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1.
We present a Bayesian approach to modelling galaxy clusters using multi-frequency pointed observations from telescopes that exploit the Sunyaev–Zel'dovich effect. We use the recently developed multinest technique to explore the high-dimensional parameter spaces and also to calculate the Bayesian evidence. This permits robust parameter estimation as well as model comparison. Tests on simulated Arcminute Microkelvin Imager observations of a cluster, in the presence of primary CMB signal, radio point sources (detected as well as an unresolved background) and receiver noise, show that our algorithm is able to analyse jointly the data from six frequency channels, sample the posterior space of the model and calculate the Bayesian evidence very efficiently on a single processor. We also illustrate the robustness of our detection process by applying it to a field with radio sources and primordial CMB but no cluster, and show that indeed no cluster is identified. The extension of our methodology to the detection and modelling of multiple clusters in multi-frequency SZ survey data will be described in a future work.  相似文献   

2.
From the point of view of the non-parametric statistics, a general estimation method of the accuracy and con?dence interval of preliminary orbit determination is proposed for the occasion without any other information but observational data. Based on the bootstrap method, the estimation relies only on the observational data and does not require the precise orbit determination as a reference, or the assumption of normal distribution of observational errors. Numerical experiments show that this method is very simple in implementa- tion, and may serve as an easy accuracy evaluation for the preliminary orbit determination and for the follow-up employments.  相似文献   

3.
数值积分方法是进行天体力学研究的重要工具, 尤其对于行星历表的研究工作而言. 由于在使用数值方法计算天体轨道时, 最终误差通常是难以预知的, 所以在面对精度要求较高或者积分时间较长的工作时具体积分方案的设计---尤其是当使用定步长方法时的步长选择---需要十分谨慎, 因为这将意味着是否能在时间成本可以被接受的范围内使解的精度达到要求. 因此, 在使用数值方法解决实际问题时如何快速寻找效率与精度之间的最佳平衡点是每一个数值积分方法的设计者与使用者都会面临的难题. 为解决这一问题, 在定步长条件下对数值积分方法的舍入误差概率分布函数以及截断误差积累量对步长的依赖关系和随时间的增长关系进行了深入研究. 基于所得结论, 提出了一种仅需较少的数值实验资料即可对选择任意时间步长积分至任意积分时刻时的舍入误差概率分布函数与截断误差积累量进行准确估计的方法, 并使用Adams-Cowell方法对该误差估计方法在圆周期轨道条件下进行了验证. 该误差估计方法在未来有望用于不同数值算法的性能对比研究, 同时也可以对数值积分方法求解实际轨道问题时的决策工作带来重要帮助.  相似文献   

4.
Modern methods of spectral estimation based on parametric time-series models are useful tools in power spectral analysis. We apply the autoregressive (AR) model to study quasi-periodic oscillations (QPOs). An empirical formula to estimate the expectation and standard deviation of the noise AR power densities is derived, which can be used to estimate the statistical significance of an apparent QPO peak in an AR spectrum. An iterative adding-noise algorithm in AR spectral analysis is proposed and applied to studying QPOs in the X-ray binary Cir X-1.  相似文献   

5.
We optimise the parameters of the Population Monte Carlo algorithm using numerical simulations. The optimisation is based on an efficiency statistic related to the number of samples evaluated prior to convergence, and is applied to a D ‐dimensional Gaussian distribution to derive optimal scaling laws for the algorithm parameters. More complex distributions such as the banana and bimodal distributions are also studied. We apply these results to a cosmological parameter estimation problem that uses CMB anisotropy data from the WMAP nine‐year release to constrain a six parameter adiabatic model and a fifteen parameter admixture model, consisting of correlated adiabatic and isocurvature perturbations. In the case of the adiabatic model and the admixture model we find that the number of sample points increase by factors of 3 and 20, respectively, relative to the optimal Gaussian case. This is due to degeneracies in the underlying parameter space. The WMAP nine‐year data constrain the admixture model to have an isocurvature fraction of 36.3 ± 2.8 %. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

6.
LP估计在星载GPS运动学定轨中的应用及精度分析   总被引：2，自引：0，他引：2  
为得到高精度的星载GPS运动学定轨,必须利用观测精度高的相位观测值,但是相位观测值预处理后,仍然存在残余小周跳．在残差服从正态分布情况下LS法是最佳参数解算方法,但该方法不能解决资料的系统误差消除问题,LP估计是处理资料残差分布含有系统误差的有效方法之一．基于LS、LP方法的有效条件和GPS数据预处理的特性,将LP估计方法引入星载GPS运动学定轨数据处理中,以CHAMP卫星资料为例,研究了LP估计在星载GPS运动学定轨中的应用及其精度分析．实践表明:在处理含有残余小周跳的相位观测值时,LP估计比LS更有效,提高了星载GPS运动学定轨精度,但随着残余周跳的进一步修复,LP估计相对于LS估计的优越性越来越弱,在资料完全没有系统误差,残差服从正态分布的情况下,LP估计不能很好地体现其优越性,精度反而低于LS估计．  相似文献   

7.
精密单点定位可以实现厘米级的定位精度,但其实时应用受到模糊度收敛时间的限制,模糊度收敛一般需要30分钟甚至更长的时间.基于相位历元间差分技术,可以避免模糊度的求解,但求解的参数为历元间坐标差.在相位历元间差分技术基础之上,推导了无模糊度模型的快速静态单点定位模型,并通过岭估计理论来进行参数的求解,两个以上历元就可以解算得到位置参数,从而实现静态状态下单点的快速定位,克服了模糊度收敛时间的局限,并讨论了不同坐标初值情况下估计值的精度.  相似文献   

8.
The key features of the matphot algorithm for precise and accurate stellar photometry and astrometry using discrete point spread functions (PSFs) are described. A discrete PSF is a sampled version of a continuous PSF, which describes the two-dimensional probability distribution of photons from a point source (star) just above the detector. The shape information about the photon scattering pattern of a discrete PSF is typically encoded using a numerical table (matrix) or an FITS (Flexible Image Transport System) image file. Discrete PSFs are shifted within an observational model using a 21-pixel-wide damped sinc function, and position-partial derivatives are computed using a five-point numerical differentiation formula. Precise and accurate stellar photometry and astrometry are achieved with undersampled CCD (charge-coupled device) observations by using supersampled discrete PSFs that are sampled two, three or more times more finely than the observational data. The precision and accuracy of the matphot algorithm is demonstrated by using the c -language mpd code to analyse simulated CCD stellar observations; measured performance is compared with a theoretical performance model. Detailed analysis of simulated Next Generation Space Telescope observations demonstrate that millipixel relative astrometry and mmag photometric precision is achievable with complicated space-based discrete PSFs.  相似文献   

9.
The principles of measuring the shapes of galaxies by a model-fitting approach are discussed in the context of shape measurement for surveys of weak gravitational lensing. It is argued that such an approach should be optimal, allowing measurement with maximal signal-to-noise ratio, coupled with estimation of measurement errors. The distinction between likelihood-based and Bayesian methods is discussed. Systematic biases in the Bayesian method may be evaluated as part of the fitting process, and overall such an approach should yield unbiased shear estimation without requiring external calibration from simulations. The principal disadvantage of model fitting for large surveys is the computational time required, but here an algorithm is presented that enables large surveys to be analysed in feasible computation times. The method and algorithm is tested on simulated galaxies from the Shear TEsting Programme (STEP).  相似文献   

10.
It is an objective fact that there exists error in the satellite dynamic model and it will be transferred to satellite orbit determination algorithm, forming a part of the connotative model error. Mixed with the systematic error and random error of the measurements, they form the unitive model error and badly restrict the precision of the orbit determination. We deduce in detail the equations of orbit improvement for a system with dynamic model error, construct the parametric model for the explicit part of the model and nonparametric model for the error that can not be explicitly described. We also construct the partially linear orbit determination model, estimate and fit the model error using a two-stage estimation and a kernel function estimation, and finally make the corresponding compensation in the orbit determination. Beginning from the data depth theory, a data depth weight kernel estimator for model error is proposed for the sake of promoting the steadiness of model error estimation. Simulation experiments of SBSS are performed. The results show clearly that the model error is one of the most important effects that will influence the precision of the orbit determination. The kernel function method can effectively estimate the model error, with the window width as a major restrict parameter. A data depth-weight-kernel estimation, however, can improve largely the robustness of the kernel function and therefore improve the precision of orbit determination.  相似文献   

11.
The traditional least square estimation (LSE) method for orbit determination will not be optimal if the error of observational data does not obey the Gaussian distribution. In order to solve this problem, the least p-norm (Lp) estimation method is presented in this paper to deal with the non-Gaussian distribution cases. We show that a suitable selection of parameter p may guarantee a reasonable orbit determination result. The character of Lp estimation is analyzed. It is shown that the traditional Lp estimation method is not a robust method. And a stable Lp estimating based on data depth weighting is put forward to deal with the model error and outlier. In the orbit determination process, the outlier of observational data and coarse model error can be quantitatively described by their weights. The farther is the data from the data center, the smaller is the value of data depth and the smaller is the weighted value accordingly. The result of the new Lp method is stabler than that of the traditional Lp estimation and the breakdown point could be up to 1/2. In addition, the orbit parameter is adaptively estimated by residual analysis and matrix estimation method, and the estimation efficiency is enhanced. Finally, by taking the Space-based Space Surveillance System as an example and performing simulation experiments, we show that if there are system error or abnormal value in the observational data or system error in satellite dynamical model and space-based observation platform, LSE will not be optimal even though the observational data obeys the Gaussian distribution, and the orbit determination precision by the self-adaptive robust Lp estimation method is much better than that by the traditional LSE method.  相似文献   

12.
The estimation of the frequency, amplitude and phase of a sinusoid from observations contaminated by correlated noise is considered. It is assumed that the observations are regularly spaced, but may suffer missing values or long time stretches with no data. The typical astronomical source of such data is high-speed photoelectric photometry of pulsating stars. The study of the observational noise properties of nearly 200 real data sets is reported: noise can almost always be characterized as a random walk with superposed white noise. A scheme for obtaining weighted non-linear least-squares estimates of the parameters of interest, as well as standard errors of these estimates, is described. Simulation results are presented for both complete and incomplete data. It is shown that, in finite data sets, results are sensitive to the initial phase of the sinusoid.  相似文献   

13.
We present a numerical algorithm designed to study the evolution of a distribution of solid particles orbiting around the Sun that could be applied to similar systems in which f c ≤ Ω/2π, where f c is the frequency of collisions, and Ω is the orbital angular speed. A number of sample particles are used to represent the whole system. Binary collisions are treated in a novel way using a Monte Carlo method that works as follows. Orbits are locally sampled to compute the velocity dispersion. Then the velocity vectors of the sample particles are modified according to random collisions with virtual particles which have velocities taken from a normal distribution computed using the previously found local velocity dispersion. The energy and momentum taken up by the virtual particles are redistributed among the neighbours of the sample particle undergoing the collision, so that conservation laws are satisfied. Simulations using this model give an estimation of the final distribution of inclinations and the associated evolutionary time-scale.  相似文献   

14.
With increasingly large data sets, weak lensing measurements are able to measure cosmological parameters with ever-greater precision. However, this increased accuracy also places greater demands on the statistical tools used to extract the available information. To date, the majority of lensing analyses use the two-point statistics of the cosmic shear field. These can be either studied directly using the two-point correlation function or in Fourier space, using the power spectrum. But analysing weak lensing data inevitably involves the masking out of regions, for example to remove bright stars from the field. Masking out the stars is common practice but the gaps in the data need proper handling. In this paper, we show how an inpainting technique allows us to properly fill in these gaps with only   N log  N   operations, leading to a new image from which we can compute straightforwardly and with a very good accuracy both the power spectrum and the bispectrum. We then propose a new method to compute the bispectrum with a polar fft algorithm, which has the main advantage of avoiding any interpolation in the Fourier domain. Finally, we propose a new method for dark matter mass map reconstruction from shear observations, which integrates this new inpainting concept. A range of examples based on 3D N -body simulations illustrates the results.  相似文献   

15.
In this work we study the performance of linear multifilters for the estimation of the amplitudes of the thermal and kinematic Sunyaev–Zel'dovich (SZ) effects. We show that when both effects are present, estimation of these effects with standard matched multifilters is intrinsically biased. This bias is due to the fact that both signals have basically the same spatial profile. We find a new family of multifilters related to the matched multifilters that cancel this systematic bias, hence we call them unbiased matched multifilters. We test the unbiased matched multifilters and compare them with the standard matched multifilters using simulations that reproduce the future Planck mission observations. We find that in the case of the standard matched multifilters the systematic bias in the estimation of the kinematic Sunyaev–Zel'dovich effect can be very large, even greater than the statistical error bars. Unbiased matched multifilters cancel this kind of bias effectively. In concordance with other works in the literature, our results indicate that the sensitivity and resolution of Planck will not be enough to give reliable estimations of the kinematic Sunyaev–Zel'dovich effects of individual clusters. However, as the estimation with the unbiased matched multifilters is not intrinsically biased, it can be possible to use them to study statistically any peculiar cosmological bulk flows via the kinematic SZ effect.  相似文献   

16.
We have suggested in a previous article that the coarse-grained evolution of a collisionless stellar system could be viewed as a diffusion process in velocity space compensated by an appropriate friction. Using a quasi-linear theory, we calculate the diffusion coefficient associated with this evolution. This provides a new self-consistent relaxation equation for f , the locally averaged distribution function. This equation bears some resemblance to the conventional Fokker–Planck equation of collisional systems but the friction term is non-linear in f (accounting for degeneracy effects) and the relaxation time is much smaller (in agreement with the concept of 'violent relaxation'). Under the condition that the diffusion current vanishes identically at equilibrium, we recover Lynden-Bell's distribution function; but if we allow stars to escape from the system at a constant rate, we can derive a truncated model which coincides with Lynden-Bell's solution in the core but provides a depletion of high-energy stars in the halo. This distribution function has a finite mass and is the generalization of the Michie–King model to the case of (possibly degenerate) collisionless stellar systems.  相似文献   

17.
Markov chain Monte Carlo (MCMC) techniques are now widely used for cosmological parameter estimation. Chains are generated to sample the posterior probability distribution obtained following the Bayesian approach. An important issue is how to optimize the efficiency of such sampling and how to diagnose whether a finite-length chain has adequately sampled the underlying posterior probability distribution. We show how the power spectrum of a single such finite chain may be used as a convergence diagnostic by means of a fitting function, and discuss strategies for optimizing the distribution for the proposed steps. The methods developed are applied to current cosmic microwave background and large-scale structure data interpreted using both a pure adiabatic cosmological model and a mixed adiabatic/isocurvature cosmological model including possible correlations between modes. For the latter application, because of the increased dimensionality and the presence of degeneracies, the need for tuning MCMC methods for maximum efficiency becomes particularly acute.  相似文献   

18.
We describe a made-to-measure (M2M) algorithm for constructing N -particle models of stellar systems from observational data (χ2M2M), extending earlier ideas by Syer & Tremaine. The algorithm properly accounts for observational errors, is flexible, and can be applied to various systems and geometries. We implement this algorithm in a parallel code nmagic and carry out a sequence of tests to illustrate its power and performance. (i) We reconstruct an isotropic Hernquist model from density moments and projected kinematics and recover the correct differential energy distribution and intrinsic kinematics. (ii) We build a self-consistent oblate three-integral maximum rotator model and compare how the distribution function is recovered from integral field and slit kinematic data. (iii) We create a non-rotating and a figure rotating triaxial stellar particle model, reproduce the projected kinematics of the figure rotating system by a non-rotating system of the same intrinsic shape, and illustrate the signature of pattern rotation in this model. From these tests, we comment on the dependence of the results from χ2M2M on the initial model, the geometry, and the amount of available data.  相似文献   

19.
A model of the gravitationally evolved dark matter distribution, in the Eulerian space, is developed. It is a simple extension of the excursion set model that is commonly used to estimate the mass function of collapsed dark matter haloes. In addition to describing the evolution of the Eulerian space distribution of the haloes, the model allows one to describe the evolution of the dark matter itself. It can also be used to describe density profiles, on scales larger than the virial radius of these haloes, and to quantify the way in which matter flows in and out of Eulerian cells. When the initial Lagrangian space distribution is white noise Gaussian, the model suggests that the Inverse Gaussian distribution should provide a reasonably good approximation to the evolved Eulerian density field, in agreement with numerical simulations. Application of this model to clustering from more general Gaussian initial conditions is discussed at the end.  相似文献   

20.
We test an analytic model for the two-point correlations of galaxy clusters in redshift space using the Hubble volume N -body simulations. The correlation function of clusters shows no enhancement along the line of sight, owing to the lack of any virialized structures in the cluster distribution. However, the distortion of the clustering pattern arising from coherent bulk motions is clearly visible. The distribution of cluster peculiar motions is well described by a Gaussian, except in the extreme high-velocity tails. The simulations produce a small but significant number of clusters with large peculiar motions. The form of the redshift-space power spectrum is strongly influenced by errors in measured cluster redshifts in extant surveys. When these errors are taken into account, the model reproduces the power spectrum recovered from the simulation to an accuracy of 15 per cent or better over a decade in wavenumber. We compare our analytic predictions with the power spectrum measured from the APM cluster redshift survey. The cluster power spectrum constrains the amplitude of density fluctuations, as measured by the linear rms variance in spheres of radius 8  h −1 Mpc, denoted by σ 8. When combined with the constraints on σ 8 and the density parameter Ω derived from the local abundance of clusters, we find a best-fitting cold dark matter model with     and     , for a power spectrum shape that matches that measured for galaxies. However, for the best-fitting value of Ω and given the value of Hubble's constant from recent measurements, the assumed shape of the power spectrum is incompatible with the most readily motivated predictions from the cold dark matter paradigm.  相似文献   

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