Approximate Bayesian Computation in State Space Models

A new approach to inference in state space models is proposed, based on approximate Bayesian computation (ABC). ABC avoids evaluation of the likelihood function by matching observed summary statistics with statistics computed from data simulated from the true process; exact inference being feasible only if the statistics are sufficient. With finite sample sufficiency unattainable in the state space setting, we seek asymptotic sufficiency via the maximum likelihood estimator (MLE) of the parameters of an auxiliary model. We prove that this auxiliary model-based approach achieves Bayesian consistency, and that - in a precise limiting sense - the proximity to (asymptotic) sufficiency yielded by the MLE is replicated by the score. In multiple parameter settings a separate treatment of scalar parameters, based on integrated likelihood techniques, is advocated as a way of avoiding the curse of dimensionality. Some attention is given to a structure in which the state variable is driven by a continuous time process, with exact inference typically infeasible in this case as a result of intractable transitions. The ABC method is demonstrated using the unscented Kalman filter as a fast and simple way of producing an approximation in this setting, with a stochastic volatility model for financial returns used for illustration

Asymptotic Properties of Approximate Bayesian Computation

Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on the rate at which the posterior distribution concentrates on sets containing the true parameter, its limiting shape, and the asymptotic distribution of the posterior mean. These results hold under given rates for the tolerance used within the method, mild regularity conditions on the summary statistics, and a condition linked to identification of the true parameters. Implications for practitioners are discussed.Comment: This 31 pages paper is a revised version of the paper, including supplementary materia

Nuclear star formation on 100 parsec scales: 10" resolution radio continuum, HI and CO observations

A program of radio line and continuum studies of star formation in nearby spiral galaxies is reported. The objective is a search for hot gas and peculiar dynamics in spiral nuclei with 10" to 30" angular resolution. Vigorous star formation is found to be a common phenomenon in the inner kpc of spirals. Arcsecond resolution observations of radio continuum emission at 6 and 2 cm were used to separate the thermal and nonthermal radio components. It was found that thermal and nonthermal emission are well mixed even on sizescales of 10 pc. To understand the reason for the increased level of star formation activity in spiral nuclei, HI and CO emission in these galaxies is studied. The CO transition was detected in M51, M82, NGC 253, NGC 6946 and IC 342 with T sub a approx. 0.5 to 2.0 K, at 20" angular resolution. The dynamics and spatial distribution of nuclear gas are being studied using VLA HI maps with 30" synthesized beams. Evidence for noncircular motions in HI was found in the nucleus of IC 342

Glomerulonephritis in the Canine

The case report given shows some of the characteristic clinical and histopathological signs of glomerulonephritis. The clinical signs include proteinuria, elevated blood urea nitrogen and creatinine levels. The histopathology of the kidney reveals glomerular tuft proliferation, hyaline formation, and Bowman\u27s capsule adhesions

Diversity, Assortment, Dissimilarity, Variety: A Study of Diversity Measures Using Low Level Features for Video Retrieval

In this paper we present a number of methods for re-ranking video search results in order to introduce diversity into the set of search results. The usefulness of these approaches is evaluated in comparison with similarity based measures, for the TRECVID 2007 collection and tasks [11]. For the MAP of the search results we find that some of our approaches perform as well as similarity based methods. We also find that some of these results can improve the P@N values for some of the lower N values. The most successful of these approaches was then implemented in an interactive search system for the TRECVID 2008 interactive search tasks. The responses from the users indicate that they find the more diverse search results extremely useful

Mutational Analysis of HIV-1 gp160-Mediated Receptor Interference: Intracellular Complex Formation

AbstractFormation of CD4–gp160 intracellular complexes represents an important mechanism leading to the induction of receptor interference. Previous studies have demonstrated that cells coexpressing gp160 and CD4 formed complexes of CD4 and gp160 which became blocked within the endoplasmic reticulum (ER), preventing CD4 from reaching the cell surface. In this report we have investigated the domains and residues of CD4 and gp160 involved in intracellular interaction. Accordingly, we have introduced mutations in both CD4 and gp160 at sites previously shown to disrupt CD4–gp120 interactions at the cell surface. Using a T7-vaccinia virus transient expression system, we expressed these gp160 and CD4 mutants in HeLa cells and analyzed their effects on intracellular complex formation and CD4 surface modulation. We observed that a number of gp160 mutants which failed to interact with CD4 at the cell surface also failed to bind and trap CD4 within the ER as expected. However, mutations at a critical residue, W427, did not abrogate intracellular CD4 binding. These gp160 mutants continued to interact with intracellular CD4 and inhibit CD4 transport to the cell surface, although gp120 produced from these mutants did not bind CD4 at the cell surface as expected. A number CD4 mutants also continued to form intracellular complexes with gp160, resulting in the loss of CD4 surface expression. Again, these CD4 mutants did not bind to gp120 at the cell surface, consistent with earlier reports. These results demonstrate that intracellular interactions between gp160 and CD4 in the ER may utilize different contact sites compared to those used during CD4 and gp120 binding at the cell surface. The data provide further evidence that the environment in which CD4 and the HIV-1 envelope glycoprotein interact can have a significant effect on their interaction

Partition Function Zeros of a Restricted Potts Model on Lattice Strips and Effects of Boundary Conditions

We calculate the partition function $Z(G,Q,v)$ of the $Q$-state Potts model exactly for strips of the square and triangular lattices of various widths $L_y$ and arbitrarily great lengths $L_x$, with a variety of boundary conditions, and with $Q$ and $v$ restricted to satisfy conditions corresponding to the ferromagnetic phase transition on the associated two-dimensional lattices. From these calculations, in the limit $L_x \to \infty$, we determine the continuous accumulation loci ${\cal B}$ of the partition function zeros in the $v$ and $Q$ planes. Strips of the honeycomb lattice are also considered. We discuss some general features of these loci.Comment: 12 pages, 12 figure