arXiv subjects

Y. Fan

Publications and source records attributed to Y. Fan.

At least 55 records · Page 3Linked to original sources

arXiv2014

Rigorous analysis of highly tunable cylindrical Transverse Magnetic mode re-entrant cavities

Cylindrical re-entrant cavities are unique three-dimensional structures that resonate with their electric and magnetic fields in separate parts of the cavity. To further understand these devices, we undertake rigorous analysis of the properties of the resonance using in-house developed Finite Element Method (FEM) software capable of dealing with small gap structures of extreme aspect ratio. Comparisons between the FEM method and experiments are consistent and we illustrate where predictions using established lumped element models work well and where they are limited. With the aid of the modeling we design a highly tunable cavity that can be tuned from 2 GHz to 22 GHz just by inserting a post into a fixed dimensioned cylindrical cavity. We show this is possible as the mode structure transforms from a re-entrant mode during the tuning process to a standard cylindrical Transverse Magnetic (TM) mode.

physics.ins-det↗

arXiv2013

Simultaneous adjustment of bias and coverage probabilities for confidence intervals

A new method is proposed for the correction of confidence intervals when the original interval does not have the correct nominal coverage probabilities in the frequentist sense. The proposed method is general and does not require any distributional assumptions. It can be applied to both frequentist and Bayesian inference where interval estimates are desired. We provide theoretical results for the consistency of the proposed estimator, and give two complex examples, on confidence interval correction for composite likelihood estimators and in approximate Bayesian computation (ABC), to demonstrate the wide applicability of the new method. Comparison is made with the double-bootstrap and other methods of improving confidence interval coverage.

stat.CO↗

arXiv2013

Polarimetric Properties of Flux-Ropes and Sheared Arcades in Coronal Prominence Cavities

The coronal magnetic field is the primary driver of solar dynamic events. Linear and circular polarization signals of certain infrared coronal emission lines contain information about the magnetic field, and to access this information, either a forward or an inversion method must be used. We study three coronal magnetic configurations that are applicable to polar-crown filament cavities by doing forward calculations to produce synthetic polarization data. We analyze these forward data to determine the distinguishing characteristics of each model. We conclude that it is possible to distinguish between cylindrical flux ropes, spheromak flux ropes, and sheared arcades using coronal polarization measurements. If one of these models is found to be consistent with observational measurements, it will mean positive identification of the magnetic morphology that surrounds certain quiescent filaments, which will lead to a greater understanding of how they form and why they erupt.

astro-ph.SR↗

arXiv2013

The Magnetic Structure of Solar Prominence Cavities: New Observational Signature Revealed by Coronal Magnetometry

The Coronal Multi-channel Polarimeter (CoMP) obtains daily full-Sun above-the-limb coronal observations in linear polarization, allowing for the first time a diagnostic of the coronal magnetic field direction in quiescent prominence cavities. We find that these cavities consistently possess a characteristic "lagomorphic" signature in linear polarization indicating twist or shear extending up into the cavity above the neutral line. We demonstrate that such a signature may be explained by a magnetic flux-rope model, a topology with implications for solar eruptions. We find corroborating evidence for a flux rope structure in the pattern of concentric rings within cavities seen in CoMP line-of-sight velocity.

astro-ph.SR↗

arXiv2012

Approximate Bayesian computation and Bayes linear analysis: Towards high-dimensional ABC

Bayes linear analysis and approximate Bayesian computation (ABC) are techniques commonly used in the Bayesian analysis of complex models. In this article we connect these ideas by demonstrating that regression-adjustment ABC algorithms produce samples for which first and second order moment summaries approximate adjusted expectation and variance for a Bayes linear analysis. This gives regression-adjustment methods a useful interpretation and role in exploratory analysis in high-dimensional problems. As a result, we propose a new method for combining high-dimensional, regression-adjustment ABC with lower-dimensional approaches (such as using MCMC for ABC). This method first obtains a rough estimate of the joint posterior via regression-adjustment ABC, and then estimates each univariate marginal posterior distribution separately in a lower-dimensional analysis. The marginal distributions of the initial estimate are then modified to equal the separately estimated marginals, thereby providing an improved estimate of the joint posterior. We illustrate this method with several examples. Supplementary materials for this article are available online.

stat.ME↗

arXiv2012

Approximate Bayesian Computation via Regression Density Estimation

Approximate Bayesian computation (ABC) methods, which are applicable when the likelihood is difficult or impossible to calculate, are an active topic of current research. Most current ABC algorithms directly approximate the posterior distribution, but an alternative, less common strategy is to approximate the likelihood function. This has several advantages. First, in some problems, it is easier to approximate the likelihood than to approximate the posterior. Second, an approximation to the likelihood allows reference analyses to be constructed based solely on the likelihood. Third, it is straightforward to perform sensitivity analyses for several different choices of prior once an approximation to the likelihood is constructed, which needs to be done only once. The contribution of the present paper is to consider regression density estimation techniques to approximate the likelihood in the ABC setting. Our likelihood approximations build on recently developed marginal adaptation density estimators by extending them for conditional density estimation. Our approach facilitates reference Bayesian inference, as well as frequentist inference. The method is demonstrated via a challenging problem of inference for stereological extremes, where we perform both frequentist and Bayesian inference.

stat.CO↗

arXiv2012

Thermal signatures of tether-cutting reconnections in pre-eruption coronal flux ropes: hot central voids in coronal cavities

Using a 3D MHD simulation, we model the quasi-static evolution and the onset of eruption of a coronal flux rope. The simulation begins with a twisted flux rope emerging at the lower boundary and pushing into a pre-existing coronal potential arcade field. At a chosen time the emergence is stopped with the lower boundary taken to be rigid. Then the coronal flux rope settles into a quasi-static rise phase during which an underlying, central sigmoid-shaped current layer forms along the so called hyperbolic flux tube (HFT), a generalization of the X-line configuration. Reconnections in the dissipating current layer effectively add twisted flux to the flux rope and thus allow it to rise quasi-statically, even though the magnetic energy is decreasing as the system relaxes. We examine the thermal features produced by the current layer formation and the associated "tether-cutting" reconnections as a result of heating and field aligned thermal conduction. It is found that a central hot, low-density channel containing reconnected, twisted flux threading under the flux rope axis forms on top of the central current layer. When viewed in the line of sight roughly aligned with the hot channel (which is roughly along the neutral line), the central current layer appears as a high-density vertical column with upward extensions as a "U" shaped dense shell enclosing a central hot, low-density void. Such thermal features have been observed within coronal prominence cavities. Our MHD simulation suggests that they are the signatures of the development of the HFT topology and the associated tether-cutting reconnections, and that the central void grows and rises with the reconnections, until the flux rope reaches the critical height for the onset of the torus instability and dynamic eruption ensues.

astro-ph.SR↗

arXiv2012

On Bayesian quantile regression curve fitting via auxiliary variables

Quantile regression has received increased attention in the statistics community in recent years. This article adapts an auxiliary variable method, commonly used in Bayesian variable selection for mean regression models, to the fitting of quantile regression curves. We focus on the fitting of regression splines, with unknown number and location of knots. We provide an efficient algorithm with Metropolis-Hastings updates whose tuning is fully automated. The method is tested on simulated and real examples and its extension to additive models is described. Finally we propose a simple postprocessing procedure to deal with the problem of the crossing of multiple separately estimated quantile curves.

stat.ME↗

arXiv2012

Discussions on Fernhead and Prangle (2012)

Two contributions to the discussion of Fearnhead P. and D. Prangle (2012). Constructing summary statistics for approximate Bayesian computation: Semi-automatic approx- imate Bayesian computation, J. Roy. Statist. Soc. B, 74 (3).

stat.CO↗

arXiv2012

Numerical Calculation of Convection with Reduced Speed of Sound Technique

Context. The anelastic approximation is often adopted in numerical calculation with low Mach number, such as stellar internal convection. This approximation requires frequent global communication, because of an elliptic partial differential equation. Frequent global communication is negative factor for the parallel computing with a large number of CPUs. Aims. The main purpose of this paper is to test the validity of a method that artificially reduces the speed of sound for the compressible fluid equations in the context of stellar internal convection. The reduction of speed of sound allows for larger time steps in spite of low Mach number, while the numerical scheme remains fully explicit and the mathematical system is hyperbolic and thus does not require frequent global communication. Methods. Two and three dimensional compressible hydrodynamic equations are solved numerically. Some statistical quantities of solutions computed with different effective Mach numbers (due to reduction of speed of sound) are compared to test the validity of our approach. Results. Numerical simulations with artificially reduced speed of sound are a valid approach as long as the effective Mach number (based on the reduced speed of sound) remains less than 0.7.

astro-ph.SR↗

arXiv2011

An MHD Model of the December 13 2006 Eruptive Flare

We present a 3D MHD simulation that qualitatively models the coronal mag- netic field evolution associated with the eruptive flare that occurred on December 13, 2006 in the emerging δ-sunspot region NOAA 10930 observed by the Hinode satellite. The simulation is set up where we drive the emergence of an east-west oriented magnetic flux rope at the lower boundary into a pre-existing coronal field constructed from the SOHO/MDI full-disk magnetogram at 20:51:01 UT on December 12, 2006. The resulting coronal flux rope embedded in the ambi- ent coronal magnetic field first settles into a stage of quasi-static rise, and then undergoes a dynamic eruption, with the leading edge of the flux rope cavity accel- erating to a steady speed of about 830 km/s. The pre-eruption coronal magnetic field shows morphology that is in qualitative agreement with that seen in the Hinode soft X-ray observation in both the magnetic connectivity as well as the development of an inverse-S shaped X-ray sigmoid. We examine the properties of the erupting flux rope and the morphology of the post-reconnection loops, and compare them with the observations.

astro-ph.SR↗

arXiv2011

Enhancing synchronization in growing networks

Most real systems are growing. In order to model the evolution of real systems, many growing network models have been proposed to reproduce some specific topology properties. As the structure strongly influences the network function, designing the function-aimed growing strategy is also a significant task with many potential applications. In this letter, we focus on synchronization in the growing networks. In order to enhance the synchronizability during the network evolution, we propose the Spectral-Based Growing (SBG) strategy. Based on the linear stability analysis of synchronization, we show that our growing mechanism yields better synchronizability than the existing topology-aimed growing strategies in both artificial and real-world networks. We also observe that there is an optimal degree of new added nodes, which means adding nodes with neither too large nor too low degree could enhance the synchronizability. Furthermore, some topology measurements are considered in the resultant networks. The results show that the degree, node betweenness centrality from SBG strategy are more homogenous than those from other growing strategies. Our work highlights the importance of the function-aimed growth of the networks and deepens our understanding of it.

physics.soc-ph↗

arXiv2010

Adaptive Optimal Scaling of Metropolis-Hastings Algorithms Using the Robbins-Monro Process

We present an adaptive method for the automatic scaling of Random-Walk Metropolis-Hastings algorithms, which quickly and robustly identifies the scaling factor that yields a specified overall sampler acceptance probability. Our method relies on the use of the Robbins-Monro search process, whose performance is determined by an unknown steplength constant. We give a very simple estimator of this constant for proposal distributions that are univariate or multivariate normal, together with a sampling algorithm for automating the method. The effectiveness of the algorithm is demonstrated with both simulated and real data examples. This approach could be implemented as a useful component in more complex adaptive Markov chain Monte Carlo algorithms, or as part of automated software packages.

stat.ME↗

arXiv2010

A note on target distribution ambiguity of likelihood-free samplers

Methods for Bayesian simulation in the presence of computationally intractable likelihood functions are of growing interest. Termed likelihood-free samplers, standard simulation algorithms such as Markov chain Monte Carlo have been adapted for this setting. In this article, by presenting generalisations of existing algorithms, we demonstrate that likelihood-free samplers can be ambiguous over the form of the target distribution. We also consider the theoretical justification of these samplers. Distinguishing between the forms of the target distribution may have implications for the future development of likelihood-free samplers.

stat.CO↗

arXiv2009

Likelihood-free Bayesian inference for alpha-stable models

$α$-stable distributions are utilised as models for heavy-tailed noise in many areas of statistics, finance and signal processing engineering. However, in general, neither univariate nor multivariate $α$-stable models admit closed form densities which can be evaluated pointwise. This complicates the inferential procedure. As a result, $α$-stable models are practically limited to the univariate setting under the Bayesian paradigm, and to bivariate models under the classical framework. In this article we develop a novel Bayesian approach to modelling univariate and multivariate $α$-stable distributions based on recent advances in "likelihood-free" inference. We present an evaluation of the performance of this procedure in 1, 2 and 3 dimensions, and provide an analysis of real daily currency exchange rate data. The proposed approach provides a feasible inferential methodology at a moderate computational cost.

stat.CO↗

arXiv2009

On sequential Monte Carlo, partial rejection control and approximate Bayesian computation

We present a sequential Monte Carlo sampler variant of the partial rejection control algorithm, and show that this variant can be considered as a sequential Monte Carlo sampler with a modified mutation kernel. We prove that the new sampler can reduce the variance of the incremental importance weights when compared with standard sequential Monte Carlo samplers. We provide a study of theoretical properties of the new algorithm, and make connections with some existing algorithms. Finally, the sampler is adapted for application under the challenging "likelihood free," approximate Bayesian computation modelling framework, where we demonstrate superior performance over existing likelihood-free samplers.

stat.CO↗

arXiv2009

On Bayesian Curve Fitting Via Auxiliary Variables

In this article we revisit the auxiliary variable method introduced in Smith and kohn (1996) for the fitting of P-th order spline regression models with an unknown number of knot points. We introduce modifications which allow the location of knot points to be random, and we further consider an extension of the method to handle models with non-Gaussian errors. We provide a new algorithm for the MCMC sampling of such models. Simulated data examples are used to compare the performance of our method with existing ones. Finally, we make a connection with some change-point problems, and show how they can be re-parameterised to the variable selection setting.

stat.ME↗

arXiv2009

Additive Self Helicity as a Kink Mode Threshold

In this paper we propose that additive self helicity, introduced by Longcope and Malanushenko (2008), plays a role in the kink instability for complex equilibria, similar to twist helicity for thin flux tubes (Hood and Priest (1979), Berger and Field (1984)). We support this hypothesis by a calculation of additive self helicity of a twisted flux tube from the simulation of Fan and Gibson (2003). As more twist gets introduced, the additive self helicity increases, and the kink instability of the tube coincides with the drop of additive self helicity, after the latter reaches the value of $H_A/Φ^2\approx 1.5$ (where $Φ$ is the flux of the tube and $H_A$ is additive self helicity). We compare additive self helicity to twist for a thin sub-portion of the tube to illustrate that $H_A/Φ^2$ is equal to the twist number, studied by Berger and Field (1984), when the thin flux tube approximation is applicable. We suggest, that the quantity $H_A/Φ^2$ could be treated as a generalization of a twist number, when thin flux tube approximation is not applicable. A threshold on a generalized twist number might prove extremely useful studying complex equilibria, just as twist number itself has proven useful studying idealized thin flux tubes. We explicitly describe a numerical method for calculating additive self helicity, which includes an algorithm for identifying a domain occupied by a flux bundle and a method of calculating potential magnetic field confined to this domain. We also describe a numerical method to calculate twist of a thin flux tube, using a frame parallelly transported along the axis of the tube.

astro-ph.SR↗