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## Filters

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Maximum Likelihood Estimation
[chapter]

2009
*
Statistics: A Series of Textbooks and Monographs
*

Chapter 1 General Linear Models I

doi:10.1201/9781420064254.ch3
fatcat:bfsusm6pdjgjpendfxw4c7ab6y
*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

doi:10.1016/b978-0-12-076948-3.50013-4
fatcat:2w7lohk4tbba5j57jyj4lkb2ta
*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

doi:10.1201/noe1584884040.ch13
fatcat:odwdw3pq5jb5daey5kipyf275u
*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
*

*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
*

*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
*

*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
*

*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
*

*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]

2003
*
Lecture Notes in Computer Science
*

It satisfies Mercer's condition

doi:10.1007/978-3-540-45167-9_6
fatcat:uxa7odqhlfbrtnrnfyoiw4lkn4
*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]

2021
*
arXiv
*
pre-print

We present a comparison

arXiv:2107.07405v2
fatcat:ttd4ktkj35doxestt4q6jvlsfi
*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

2016
*
Journal of Computational Physics
*

Both the model evidence

doi:10.1016/j.jcp.2015.12.047
fatcat:zylmuewh3jaq5khx5uq66qvgmu
*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

2006
*
The Review of financial studies
*

This article develops a direct filtration-

doi:10.1093/rfs/hhj022
fatcat:vfiiisrqkfbpbpc6n27ok6ms3i
*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

2018
*
Acta Crystallographica Section D: Structural Biology
*

This method is

doi:10.1107/s2059798317013468
pmid:29533235
pmcid:PMC5947773
fatcat:rgjwg7mfvvgrxpf6twi5tq52ki
*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

2010
*
Journal of Financial Econometrics
*

Our approach is

doi:10.1093/jjfinec/nbp027
fatcat:jss22acczvhjfaemyxk6yld6zy
*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

2000
*
Journal of Econometrics
*

Two

doi:10.1016/s0304-4076(99)00046-9
fatcat:42rjcv6i3vgutarknpus6ethrq
*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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