اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدMaximum-likelihood fits to histograms for improved parameter estimation
162
0
0.0
(
0
)
تأليف
Joseph W. Fowler
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Straightforward methods for adapting the familiar chi^2 statistic to histograms of discrete events and other Poisson distributed data generally yield biased estimates of the parameters of a model. The bias can be important even when the total number of events is large. For the case of estimating a microcalorimeters energy resolution at 6 keV from the observed shape of the Mn K-alpha fluorescence spectrum, a poor choice of chi^2 can lead to biases of at least 10% in the estimated resolution when up to thousands of photons are observed. The best remedy is a Poisson maximum-likelihood fit, through a simple modification of the standard Levenberg-Marquardt algorithm for chi^2 minimization. Where the modification is not possible, another approach allows iterative approximation of the maximum-likelihood fit.
قيم البحث
اقرأ أيضاً
We present a maximum-likelihood method for parameter estimation in terahertz time-domain spectroscopy. We derive the likelihood function for a parameterized frequency response function, given a pair of time-domain waveforms with known time-dependent
noise amplitudes. The method provides parameter estimates that are superior to other commonly-used methods, and provides a reliable measure of the goodness of fit. We also develop a simple noise model that is parameterized by three dominant sources, and derive the likelihood function for their amplitudes in terms of a set of repeated waveform measurements. We demonstrate the method with applications to material characterization.
LISA is the upcoming space-based Gravitational Wave telescope. LISA Pathfinder, to be launched in the coming years, will prove and verify the detection principle of the fundamental Doppler link of LISA on a flight hardware identical in design to that
of LISA. LISA Pathfinder will collect a picture of all noise disturbances possibly affecting LISA, achieving the unprecedented pureness of geodesic motion necessary for the detection of gravitational waves. The first steps of both missions will crucially depend on a very precise calibration of the key system parameters. Moreover, robust parameters estimation is of fundamental importance in the correct assessment of the residual force noise, an essential part of the data processing for LISA. In this paper we present a maximum likelihood parameter estimation technique in time domain being devised for this calibration and show its proficiency on simulated data and validation through Monte Carlo realizations of independent noise runs. We discuss its robustness to non-standard scenarios possibly arising during the real-life mission, as well as its independence to the initial guess and non-gaussianities. Furthermore, we apply the same technique to data produced in mission-like fashion during operational exercises with a realistic simulator provided by ESA.
In this paper, we consider a surrogate modeling approach using a data-driven nonparametric likelihood function constructed on a manifold on which the data lie (or to which they are close). The proposed method represents the likelihood function using
a spectral expansion formulation known as the kernel embedding of the conditional distribution. To respect the geometry of the data, we employ this spectral expansion using a set of data-driven basis functions obtained from the diffusion maps algorithm. The theoretical error estimate suggests that the error bound of the approximate data-driven likelihood function is independent of the variance of the basis functions, which allows us to determine the amount of training data for accurate likelihood function estimations. Supporting numerical results to demonstrate the robustness of the data-driven likelihood functions for parameter estimation are given on instructive examples involving stochastic and deterministic differential equations. When the dimension of the data manifold is strictly less than the dimension of the ambient space, we found that the proposed approach (which does not require the knowledge of the data manifold) is superior compared to likelihood functions constructed using standard parametric basis functions defined on the ambient coordinates. In an example where the data manifold is not smooth and unknown, the proposed method is more robust compared to an existing polynomial chaos surrogate model which assumes a parametric likelihood, the non-intrusive spectral projection.
This paper presents a statistical method to subtract background in maximum likelihood fit, without relying on any separate sideband or simulation for background modeling. The method, called sFit, is an extension to the sPlot technique originally deve
loped to reconstruct true distribution for each date component. The sWeights defined for the sPlot technique allow to construct a modified likelihood function using only the signal probability density function and events in the signal region. Contribution of background events in the signal region to the likelihood function cancels out on a statistical basis. Maximizing this likelihood function leads to unbiased estimates of the fit parameters in the signal probability density function.
Quantum state tomography aims to determine the quantum state of a system from measured data and is an essential tool for quantum information science. When dealing with continuous variable quantum states of light, tomography is often done by measuring
the field amplitudes at different optical phases using homodyne detection. The quadrature-phase homodyne measurement outputs a continuous variable, so to reduce the computational cost of tomography, researchers often discretize the measurements. We show that this can be done without significantly degrading the fidelity between the estimated state and the true state. This paper studies different strategies for determining the histogram bin widths. We show that computation time can be significantly reduced with little loss in the fidelity of the estimated state when the measurement operators corresponding to each histogram bin are integrated over the bin width.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
