17,013 research outputs found
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
Auxiliary Likelihood-Based Approximate Bayesian Computation in State Space Models
A computationally simple approach to inference in state space models is
proposed, using approximate Bayesian computation (ABC). ABC avoids evaluation
of an intractable likelihood by matching summary statistics for the observed
data with statistics computed from data simulated from the true process, based
on parameter draws from the prior. Draws that produce a 'match' between
observed and simulated summaries are retained, and used to estimate the
inaccessible posterior. With no reduction to a low-dimensional set of
sufficient statistics being possible in the state space setting, we define the
summaries as the maximum of an auxiliary likelihood function, and thereby
exploit the asymptotic sufficiency of this estimator for the auxiliary
parameter vector. We derive conditions under which this approach - including a
computationally efficient version based on the auxiliary score - achieves
Bayesian consistency. To reduce the well-documented inaccuracy of ABC in
multi-parameter settings, we propose the separate treatment of each parameter
dimension using an integrated likelihood technique. Three stochastic volatility
models for which exact Bayesian inference is either computationally
challenging, or infeasible, are used for illustration. We demonstrate that our
approach compares favorably against an extensive set of approximate and exact
comparators. An empirical illustration completes the paper.Comment: This paper is forthcoming at the Journal of Computational and
Graphical Statistics. It also supersedes the earlier arXiv paper "Approximate
Bayesian Computation in State Space Models" (arXiv:1409.8363
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
Direct Measurement of a 27-Dimensional Orbital-Angular-Momentum State Vector
The measurement of a quantum state poses a unique challenge for
experimentalists. Recently, the technique of "direct measurement" was proposed
for characterizing a quantum state in-situ through sequential weak and strong
measurements. While this method has been used for measuring polarization
states, its real potential lies in the measurement of states with a large
dimensionality. Here we show the practical direct measurement of a
high-dimensional state vector in the discrete basis of orbital-angular
momentum. Through weak measurements of orbital-angular momentum and strong
measurements of angular position, we measure the complex probability amplitudes
of a pure state with a dimensionality, d=27. Further, we use our method to
directly observe the relationship between rotations of a state vector and the
relative phase between its orbital-angular-momentum components. Our technique
has important applications in high-dimensional classical and quantum
information systems, and can be extended to characterize other types of large
quantum states.Comment: 8 pages, 3 figure
Partition Function Zeros of a Restricted Potts Model on Lattice Strips and Effects of Boundary Conditions
We calculate the partition function of the -state Potts model
exactly for strips of the square and triangular lattices of various widths
and arbitrarily great lengths , with a variety of boundary
conditions, and with and restricted to satisfy conditions corresponding
to the ferromagnetic phase transition on the associated two-dimensional
lattices. From these calculations, in the limit , we determine
the continuous accumulation loci of the partition function zeros in
the and planes. Strips of the honeycomb lattice are also considered. We
discuss some general features of these loci.Comment: 12 pages, 12 figure
- …