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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.
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
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
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
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
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