business process model collections. The tool presented in this paper can efficiently cluster approximate clones in large process model repositories. Once a repository is clustered, users can filter and browse the clusters using different filtering parameters. Our tool can also visualize clusters in the 2D space, allowing a better understanding of clusters and their member fragments. This demonstration will be useful for researchers and practitioners working on large process model repositories, where process standardization is a critical task for increasing the consistency and reducing the complexity of the repository.

Exact and approximate Bayesian inference for low count time series models with intractable likelihoods

In this paper we present a new simulation methodology in order to obtain exact or approximate Bayesian inference for models for low-valued count time series data that have computationally demanding likelihood functions. The algorithm fits within the framework of particle Markov chain Monte Carlo (PMCMC) methods. The particle filter requires only model simulations and, in this regard, our approach has connections with approximate Bayesian computation (ABC). However, an advantage of using the PMCMC approach in this setting is that simulated data can be matched with data observed one-at-a-time, rather than attempting to match on the full dataset simultaneously or on a low-dimensional non-sufficient summary statistic, which is common practice in ABC. For low-valued count time series data we find that it is often computationally feasible to match simulated data with observed data exactly. Our particle filter maintains $N$ particles by repeating the simulation until $N+1$ exact matches are obtained. Our algorithm creates an unbiased estimate of the likelihood, resulting in exact posterior inferences when included in an MCMC algorithm. In cases where exact matching is computationally prohibitive, a tolerance is introduced as per ABC. A novel aspect of our approach is that we introduce auxiliary variables into our particle filter so that partially observed and/or non-Markovian models can be accommodated. We demonstrate that Bayesian model choice problems can be easily handled in this framework.