Uniform stability of a particle approximation of the optimal filter derivative

Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity, or derivative, of the optimal filter with respect to the static parameters of the state-space model; for instance, in order to obtain maximum likelihood model parameters of interest, or to compute the optimal controller in an optimal control problem. In Poyiadjis et al. [2011] an original particle algorithm to compute the filter derivative was proposed and it was shown using numerical examples that the particle estimate was numerically stable in the sense that it did not deteriorate over time. In this paper we substantiate this claim with a detailed theoretical study. Lp bounds and a central limit theorem for this particle approximation of the filter derivative are presented. It is further shown that under mixing conditions these Lp bounds and the asymptotic variance characterized by the central limit theorem are uniformly bounded with respect to the time index. We demon- strate the performance predicted by theory with several numerical examples. We also use the particle approximation of the filter derivative to perform online maximum likelihood parameter estimation for a stochastic volatility model.

The statistics of the second order response of an FPSO in spreading seas

An expression for the probability density function of the second order response of a general FPSO in spreading seas is derived by using the Kac-Siegert approach. Various approximations of the second order force transfer functions are investigated for a ship-shaped FPSO. It is found that, when expressed in non-dimensional form, the probability density function of the response is not particularly sensitive to wave spreading, although the mean squared response and the resulting dimensional extreme values can be sensitive. The analysis is then applied to a Sevan FPSO, which is a large cylindrical buoy-like structure. The second order force transfer functions are derived by using an efficient semi-analytical hydrodynamic approach, and these are then employed to yield the extreme response. However, a significant effect of wave spreading on the statistics for a Sevan FPSO is found even in non-dimensional form. It implies that the exact statistics of a general ship-shaped FPSO may be sensitive to the wave direction, which needs to be verified in future work. It is also pointed out that the Newman's approximation regarding the frequency dependency of force transfer function is acceptable even for the spreading seas. An improvement on the results may be attained when considering the angular dependency exactly. Copyright © 2009 by ASME.

A Salmonella Typhimurium-Typhi genomic chimera: a model to study Vi polysaccharide capsule function in vivo.

The Vi capsular polysaccharide is a virulence-associated factor expressed by Salmonella enterica serotype Typhi but absent from virtually all other Salmonella serotypes. In order to study this determinant in vivo, we characterised a Vi-positive S. Typhimurium (C5.507 Vi(+)), harbouring the Salmonella pathogenicity island (SPI)-7, which encodes the Vi locus. S. Typhimurium C5.507 Vi(+) colonised and persisted in mice at similar levels compared to the parent strain, S. Typhimurium C5. However, the innate immune response to infection with C5.507 Vi(+) and SGB1, an isogenic derivative not expressing Vi, differed markedly. Infection with C5.507 Vi(+) resulted in a significant reduction in cellular trafficking of innate immune cells, including PMN and NK cells, compared to SGB1 Vi(-) infected animals. C5.507 Vi(+) infection stimulated reduced numbers of TNF-α, MIP-2 and perforin producing cells compared to SGB1 Vi(-). The modulating effect associated with Vi was not observed in MyD88(-/-) and was reduced in TLR4(-/-) mice. The presence of the Vi capsule also correlated with induction of the anti-inflammatory cytokine IL-10 in vivo, a factor that impacted on chemotaxis and the activation of immune cells in vitro.