Gaussian processes and Bayesian moment estimation

Given a set of moment restrictions (MRs) that overidentify a parameter $\theta$, we investigate a semiparametric Bayesian approach for inference on $\theta$ that does not restrict the data distribution $F$ apart from the MRs. As main contribution, we construct a degenerate Gaussian process prior that, conditionally on $\theta$, restricts the $F$ generated by this prior to satisfy the MRs with probability one. Our prior works even in the more involved case where the number of MRs is larger than the dimension of $\theta$. We demonstrate that the corresponding posterior for $\theta$ is computationally convenient. Moreover, we show that there exists a link between our procedure, the Generalized Empirical Likelihood with quadratic criterion and the limited information likelihood-based procedures. We provide a frequentist validation of our procedure by showing consistency and asymptotic normality of the posterior distribution of $\theta$. The finite sample properties of our method are illustrated through Monte Carlo experiments and we provide an application to demand estimation in the airline market

Nonparametric Estimation of An Instrumental Regression: A Quasi-Bayesian Approach Based on Regularized Posterior

We propose a Quasi-Bayesian nonparametric approach to estimating the structural relationship ' among endogenous variables when instruments are available. We show that the posterior distribution of ' is inconsistent in the frequentist sense. We interpret this fact as the ill-posedness of the Bayesian inverse problem defined by the relation that characterizes the structural function '. To solve this problem, we construct a regularized posterior distribution, based on a Tikhonov regularization of the inverse of the marginal variance of the sample, which is justified by a penalized projection argument. This regularized posterior distribution is consistent in the frequentist sense and its mean can be interpreted as the mean of the exact posterior distribution resulting from a gaussian prior distribution with a shrinking covariance operator.

History and the nation in the work of Fionn MacColla

It is the object of this thesis to undertake a revisionary analysis of the work of Scottish author, historiographer and pioneering nationalist, Fionn MacColla. Generally, MacColla has been regarded as an excessively radical figure whose allegedly dogmatic approach has too often obscured the more promising aspects of his work. He continues to feature in the most up-to-date accounts of twentieth-century Scottish literature as the voice of an unpalatable extremism which, with religion at its core, is too controversial, too sensitive and too antagonistic to be considered constructive. This thesis argues, however, that MacColla has been typecast as a Catholic propagandist and erroneously categorised under the assumption that his motives were purely religious or his views extreme. It shows that such a view not only overlooks the complexity and significance of his often esoteric, though not impenetrable, ideas, but grossly oversimplifies and misrepresents them.The thesis focuses, particularly, on MacColla's theoretical approach to history while exploring the techniques which he develops in his attempt to construct a narrative method capable of re-presenting the issues raised in his theoretical material. Importantly, it does not attempt to situate MacColla within a specific context, other than that of his role within the twentieth-century Scottish Renaissance Movement. It is the aim of this thesis, rather, to identify and explore the conceptual content of MacColla's theory and fiction as part of a need to consolidate a greater understanding of a writer who, at best, has only been dealt with fleetingly within the Scottish critical canon

Regularizing priors for linear inverse problems

We consider statistical linear inverse problems in Hilbert spaces of the type ˆ Y = Kx + U where we want to estimate the function x from indirect noisy functional observations ˆY . In several applications the operator K has an inverse that is not continuous on the whole space of reference; this phenomenon is known as ill-posedness of the inverse problem. We use a Bayesian approach and a conjugate-Gaussian model. For a very general specification of the probability model the posterior distribution of x is known to be inconsistent in a frequentist sense. Our first contribution consists in constructing a class of Gaussian prior distributions on x that are shrinking with the measurement error U and we show that, under mild conditions, the corresponding posterior distribution is consistent in a frequentist sense and converges at the optimal rate of contraction. Then, a class ^ of posterior mean estimators for x is given. We propose an empirical Bayes procedure for selecting an estimator in this class that mimics the posterior mean that has the smallest risk on the true x

Regularizing priors for linear inverse problems

We consider statistical linear inverse problems in Hilbert spaces of the type ˆ Y = Kx + U where we want to estimate the function x from indirect noisy functional observations ˆY . In several applications the operator K has an inverse that is not continuous on the whole space of reference; this phenomenon is known as ill-posedness of the inverse problem. We use a Bayesian approach and a conjugate-Gaussian model. For a very general specification of the probability model the posterior distribution of x is known to be inconsistent in a frequentist sense. Our first contribution consists in constructing a class of Gaussian prior distributions on x that are shrinking with the measurement error U and we show that, under mild conditions, the corresponding posterior distribution is consistent in a frequentist sense and converges at the optimal rate of contraction. Then, a class ^ of posterior mean estimators for x is given. We propose an empirical Bayes procedure for selecting an estimator in this class that mimics the posterior mean that has the smallest risk on the true x

Regularizing Priors for Linear Inverse Problems

This paper proposes a new Bayesian approach for estimating, nonparametrically, parameters in econometric models that are characterized as the solution of a linear inverse problem. By using a Gaussian process prior distribution we propose the posterior mean as an estimator and prove consistency, in the frequentist sense, of the posterior distribution. Consistency of the posterior distribution provides a frequentist validation of our Bayesian procedure. We show that the minimax rate of contraction of the posterior distribution can be obtained provided that either the regularity of the prior matches the regularity of the true parameter or the prior is scaled at an appropriate rate. The scaling parameter of the prior distribution plays the role of a regularization parameter. We propose a new, and easy-to-implement, data-driven method for optimally selecting in practice this regularization parameter. Moreover, we make clear that the posterior mean, in a conjugate-Gaussian setting, is equal to a Tikhonov-type estimator in a frequentist setting so that our data-driven method can be used in frequentist estimation as well. Finally, we apply our general methodology to two leading examples in econometrics: instrumental regression and functional regression estimation

Opinions on the use of technology to improve tablet taking in >65-year-old patients on cardiovascular medications.

Objective This study was performed to evaluate the perceptions of the use of technology to improve cardiovascular medicine taking among patients aged >65 years. Methods This qualitative study used focus groups with people aged >65 years taking cardiovascular medications from two East London community centres. Thematic analysis was informed by the Perceptions and Practicalities Approach framework. Results Participants welcomed technologies they considered familiar, accessible, and easy to use. They valued the opportunity to receive alerts to help with forgetting and monitoring their treatment. More advanced technologies such as ingestible sensor systems were considered helpful for elderly people with significant cognitive impairments still living in the community because of improved monitoring by caregivers and clinicians and prolonging independence. Although generally adapting to the increase in technology in everyday life, participants raised a number of concerns that included potential reduction in face-to-face communication, data security, becoming dependent on technology, and worrying about the consequences of technological failure. Conclusions Participants raised a number of concerns and practical barriers that would need to be addressed for technologies to be accepted and adopted in this patient group

Stroke survivors and their families receive information and support on an individual basis from an online forum: descriptive analysis of a population of 2348 patients and qualitative study of a sample of participants.

OBJECTIVE: To describe the characteristics of participants of an online stroke forum, their reasons for posting in the forum and whether responses addressed users' needs. METHODS: Descriptive analysis of the population of 2004-2011 archives of Talkstroke, the online forum of the Stroke Association, and comparison with patients admitted to hospital with stroke (Sentinel Stroke National Audit Programme, SSNAP). Thematic analysis of posts from a sample of 59 participants representative of age at stroke and sex. SETTINGS: UK. MAIN OUTCOME MEASURES: Characteristics of participants: age, sex, survivor versus patient by third party, side of stroke (R, L), social class; (from the sample of 59 participants): level of disability, stroke type, classification of users' intents for writing a post in the forum, quantification of needs addressed by the forum, topics of discussion. PARTICIPANTS: 2348 participants (957 stroke survivors, 1391 patients with stroke talked about by third party). RESULTS: Patients of both sexes and from a wide range of ages at stroke (0 to 95 years) and degrees of disability were represented in the forum, although younger than the UK stroke population (mean age 52 years vs 77 years in SSNAP). Analysis of 841 posts showed that the main users' intents for writing in the forum were requests/offers of information and support (58%) and sharing own experiences of stroke (35%). Most information needs were around stroke-related physical impairments, understanding the cause of stroke and the potential for recovery. Up to 95% of the users' intents were met by the replies received. CONCLUSIONS: Patients' needs expressed in the online forum confirm and widen the evidence from traditional research studies, showing that such forums are a potential resource for studying needs in this population. The forum provided an opportunity for patients and families to give and receive advice and social support.This study was funded by a NIHR Academic Clinical Lectureship to Anna De Simoni. The Evelyn Trust funded Chantal Balasooriya-Smeekens’s work.This is the final published version. It first appeared at http://bmjopen.bmj.com/content/6/4/e010501.abstract

How primary care can help stroke survivors with returning to work: focus groups with stakeholders from a UK community

Background Evidence about how primary care can best enable survivors of transient ischaemic attack (TIA)/stroke return to work is limited. Aim This study explored the role of primary care in supporting survivors of transient ischaemic attack (TIA)/stroke return to work with stakeholders from a local UK community. Design A qualitative study using framework analysis. Method Four focus groups were carried out in Cambridgeshire, UK, between September and November 2015. The 18 participants included survivors of TIA/stroke, carers, an employer representative, GPs, occupational therapists (OTs), and clinical commissioners. Results There was a mismatch between patient and carer needs and what is provided by primary care. This included: lack of GP awareness of invisible impairments; uncertainty how primary care could help in time-limited consultations; and complexity of return-to-work issues. Primary care physicians were not aware of relevant services they could refer patients to, such as OT support. In addition, there was an overall lack of coordination between different stakeholders in the return-to-work process. Linking with other services was considered important but challenging because of ongoing changes in service structure and the commissioning model. Suggestions for improvement include: a central contact in primary care for signposting to available services; a rehabilitation assessment integrated with the electronic record; and a patient-held shared-care plan at discharge from stroke wards. Conclusion Improving the role for primary care in helping survivors of TIA/stroke return to work is challenging. However, primary care could play a central role in initiating/coordinating vocational rehabilitation. Through focus group discussions with stakeholders from a local community, patients, carers, and clinical commissioners were able to put forward concrete proposals to address the barriers identified.This study was funded by the Evelyn Trust (grant reference14/33). Anna De Simoni was funded by a NIHR Academic Clinical Lectureship. Andrew Bateman was supported by the National Institute for Health Research (NIHR) Collaboration for Leadership in Applied Health Research and Care East of England at Cambridgeshire and Peterborough NHS Foundation Trust. Jonathan Mant is an NIHR Senior Investigator. The views expressed are those of the author(s) and not necessarily those of the NHS, the NIHR or the Department of Healt