522 research outputs found
Microstructure Effects on Daily Return Volatility in Financial Markets
We simulate a series of daily returns from intraday price movements initiated
by microstructure elements. Significant evidence is found that daily returns
and daily return volatility exhibit first order autocorrelation, but trading
volume and daily return volatility are not correlated, while intraday
volatility is. We also consider GARCH effects in daily return series and show
that estimates using daily returns are biased from the influence of the level
of prices. Using daily price changes instead, we find evidence of a significant
GARCH component. These results suggest that microstructure elements have a
considerable influence on the return generating process.Comment: 15 pages, as presented at the Complexity Workshop in Aix-en-Provenc
A Bayesian reassessment of nearest-neighbour classification
The k-nearest-neighbour procedure is a well-known deterministic method used
in supervised classification. This paper proposes a reassessment of this
approach as a statistical technique derived from a proper probabilistic model;
in particular, we modify the assessment made in a previous analysis of this
method undertaken by Holmes and Adams (2002,2003), and evaluated by Manocha and
Girolami (2007), where the underlying probabilistic model is not completely
well-defined. Once a clear probabilistic basis for the k-nearest-neighbour
procedure is established, we derive computational tools for conducting Bayesian
inference on the parameters of the corresponding model. In particular, we
assess the difficulties inherent to pseudo-likelihood and to path sampling
approximations of an intractable normalising constant, and propose a perfect
sampling strategy to implement a correct MCMC sampler associated with our
model. If perfect sampling is not available, we suggest using a Gibbs sampling
approximation. Illustrations of the performance of the corresponding Bayesian
classifier are provided for several benchmark datasets, demonstrating in
particular the limitations of the pseudo-likelihood approximation in this
set-up
D-optimal designs via a cocktail algorithm
A fast new algorithm is proposed for numerical computation of (approximate)
D-optimal designs. This "cocktail algorithm" extends the well-known vertex
direction method (VDM; Fedorov 1972) and the multiplicative algorithm (Silvey,
Titterington and Torsney, 1978), and shares their simplicity and monotonic
convergence properties. Numerical examples show that the cocktail algorithm can
lead to dramatically improved speed, sometimes by orders of magnitude, relative
to either the multiplicative algorithm or the vertex exchange method (a variant
of VDM). Key to the improved speed is a new nearest neighbor exchange strategy,
which acts locally and complements the global effect of the multiplicative
algorithm. Possible extensions to related problems such as nonparametric
maximum likelihood estimation are mentioned.Comment: A number of changes after accounting for the referees' comments
including new examples in Section 4 and more detailed explanations throughou
An approximate Bayesian marginal likelihood approach for estimating finite mixtures
Estimation of finite mixture models when the mixing distribution support is
unknown is an important problem. This paper gives a new approach based on a
marginal likelihood for the unknown support. Motivated by a Bayesian Dirichlet
prior model, a computationally efficient stochastic approximation version of
the marginal likelihood is proposed and large-sample theory is presented. By
restricting the support to a finite grid, a simulated annealing method is
employed to maximize the marginal likelihood and estimate the support. Real and
simulated data examples show that this novel stochastic
approximation--simulated annealing procedure compares favorably to existing
methods.Comment: 16 pages, 1 figure, 3 table
Characterizing and Improving Generalized Belief Propagation Algorithms on the 2D Edwards-Anderson Model
We study the performance of different message passing algorithms in the two
dimensional Edwards Anderson model. We show that the standard Belief
Propagation (BP) algorithm converges only at high temperature to a paramagnetic
solution. Then, we test a Generalized Belief Propagation (GBP) algorithm,
derived from a Cluster Variational Method (CVM) at the plaquette level. We
compare its performance with BP and with other algorithms derived under the
same approximation: Double Loop (DL) and a two-ways message passing algorithm
(HAK). The plaquette-CVM approximation improves BP in at least three ways: the
quality of the paramagnetic solution at high temperatures, a better estimate
(lower) for the critical temperature, and the fact that the GBP message passing
algorithm converges also to non paramagnetic solutions. The lack of convergence
of the standard GBP message passing algorithm at low temperatures seems to be
related to the implementation details and not to the appearance of long range
order. In fact, we prove that a gauge invariance of the constrained CVM free
energy can be exploited to derive a new message passing algorithm which
converges at even lower temperatures. In all its region of convergence this new
algorithm is faster than HAK and DL by some orders of magnitude.Comment: 19 pages, 13 figure
First results from the Very Small Array -- IV. Cosmological parameter estimation
We investigate the constraints on basic cosmological parameters set by the
first compact-configuration observations of the Very Small Array (VSA), and
other cosmological data sets, in the standard inflationary LambdaCDM model.
Using a weak prior 40 < H_0 < 90 km/s/Mpc and 0 < tau < 0.5 we find that the
VSA and COBE_DMR data alone produce the constraints Omega_tot =
1.03^{+0.12}_{-0.12}, Omega_bh^2 = 0.029^{+0.009}_{-0.009}, Omega_cdm h^2 =
0.13^{+0.08}_{-0.05} and n_s = 1.04^{+0.11}_{-0.08} at the 68 per cent
confidence level. Adding in the type Ia supernovae constraints, we additionally
find Omega_m = 0.32^{+0.09}_{-0.06} and Omega_Lambda = 0.71^{+0.07}_{-0.07}.
These constraints are consistent with those found by the BOOMERanG, DASI and
MAXIMA experiments. We also find that, by combining all the recent CMB
experiments and assuming the HST key project limits for H_0 (for which the
X-ray plus Sunyaev--Zel'dovich route gives a similar result), we obtain the
tight constraints Omega_m=0.28^{+0.14}_{-0.07} and Omega_Lambda=
0.72^{+0.07}_{-0.13}, which are consistent with, but independent of, those
obtained using the supernovae data.Comment: 10 pages, 6 figures, MNRAS in pres
AMI-LA Observations of the SuperCLASS Super-cluster
We present a deep survey of the SuperCLASS super-cluster - a region of sky
known to contain five Abell clusters at redshift - performed using
the Arcminute Microkelvin Imager (AMI) Large Array (LA) at 15.5GHz. Our
survey covers an area of approximately 0.9 square degrees. We achieve a nominal
sensitivity of Jy beam toward the field centre, finding 80
sources above a threshold. We derive the radio colour-colour
distribution for sources common to three surveys that cover the field and
identify three sources with strongly curved spectra - a high-frequency-peaked
source and two GHz-peaked-spectrum sources. The differential source count (i)
agrees well with previous deep radio source count, (ii) exhibits no evidence of
an emerging population of star-forming galaxies, down to a limit of 0.24mJy,
and (iii) disagrees with some models of the 15GHz source population.
However, our source count is in agreement with recent work that provides an
analytical correction to the source count from the SKADS Simulated Sky,
supporting the suggestion that this discrepancy is caused by an abundance of
flat-spectrum galaxy cores as-yet not included in source population models.Comment: 17 pages, 14 figures, 3 tables. Accepted for publication in MNRA
The Arcminute Microkelvin Imager catalogue of gamma-ray burst afterglows at 15.7 GHz
We present the Arcminute Microkelvin Imager (AMI) Large Array catalogue of 139 gamma-ray bursts (GRBs). AMI observes at a central frequency of 15.7 GHz and is equipped with a fully automated rapid-response mode, which enables the telescope to respond to high-energy transients detected by Swift. On receiving a transient alert, AMI can be on-target within 2 min, scheduling later start times if the source is below the horizon. Further AMI observations are manually scheduled for several days following the trigger. The AMI GRB programme probes the early-time (<1 d) radio properties of GRBs, and has obtained some of the earliest radio detections (GRB 130427A at 0.36 and GRB 130907A at 0.51 d post-burst). As all Swift GRBs visible to AMI are observed, this catalogue provides the first representative sample of GRB radio properties, unbiased by multiwavelength selection criteria. We report the detection of six GRB radio afterglows that were not previously detected by other radio telescopes, increasing the rate of radio detections by 50 per cent over an 18-month period. The AMI catalogue implies a Swift GRB radio detection rate of ≳ 15 per cent, down to ∼0.2 mJy beam−1. However, scaling this by the fraction of GRBs AMI would have detected in the Chandra & Frail sample (all radio-observed GRBs between 1997 and 2011), it is possible ∼ 44–56 per cent of Swift GRBs are radio bright, down to ∼0.1–0.15 mJy beam−1. This increase from the Chandra & Frail rate (∼30 per cent) is likely due to the AMI rapid-response mode, which allows observations to begin while the reverse-shock is contributing to the radio afterglow
First results from the Very Small Array -- I. Observational methods
The Very Small Array (VSA) is a synthesis telescope designed to image faint
structures in the cosmic microwave background on degree and sub-degree angular
scales. The VSA has key differences from other CMB interferometers with the
result that different systematic errors are expected. We have tested the
operation of the VSA with a variety of blank-field and calibrator observations
and cross-checked its calibration scale against independent measurements. We
find that systematic effects can be suppressed below the thermal noise level in
long observations; the overall calibration accuracy of the flux density scale
is 3.5 percent and is limited by the external absolute calibration scale.Comment: 9 pages, 10 figures, MNRAS in press (Minor revisions
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