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.

Dynamical properties of S-gap shifts and other shift spaces

We study the dynamical properties of certain shift spaces. To help study these properties we introduce two new classes of shifts, namely boundedly supermultiplicative (BSM) shifts and balanced shifts. It turns out that any almost specified shift is both BSM and balanced, and any balanced shift is BSM. However, as we will demonstrate, there are examples of shifts which are BSM but not balanced. We also study the measure theoretic properties of balanced shifts. We show that a shift space admits a Gibbs state if and only if it is balanced. Restricting ourselves to S-gap shifts, we relate certain dynamical properties of an S-gap shift to combinatorial properties from expansions in non-integer bases. This identification allows us to use the machinery from expansions in non-integer bases to give straightforward constructions of S -gap shifts with certain desirable properties. We show that for any q∈(0,1) there is an S-gap shift which has the specification property and entropy q . We also use this identification to address the question, for a given q∈(0,1), how many S-gap shifts exist with entropy q? For certain exceptional values of q there is a unique S-gap shift with this entropy.

The Phantom Carriage (1921)

The reputation of The Phantom Carriage (Körkarlen) as one of the major films of Swedish silent cinema is in some respects securely established. Yet the film has attracted surprisingly little detailed discussion. It may be that its most striking stylistic features have deflected or discouraged closer scrutiny. Tom Gunning, for instance, in making the case for Sjöström’s Masterman, argues that ‘Körkarlen wears its technique on its sleeve, overtly displays its unquestionable mastery of superimposition and complex narrative structure. Mästerman tucks its mastery of editing and composition up its sleeve, so to speak’. This article makes an argument for a different evaluation of The Phantom Carriage, bringing a critical and interpretative understanding of the film’s style into conversation with the historical accounts of film form which predominate in the scholarship around silent cinema. It suggests that the film achieves ‘mastery of editing and composition’ with a flexibility and fluidity in the construction of dramatic space that is in itself remarkable for its period, but that Sjöström’s achievements extend well beyond his handling of film space. Specifically, it discusses a segment which is in several respects at the heart of the film: the first meeting between the two central characters, David Holm (Victor Sjöström) and Sister Edit (Astrid Holm); it spans the film’s exact mid-point; and at almost twelve and a half minutes it is the longest uninterrupted passage to take place in a single setting. The chapter argues that the dramatic and structural centrality of the hostel segment is paralleled by its remarkably rich articulation of the relationships between action, character and space. We show how Sjöström’s creation of a three-dimensional filmic space - with no hint of frontality - becomes the basis for a reciprocal relationship between spatial naturalism and performance style, and for a mise-en-scene that can take on discrete interpretive force. The argument also places the hostel sequences within the film as a whole in order to show how relationships articulated through the detailed decisions in this section take on their full resonance within patterns and motifs that develop across the film.

Fighting merchants

Selected essays from a conference held in November 2013 to celebrate the contribution to scholarship of the medieval historian Professor James L. Bolton.

The Phantom Carriage: a revaluation

This is a two-part audiovisual essay on Victor Sjöström’s extraordinary film The Phantom Carriage (Körkarlen), which was released on New Year’s Day 1921. Part 1 explores a sequence in detail, revealing a mastery of three-dimensional film space which is remarkable for its period; the essay then look at the ways in which this handling of space is integral to the film’s rich articulation of character and action. Part 2 considers aspects of the film’s mise-en-scène and shows how the features of the sequence explored in Part 1 take on their full resonance within patterns and motifs that develop across the film. Published by Movie: a journal of film criticism, the essay complements our chapter on the film in the volume Silent Features, edited by Steve Neale (Exeter University Press, 2016).

Opening movements in Ophuls: Caught (and Madame de …)

This audiovisual essay was created at the wonderful NEH-funded workshop in videographic criticism at Middlebury College, ‘Scholarship in Sound and Image’. The essay provides an analysis of the orchestration of long takes and camera movement in the opening of Caught (Ophuls, 1949), and develops a comparison with the opening of Madame de… (Ophuls, 1953 – U.S. release title The Earrings of Madame de…), not least through a series of juxtapositions, which can be directly presented and compared in an audiovisual essay. The openings share a concern with the subjectivity of the female protagonists and our relationship toward it, evoking the women’s experience while balancing this with other kinds of perspective. As has been noted in the critical literature on Ophuls, and on melodramas of passion more generally, such views enable us to perceive the women concerned to be caught in material and ideological frameworks of which they are at best partially aware. Among the interests of this particular comparison, however, is the extent to which the dynamic around female subjectivity is played in relation to luxury goods, imagined, owned or admired. Tensions between on- and off-screen spaces and sounds are critical to the interest of the long takes under discussion. Camera movements subtly inflect the extent to which we are aligned (or otherwise) with the characters and the ways in which their material circumstances are revealed to us.