Automatic Re-weighting of maximum likelihood functions for parameter regression

2000 ◽  
pp. 85-90
Author(s):  
Yu Xin ◽  
Victor R. Vasquez ◽  
Wallace B. Whiting
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Functions

scholarly journals On Local Linear Approximations to Diffusion Processes

2011 ◽  
Vol 2011 ◽  
pp. 1-26
Author(s):  
X. L. Duan ◽  
Z. M. Qian ◽  
W. A. Zheng
Keyword(s):  
Maximum Likelihood ◽  
Diffusion Processes ◽  
Gaussian Approximation ◽  
Diffusion Models ◽  
Likelihood Method ◽  
Unknown Parameters ◽  
Likelihood Functions ◽  
The Past ◽  
Local Linear ◽  
Exact Maximum Likelihood

Diffusion models have been used extensively in many applications. These models, such as those used in the financial engineering, usually contain unknown parameters which we wish to determine. One way is to use the maximum likelihood method with discrete samplings to devise statistics for unknown parameters. In general, the maximum likelihood functions for diffusion models are not available, hence it is difficult to derive the exact maximum likelihood estimator (MLE). There are many different approaches proposed by various authors over the past years, see, for example, the excellent books and Kutoyants (2004), Liptser and Shiryayev (1977), Kushner and Dupuis (2002), and Prakasa Rao (1999), and also the recent works by Aït-Sahalia (1999), (2004), (2002), and so forth. Shoji and Ozaki (1998; see also Shoji and Ozaki (1995) and Shoji and Ozaki (1997)) proposed a simple local linear approximation. In this paper, among other things, we show that Shoji's local linear Gaussian approximation indeed yields a good MLE.

scholarly journals Detection of translational noncrystallographic symmetry in Patterson functions

2021 ◽  
Vol 77 (2) ◽  
pp. 131-141
Author(s):  
Iracema Caballero ◽  
Massimo D. Sammito ◽  
Pavel V. Afonine ◽  
Isabel Usón ◽  
Randy J. Read ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Protein Structures ◽  
Data Bank ◽  
Molecular Replacement ◽  
Asymmetric Unit ◽  
Intensity Factors ◽  
Patterson Function ◽  
Likelihood Functions ◽  
Structure Solution ◽  
Ranked List

Detection of translational noncrystallographic symmetry (TNCS) can be critical for success in crystallographic phasing, particularly when molecular-replacement models are poor or anomalous phasing information is weak. If the correct TNCS is detected then expected intensity factors for each reflection can be refined, so that the maximum-likelihood functions underlying molecular replacement and single-wavelength anomalous dispersion use appropriate structure-factor normalization and variance terms. Here, an analysis of a curated database of protein structures from the Protein Data Bank to investigate how TNCS manifests in the Patterson function is described. These studies informed an algorithm for the detection of TNCS, which includes a method for detecting the number of vectors involved in any commensurate modulation (the TNCS order). The algorithm generates a ranked list of possible TNCS associations in the asymmetric unit for exploration during structure solution.

STOCHASTIC DISCRETE-TIME AGE-OF-INFECTION EPIDEMIC MODELS

2013 ◽  
Vol 06 (01) ◽  
pp. 1250066 ◽  
Author(s):  
GUY KATRIEL
Keyword(s):  
Maximum Likelihood ◽  
Deterministic Model ◽  
Demographic Stochasticity ◽  
Final Size ◽  
Incidence Data ◽  
Likelihood Functions ◽  
Age Of Infection ◽  
Large Populations ◽  
Rapid Generation ◽  
Fitting Parameters

We present an epidemic model which can incorporate essential biological detail as well as the intrinsic demographic stochasticity of the epidemic process, yet is very simple, enabling rapid generation of a large number of simulations. A deterministic version of the model is also derived, in the limit of infinitely large populations, and a final-size formula for the deterministic model is proved. A key advantage of the model proposed is that it is possible to write down an explicit likelihood functions for it, which enables a systematic procedure for fitting parameters to real incidence data, using maximum likelihood.

FIRST MEASUREMENTS OF THE ρ3 SPIN DENSITY MATRIX ELEMENTS IN γp → pω USING CLAS AT JLAB

2014 ◽  
Vol 26 ◽  
pp. 1460063 ◽  
Author(s):  
◽  
BRIAN VERNARSKY
Keyword(s):  
Maximum Likelihood ◽  
Density Matrix ◽  
Spin Density ◽  
Photon Beam ◽  
Spin Density Matrix ◽  
Matrix Elements ◽  
Circularly Polarized ◽  
Likelihood Functions ◽  
Large Acceptance ◽  
Unpolarized Target

In an effort towards a "complete" experiment for the ω meson, we present studies from an experiment with an unpolarized target and a circularly polarized photon beam (g1c), carried out using the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab. The experiment was analyzed using an extended maximum likelihood fit with partial wave amplitudes. New likelihood functions were calculated to account for the polarization of the photon beam. Both circular and linear polarizations are explored. The results of these fits are then used to project out the spin density matrix for the ω. First measurements of the ρ3 spin density matrix elements will be presented using this method.

scholarly journals Maximum Likelihood for Matrices with Rank Constraints

2014 ◽  
Vol 5 (1) ◽  
Author(s):  
Jonathan Hauenstein
Keyword(s):  
Algebraic Geometry ◽  
Maximum Likelihood ◽  
Optimization Problem ◽  
Likelihood Estimation ◽  
Numerical Algebraic Geometry ◽  
Likelihood Functions ◽  
Determinantal Varieties ◽  
Discrete Random Variables ◽  
Rank Constraints ◽  
Bounded Rank

Maximum likelihood estimation is a fundamental optimization problem in statistics. Westudy this problem on manifolds of matrices with bounded rank. These represent mixtures of distributionsof two independent discrete random variables. We determine the maximum likelihood degree for a rangeof determinantal varieties, and we apply numerical algebraic geometry to compute all critical points oftheir likelihood functions. This led to the discovery of maximum likelihood duality between matrices ofcomplementary ranks, a result proved subsequently by Draisma and Rodriguez.

Exact Maximum Likelihood Estimate of a Finite Population Size

1987 ◽  
Vol 1 (2) ◽  
pp. 225-236 ◽  
Author(s):  
Jose Galvão Leite ◽  
Jorge Oishi ◽  
Carlos Alberto de Bragança Pereira
Keyword(s):  
Maximum Likelihood ◽  
Population Size ◽  
Finite Population ◽  
Sequential Sampling ◽  
Likelihood Functions ◽  
Exact Analytical Expression ◽  
Sampling Process ◽  
Capture Recapture ◽  
Using Data ◽  
Exact Maximum Likelihood

Using data obtained by the general capture/recapture sequential sampling process, an exact analytical expression for the maximum likelihood (ML) estimate of the population size, N, is introduced. As a consequence, it is shown that bounded likelihood functions have at most two maxima. For the simple one-by-one case the ML estimate is unique.

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