Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels

Monte Carlo algorithms often aim to draw from a distribution π by simulating a Markov chain with transition kernel P such that π is invariant under P. However, there are many situations for which it is impractical or impossible to draw from the transition kernel P. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace P by an approximation Pˆ. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how ’close’ the chain given by the transition kernel Pˆ is to the chain given by P . We apply these results to several examples from spatial statistics and network analysis.

Plane wave discontinuous Galerkin methods: exponential convergence of the hp-version

We consider the two-dimensional Helmholtz equation with constant coefficients on a domain with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft obstacle. Our discretisation relies on the Trefftz-discontinuous Galerkin approach with plane wave basis functions on meshes with very general element shapes, geometrically graded towards domain corners. We prove exponential convergence of the discrete solution in terms of number of unknowns.

Convergence and accommodation development is pre-programmed in premature infants

Purpose This study investigated whether vergence and accommodation development in pre-term infants is pre-programmed or is driven by experience. Methods 32 healthy infants, born at mean 34 weeks gestation (range 31.2-36 weeks) were compared with 45 healthy full-term infants (mean 40.0 weeks) over a 6 month period, starting at 4-6 weeks post-natally. Simultaneous accommodation and convergence to a detailed target were measured using a Plusoptix PowerRefII infra-red photorefractor as a target moved between 0.33m and 2m. Stimulus/response gains and responses at 0.33m and 2m were compared by both corrected (gestational) age and chronological (post-natal) age. Results When compared by their corrected age, pre-term and full-term infants showed few significant differences in vergence and accommodation responses after 6-7 weeks of age. However, when compared by chronological age, pre-term infants’ responses were more variable, with significantly reduced vergence gains, reduced vergence response at 0.33m, reduced accommodation gain, and increased accommodation at 2m, compared to full-term infants between 8-13 weeks after birth. Conclusions When matched by corrected age, vergence and accommodation in pre-term infants show few differences from full-term infants’ responses. Maturation appears pre-programmed and is not advanced by visual experience. Longer periods of immature visual responses might leave pre-term infants more at risk of development of oculomotor deficits such as strabismus.  

Follow the leaders? An analysis of convergence and innovation of faculty recruiting practices in US business schools

The debate associated with the qualifications of business school faculty has raged since the 1959 release of the Gordon–Howell and Pierson reports, which encouraged business schools in the USA to enhance their legitimacy by increasing their faculties’ doctoral qualifications and scholarly rigor. Today, the legitimacy of specific faculty qualifications remains one of the most discussed topics in management education, attracting the interest of administrators, faculty, and accreditation agencies. Based on new institutional theory and the institutional logics perspective, this paper examines convergence and innovation in business schools through an analysis of faculty hiring criteria. The qualifications examined are academic degree, scholarly publications, teaching experience, and professional experience. Three groups of schools are examined based on type of university, position within a media ranking system, and accreditation by the Association to Advance Collegiate Schools of Business. Data are gathered using a content analysis of 441 faculty postings from business schools based in the USA over two time periods. Contrary to claims of global convergence, we find most qualifications still vary by group, even in the mature US market. Moreover, innovative hiring is more likely to be found in non-elite schools.

Convergence accommodation in orthoptic practice

Aims. Orthoptists are familiar with AC/A ratios and the concept that accommodation drives convergence, but the reverse relationship, that of the accommodation associated with convergence, is rarely considered. Methods. This article reviews published evidence from our laboratory which has investigated the drives to both vergence and accommodation. All studies involved a method by which accommodation and vergence were measured concurrently and objectively to a range of visual stimuli which manipulate blur, disparity and proximal/looming cues in different combinations. Results Results are summarised for both typical and atypical participants, and over development between birth and adulthood. Conclusions For the majority of typical children and adults, as well as patients with most heterophorias and intermittent exotropia, disparity is the main cue to both vergence and accommodation. Thus the convergence→accommodation relationship is more influential than that of accommodative vergence. Differences in “style” of near cue use may be a more useful way to think about responses to stimuli moving in depth, and their consequences for orthoptic patients, than either AC/A or CA/C ratios. The implications of a strong role for vergence accommodation in orthoptic practice are considered.