A variational method for parameter estimation in a logistic spatial regression

Hardouin, Cécile

doi:10.1016/j.spasta.2019.100365

Cited by 4 publications

(6 citation statements)

References 19 publications

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“…To do the comparison, the measurements to be used are the estimates value and MSE. These measures are also used in a similar comparison study for variational method by Hardouin [17]. The two measures are the easiest indication of how good the estimates are [2].…”

Section: Resultsmentioning

confidence: 99%

“…The two measures are the easiest indication of how good the estimates are [2]. In addition, the average of squared differences between the true parameters value and the estimates is used following [17] and [19] in order to analyze the consistency of the estimate's quality. Lastly, to study the closeness of the parameter estimates, graphical representations of the value estimates for the two methods are also used.…”

Section: Resultsmentioning

confidence: 99%

“…The variational estimation method is an iterative parameter estimation method that is widely used in machine learning to estimate unknown values based on the distribution function through an optimization process [15]. Some examples of the application of this method are the estimation of the logistic regression coefficient [16], the estimation of the spatial logistic regression coefficient [17], and the estimation of the probability equation parameter equation [18]. While the application has been used by many, a basic and easy-touse algorithm of variational method for linear regression has not been explored deeply.…”

Section: Introductionmentioning

confidence: 99%

“…Obviously, since variational method does not have closed form for its estimate, this study used the average values of the estimates instead of expected value. The idea behind this performance comparison is derived from the performance comparison study for different model by Hardouin [17].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Performance comparison between maximum likelihood estimation and variational method for estimating simple linear regression parameter

Widyaningsih,

Rizka,

Siswantining

2024

ITM Web Conf.

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Variational estimation method is a deterministic approximation technique which involves Bayesian framework while giving a point estimate instead of the usual Bayesian interval estimation. The linear regression model, which has always been a popular model, can benefit from the implementation of variational estimation method. In this paper, the theoretical basis on why variational method can reduce overfitting in linear regression is reviewed. Based on the review, in theory, variational method is more robust to overfitting than MLE. This paper also performed a simulation study. The simulation is done in a manner such that the simulation represents the situation of predicting for new or hidden data. The simulation starts from generating random explanatory data and generates the appropriate response data based on linear regression equation. Then, the randomly generated data is used to estimate the linear regression parameters. The simulation is performed to compare the parameters estimation results from variational method with the method of MLE. The comparison is done using the estimation values and the squared differences between true parameters value and the estimates. Empirical findings show that both methods have relatively close estimate values. It can be seen as the simulation study concludes that both variational and ML yield rather close parameters estimates for simple linear regression case. The estimates closeness gets more obvious as the sample size grows. The study also found that Variational method has performs better in terms of parameters estimation in linear regression when the sample size is small or the data has large variance.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Performance comparison between maximum likelihood estimation and variational method for estimating simple linear regression parameter

Widyaningsih,

Rizka,

Siswantining

2024

ITM Web Conf.

View full text Add to dashboard Cite

show abstract

“…Pfarrhofer and Piribauer (2019) proposed two shrinkage priors to make Bayesian variable selection for high-dimensional spatial autoregressive models. Hardouin (2019) proposed a variational bayesian method to estimate the logistic spatial regression. Wang and Tang (2020) considered Bayesian inference on a quantile regression model in the presence of nonignorable missing covariates.…”

Section: Introductionmentioning

confidence: 99%

Bayesian estimation for partially linear varying coefficient spatial autoregressive models

Tian

Xu²,

et al. 2022

Statistics and Its Interface

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We propose a fully Bayesian estimation approach for partially linear varying coefficient spatial autoregressive models on the basis of B-spline approximations of nonparametric components. A computational efficient MCMC method that combines the Gibbs sampler with Metropolis-Hastings algorithm is implemented to simultaneously obtain the Bayesian estimates of unknown parameters, as well as their standard error estimates. Monte Carlo simulations are used to investigate the finite sample performance of the proposed method. Finally, a real data analysis of Boston housing data is used to illustrate the usefulness of the proposed methodology.

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Propensity score estimation using variational method on spatial logistic regression

Rizka¹,

Widyaningsih²

2021

AIP Conference Proceedings

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A variational method for parameter estimation in a logistic spatial regression

Cited by 4 publications

References 19 publications

Performance comparison between maximum likelihood estimation and variational method for estimating simple linear regression parameter

Performance comparison between maximum likelihood estimation and variational method for estimating simple linear regression parameter

Bayesian estimation for partially linear varying coefficient spatial autoregressive models

Propensity score estimation using variational method on spatial logistic regression

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