Search results for: invariant manifolds

Authors: Majid Alenezi, Abdelbare Algamode, Amy Hayes, Gavin Lawrence, Nichola Callow

Abstract:

The purpose of this study was to translate and culturally adapt the Vividness of Movement Imagery Questionnaire-2 (VMIQ-2) from English to produce a new Arabic version (VMIQ-2A), and to evaluate the reliability and validity of the translated questionnaire. The questionnaire assesses how vividly and clearly individuals are able to imagine themselves performing everyday actions. Its purpose is to measure individuals’ ability to conduct movement imagery, which can be defined as “the cognitive rehearsal of a task in the absence of overt physical movement.” Movement imagery has been introduced in physiotherapy as a promising intervention technique, especially when physical exercise is not possible (e.g. pain, immobilisation.) Considerable evidence indicates movement imagery interventions improve physical function, but to maximize efficacy it is important to know the imagery abilities of the individuals being treated. Given the increase in the global sharing of knowledge it is desirable to use standard measures of imagery ability across language and cultures, thus motivating this project. The translation procedure followed guidelines from the Translation and Cultural Adaptation group of the International Society for Pharmacoeconomics and Outcomes Research and involved the following phases: Preparation; the original VMIQ-2 was adapted slightly to provide additional information and simplified grammar. Forward translation; three native speakers resident in Saudi Arabia translated the original VMIQ-2 from English to Arabic, following instruction to preserve meaning (not literal translation), and cultural relevance. Reconciliation; the project manager (first author), the primary translator and a physiotherapist reviewed the three independent translations to produce a reconciled first Arabic draft of VMIQ-2A. Backward translation; a fourth translator (native Arabic speaker fluent in English) translated literally the reconciled first Arabic draft to English. The project manager and two study authors compared the English back translation to the original VMIQ-2 and produced the second Arabic draft. Cognitive debriefing; to assess participants’ understanding of the second Arabic draft, 7 native Arabic speakers resident in the UK completed the questionnaire, and rated the clearness of the questions, specified difficult words or passages, and wrote in their own words their understanding of key terms. Following review of this feedback, a final Arabic version was created. 142 native Arabic speakers completed the questionnaire in community meeting places or at home; a subset of 44 participants completed the questionnaire a second time 1 week later. Results showed the translated questionnaire to be valid and reliable. Correlation coefficients indicated good test-retest reliability. Cronbach’s a indicated high internal consistency. Construct validity was tested in two ways. Imagery ability scores have been found to be invariant across gender; this result was replicated within the current study, assessed by independent-samples t-test. Additionally, experienced sports participants have higher imagery ability than those less experienced; this result was also replicated within the current study, assessed by analysis of variance, supporting construct validity. Results provide preliminary evidence that the VMIQ-2A is reliable and valid to be used with a general population who are native Arabic speakers. Future research will include validation of the VMIQ-2A in a larger sample, and testing validity in specific patient populations.

Keywords: motor imagery, physiotherapy, translation and validation, imagery ability

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Authors: Jeremie Coullon, Robert J. Webber

Abstract:

We introduce a Markov chain Monte Carlo (MCMC) sam-pler for infinite-dimensional inverse problems. Our sam-pler is based on the affine invariant ensemble sampler, which uses interacting walkers to adapt to the covariance structure of the target distribution. We extend this ensem-ble sampler for the first time to infinite-dimensional func-tion spaces, yielding a highly efficient gradient-free MCMC algorithm. Because our ensemble sampler does not require gradients or posterior covariance estimates, it is simple to implement and broadly applicable. In many Bayes-ian inverse problems, Markov chain Monte Carlo (MCMC) meth-ods are needed to approximate distributions on infinite-dimensional function spaces, for example, in groundwater flow, medical imaging, and traffic flow. Yet designing efficient MCMC methods for function spaces has proved challenging. Recent gradi-ent-based MCMC methods preconditioned MCMC methods, and SMC methods have improved the computational efficiency of functional random walk. However, these samplers require gradi-ents or posterior covariance estimates that may be challenging to obtain. Calculating gradients is difficult or impossible in many high-dimensional inverse problems involving a numerical integra-tor with a black-box code base. Additionally, accurately estimating posterior covariances can require a lengthy pilot run or adaptation period. These concerns raise the question: is there a functional sampler that outperforms functional random walk without requir-ing gradients or posterior covariance estimates? To address this question, we consider a gradient-free sampler that avoids explicit covariance estimation yet adapts naturally to the covariance struc-ture of the sampled distribution. This sampler works by consider-ing an ensemble of walkers and interpolating and extrapolating between walkers to make a proposal. This is called the affine in-variant ensemble sampler (AIES), which is easy to tune, easy to parallelize, and efficient at sampling spaces of moderate dimen-sionality (less than 20). The main contribution of this work is to propose a functional ensemble sampler (FES) that combines func-tional random walk and AIES. To apply this sampler, we first cal-culate the Karhunen–Loeve (KL) expansion for the Bayesian prior distribution, assumed to be Gaussian and trace-class. Then, we use AIES to sample the posterior distribution on the low-wavenumber KL components and use the functional random walk to sample the posterior distribution on the high-wavenumber KL components. Alternating between AIES and functional random walk updates, we obtain our functional ensemble sampler that is efficient and easy to use without requiring detailed knowledge of the target dis-tribution. In past work, several authors have proposed splitting the Bayesian posterior into low-wavenumber and high-wavenumber components and then applying enhanced sampling to the low-wavenumber components. Yet compared to these other samplers, FES is unique in its simplicity and broad applicability. FES does not require any derivatives, and the need for derivative-free sam-plers has previously been emphasized. FES also eliminates the requirement for posterior covariance estimates. Lastly, FES is more efficient than other gradient-free samplers in our tests. In two nu-merical examples, we apply FES to challenging inverse problems that involve estimating a functional parameter and one or more scalar parameters. We compare the performance of functional random walk, FES, and an alternative derivative-free sampler that explicitly estimates the posterior covariance matrix. We conclude that FES is the fastest available gradient-free sampler for these challenging and multimodal test problems.

Keywords: Bayesian inverse problems, Markov chain Monte Carlo, infinite-dimensional inverse problems, dimensionality reduction

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