Material parameter estimation and hypothesis testing on a 1D viscoelastic stenosis model: Methodology

This is the post-print version of the final published paper that is available from the link below. Copyright @ 2013 Walter de Gruyter GmbH.Non-invasive detection, localization and characterization of an arterial stenosis (a blockage or partial blockage in the artery) continues to be an important problem in medicine. Partial blockage stenoses are known to generate disturbances in blood flow which generate shear waves in the chest cavity. We examine a one-dimensional viscoelastic model that incorporates Kelvin–Voigt damping and internal variables, and develop a proof-of-concept methodology using simulated data. We first develop an estimation procedure for the material parameters. We use this procedure to determine confidence intervals for the estimated parameters, which indicates the efficacy of finding parameter estimates in practice. Confidence intervals are computed using asymptotic error theory as well as bootstrapping. We then develop a model comparison test to be used in determining if a particular data set came from a low input amplitude or a high input amplitude; this we anticipate will aid in determining when stenosis is present. These two thrusts together will serve as the methodological basis for our continuing analysis using experimental data currently being collected.National Institute of Allergy and Infectious Diseases, Air Force Office of Scientific Research, Department of Education, and Engineering and Physical Sciences Research Council

Model validation for a noninvasive arterial stenosis detection problem

Copyright @ 2013 American Institute of Mathematical SciencesA current thrust in medical research is the development of a non-invasive method for detection, localization, and characterization of an arterial stenosis (a blockage or partial blockage in an artery). A method has been proposed to detect shear waves in the chest cavity which have been generated by disturbances in the blood flow resulting from a stenosis. In order to develop this methodology further, we use both one-dimensional pressure and shear wave experimental data from novel acoustic phantoms to validate corresponding viscoelastic mathematical models, which were developed in a concept paper [8] and refined herein. We estimate model parameters which give a good fit (in a sense to be precisely defined) to the experimental data, and use asymptotic error theory to provide confidence intervals for parameter estimates. Finally, since a robust error model is necessary for accurate parameter estimates and confidence analysis, we include a comparison of absolute and relative models for measurement error.The National Institute of Allergy and Infectious Diseases, the Air Force Office of Scientific Research, the Deopartment of Education and the Engineering and Physical Sciences Research Council (EPSRC)

Joining Forces of Bayesian and Frequentist Methodology: A Study for Inference in the Presence of Non-Identifiability

Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take advantage of both Bayesian and frequentist methods. The elegance of Bayesian methodology is founded in the propagation of information content provided by experimental data and prior assumptions to the posterior probability distribution of model predictions. However, for complex applications experimental data and prior assumptions potentially constrain the posterior probability distribution insufficiently. In these situations Bayesian Markov chain Monte Carlo sampling can be infeasible. From a frequentist point of view insufficient experimental data and prior assumptions can be interpreted as non-identifiability. The profile likelihood approach offers to detect and to resolve non-identifiability by experimental design iteratively. Therefore, it allows one to better constrain the posterior probability distribution until Markov chain Monte Carlo sampling can be used securely. Using an application from cell biology we compare both methods and show that a successive application of both methods facilitates a realistic assessment of uncertainty in model predictions.Comment: Article to appear in Phil. Trans. Roy. Soc.

The Bounded Confidence Model Of Opinion Dynamics

The bounded confidence model of opinion dynamics, introduced by Deffuant et al, is a stochastic model for the evolution of continuous-valued opinions within a finite group of peers. We prove that, as time goes to infinity, the opinions evolve globally into a random set of clusters too far apart to interact, and thereafter all opinions in every cluster converge to their barycenter. We then prove a mean-field limit result, propagation of chaos: as the number of peers goes to infinity in adequately started systems and time is rescaled accordingly, the opinion processes converge to i.i.d. nonlinear Markov (or McKean-Vlasov) processes; the limit opinion processes evolves as if under the influence of opinions drawn from its own instantaneous law, which are the unique solution of a nonlinear integro-differential equation of Kac type. This implies that the (random) empirical distribution processes converges to this (deterministic) solution. We then prove that, as time goes to infinity, this solution converges to a law concentrated on isolated opinions too far apart to interact, and identify sufficient conditions for the limit not to depend on the initial condition, and to be concentrated at a single opinion. Finally, we prove that if the equation has an initial condition with a density, then its solution has a density at all times, develop a numerical scheme for the corresponding functional equation, and show numerically that bifurcations may occur.Comment: 43 pages, 7 figure

Probabilistic Logic Programming with Beta-Distributed Random Variables

We enable aProbLog---a probabilistic logical programming approach---to reason in presence of uncertain probabilities represented as Beta-distributed random variables. We achieve the same performance of state-of-the-art algorithms for highly specified and engineered domains, while simultaneously we maintain the flexibility offered by aProbLog in handling complex relational domains. Our motivation is that faithfully capturing the distribution of probabilities is necessary to compute an expected utility for effective decision making under uncertainty: unfortunately, these probability distributions can be highly uncertain due to sparse data. To understand and accurately manipulate such probability distributions we need a well-defined theoretical framework that is provided by the Beta distribution, which specifies a distribution of probabilities representing all the possible values of a probability when the exact value is unknown.Comment: Accepted for presentation at AAAI 201

BPRS: Belief Propagation Based Iterative Recommender System

In this paper we introduce the first application of the Belief Propagation (BP) algorithm in the design of recommender systems. We formulate the recommendation problem as an inference problem and aim to compute the marginal probability distributions of the variables which represent the ratings to be predicted. However, computing these marginal probability functions is computationally prohibitive for large-scale systems. Therefore, we utilize the BP algorithm to efficiently compute these functions. Recommendations for each active user are then iteratively computed by probabilistic message passing. As opposed to the previous recommender algorithms, BPRS does not require solving the recommendation problem for all the users if it wishes to update the recommendations for only a single active. Further, BPRS computes the recommendations for each user with linear complexity and without requiring a training period. Via computer simulations (using the 100K MovieLens dataset), we verify that BPRS iteratively reduces the error in the predicted ratings of the users until it converges. Finally, we confirm that BPRS is comparable to the state of art methods such as Correlation-based neighborhood model (CorNgbr) and Singular Value Decomposition (SVD) in terms of rating and precision accuracy. Therefore, we believe that the BP-based recommendation algorithm is a new promising approach which offers a significant advantage on scalability while providing competitive accuracy for the recommender systems

Trust Based Participant Driven Privacy Control in Participatory Sensing

Widespread use of sensors and multisensory personal devices generate a lot of personal information. Sharing this information with others could help in various ways. However, this information may be misused when shared with all. Sharing of information between trusted parties overcomes this problem. This paper describes a model to share information based on interactions and opinions to build trust among peers. It also considers institutional and other controls, which influence the behaviour of the peers. The trust and control build confidence. The computed confidence bespeaks whether to reveal information or not thereby increasing trusted cooperation among peers.Comment: 14 page