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Maximum Likelihood Estimation [chapter]

2009 Statistics: A Series of Textbooks and Monographs
Chapter 1 General Linear Models I Maximum Likelihood Estimation We can learn the mean and variance of a Gaussian distribution using the Maximum Likelihood (ML) framework as follows.  ...  Estimation in a Bayesian GLM is therefore equivalent to Maximum Likelihood estimation (ie. for IID covariances this is the same as Weighted Least Squares) with augmented data.  ...  A two-layer MLP is given by with D is the dimension of the input x, H is the number of 'hidden units' in the 'first layer', and z h is the output of the hth unit.  ...

Maximum Likelihood Estimation [chapter]

1991 Order Statistics and Inference
Chapter 1 General Linear Models I Maximum Likelihood Estimation We can learn the mean and variance of a Gaussian distribution using the Maximum Likelihood (ML) framework as follows.  ...  Estimation in a Bayesian GLM is therefore equivalent to Maximum Likelihood estimation (ie. for IID covariances this is the same as Weighted Least Squares) with augmented data.  ...  A two-layer MLP is given by with D is the dimension of the input x, H is the number of 'hidden units' in the 'first layer', and z h is the output of the hth unit.  ...

Maximum Likelihood Estimation [chapter]

2003 Handbook of Statistical Analyses Using Stata, Fourth Edition
Chapter 1 General Linear Models I Maximum Likelihood Estimation We can learn the mean and variance of a Gaussian distribution using the Maximum Likelihood (ML) framework as follows.  ...  Estimation in a Bayesian GLM is therefore equivalent to Maximum Likelihood estimation (ie. for IID covariances this is the same as Weighted Least Squares) with augmented data.  ...  A two-layer MLP is given by with D is the dimension of the input x, H is the number of 'hidden units' in the 'first layer', and z h is the output of the hth unit.  ...

Maximum Likelihood Estimation [chapter]

2008 Studying Human Populations
Chapter 1 General Linear Models I Maximum Likelihood Estimation We can learn the mean and variance of a Gaussian distribution using the Maximum Likelihood (ML) framework as follows.  ...  Estimation in a Bayesian GLM is therefore equivalent to Maximum Likelihood estimation (ie. for IID covariances this is the same as Weighted Least Squares) with augmented data.  ...  A two-layer MLP is given by with D is the dimension of the input x, H is the number of 'hidden units' in the 'first layer', and z h is the output of the hth unit.  ...

Maximum Likelihood Estimation [chapter]

2012 Essential Mathematics for Market Risk Management
Chapter 1 General Linear Models I Maximum Likelihood Estimation We can learn the mean and variance of a Gaussian distribution using the Maximum Likelihood (ML) framework as follows.  ...  Estimation in a Bayesian GLM is therefore equivalent to Maximum Likelihood estimation (ie. for IID covariances this is the same as Weighted Least Squares) with augmented data.  ...  A two-layer MLP is given by with D is the dimension of the input x, H is the number of 'hidden units' in the 'first layer', and z h is the output of the hth unit.  ...

Maximum Likelihood Estimation [chapter]

2013 Methods of Statistical Model Estimation
Chapter 1 General Linear Models I Maximum Likelihood Estimation We can learn the mean and variance of a Gaussian distribution using the Maximum Likelihood (ML) framework as follows.  ...  Estimation in a Bayesian GLM is therefore equivalent to Maximum Likelihood estimation (ie. for IID covariances this is the same as Weighted Least Squares) with augmented data.  ...  A two-layer MLP is given by with D is the dimension of the input x, H is the number of 'hidden units' in the 'first layer', and z h is the output of the hth unit.  ...

Maximum Likelihood Estimation [chapter]

2000 Statistical Methods for Categorical Data Analysis
Chapter 1 General Linear Models I Maximum Likelihood Estimation We can learn the mean and variance of a Gaussian distribution using the Maximum Likelihood (ML) framework as follows.  ...  Estimation in a Bayesian GLM is therefore equivalent to Maximum Likelihood estimation (ie. for IID covariances this is the same as Weighted Least Squares) with augmented data.  ...  A two-layer MLP is given by with D is the dimension of the input x, H is the number of 'hidden units' in the 'first layer', and z h is the output of the hth unit.  ...

Maximum Likelihood Estimation [chapter]

2000 Handbook of Statistical Analyses Using Stata, Fourth Edition
Chapter 1 General Linear Models I Maximum Likelihood Estimation We can learn the mean and variance of a Gaussian distribution using the Maximum Likelihood (ML) framework as follows.  ...  Estimation in a Bayesian GLM is therefore equivalent to Maximum Likelihood estimation (ie. for IID covariances this is the same as Weighted Least Squares) with augmented data.  ...  A two-layer MLP is given by with D is the dimension of the input x, H is the number of 'hidden units' in the 'first layer', and z h is the output of the hth unit.  ...

Bhattacharyya and Expected Likelihood Kernels [chapter]

Tony Jebara, Risi Kondor
2003 Lecture Notes in Computer Science
It satisfies Mercer's condition and can be computed in closed form for a large class of models, including exponential family models, mixtures, hidden Markov models and Bayesian networks.  ...  The kernel is then computed by integrating the product of the two generative models corresponding to two data points.  ...  Acknowledgments Thanks to A. Jagota and R. Lyngsoe for profile HMM comparison code, C. Leslie and R. Kuang for SCOP data and the referees for important corrections.  ...

Lossless, Scalable Implicit Likelihood Inference for Cosmological Fields [article]

T. Lucas Makinen, Tom Charnock, Justin Alsing, Benjamin D. Wandelt
2021 arXiv   pre-print
We present a comparison of simulation-based inference to full, field-based analytical inference in cosmological data analysis.  ...  the lognormal cases, b) simulation-based inference using these maximally informative nonlinear summaries recovers nearly losslessly the exact posteriors of field-level inference, bypassing the need to  ...  We present a comparison of simulation-based inference to full, field-based analytical inference in cosmological data analysis.  ...

Spectral likelihood expansions for Bayesian inference

Joseph B. Nagel, Bruno Sudret
2016 Journal of Computational Physics
Both the model evidence and the posterior moments are related to the expansion coefficients.  ...  A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density.  ...  In addition to the SLE approximations, the prior density π(µ) = N (µ|µ 0 , σ 2 0 ) and the exact solution π(µ|y) = N (µ|µ N , σ 2 N ) from a conjugate analysis based on Eq. (57) are shown.  ...

Maximum Likelihood Estimation of Latent Affine Processes

David S. Bates
2006 The Review of financial studies
This article develops a direct filtration-based maximum likelihood methodology for estimating the parameters and realizations of latent affine processes.  ...  An application to daily stock returns over 1953-96 reveals substantial divergences from EMM-based estimates; in particular, more substantial and time-varying jump risk.  ...  The G t * t (ψ) overall estimation procedure is consequently termed approximate maximum likelihood (AML), with potentially some loss of estimation efficiency relative to an exact maximum likelihood procedure  ...

Maximum-likelihood determination of anomalous substructures

Randy J. Read, Airlie J. McCoy
2018 Acta Crystallographica Section D: Structural Biology
This method is based on the maximum-likelihood SAD phasing function, which accounts for measurement errors and for correlations between the observed and calculated Bijvoet mates.  ...  A fast Fourier transform (FFT) method is described for determining the substructure of anomalously scattering atoms in macromolecular crystals that allows successful structure determination by X-ray single-wavelength  ...  Terwilliger (1994) showed that a Bayesian analysis of the MAD data, applying prior probabilities to the F A estimates based on the expected scattering, improved estimates of the F A in the presence of  ...

Bayesian Inference for Discretely Sampled Markov Processes with Closed-Form Likelihood Expansions

O. Stramer, M. Bognar, P. Schneider
2010 Journal of Financial Econometrics
Our approach is based on the closed-form (CF) likelihood approximations of Aït-Sahalia (CF likelihood approximation does not integrate to one; it is very close to one when near the MLE, but can markedly  ...  The efficacy of our approach is demonstrated in a simulation study of the Cox-Ingersoll-Ross (CIR) and Heston models, and is applied to two well known real-world datasets.  ...  We perform three Bayesian analyses using the exact likelihood, the Euler likelihood, and the normalized closed-form (CF) likelihood.  ...

Using a likelihood perspective to sharpen econometric discourse: Three examples

Christopher A. Sims
2000 Journal of Econometrics
Two of the applied areas are related and have in common that they involve nonstationarity: macroeconomic time series modeling, and analysis of panel data in the presence of potential nonstationarity.  ...  The conclusion is that in these areas a likelihood perspective leads to more useful, honest and objective reporting of results and characterization of uncertainty.  ...  Therefore maximum likelihood estimation based on the distribution of the differenced data is consistent under these assumptions.  ...
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