Application of the Nelder–Mead Method to Optimize the Way for Selection of the Likhachev–Volkov Model Constants

Ivanov, Aleksei; Belyaev, Fedor S.; Volkov, A. E.; Belyaev, Sergey; Resnina, Natalia

doi:10.1134/s1063454122040112

Cited by 1 publication

(2 citation statements)

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“…Finally, we search

\alpha

and

\left({t}_1,\dots, {t}_K\right)

that minimize

\mathrm{KL}\left(\alpha, {t}_1,\dots, {t}_K\right)

using the Nelder–Mead method, which is the algorithm for the optimization problem proposed by Nelder and Mead [21]. This method is still used today when the gradient function cannot be computed [12, 28]. In a series of programs, the user only needs to provide the prior samples

\left({\boldsymbol{\theta}}_1,\dots, {\boldsymbol{\theta}}_N\right)

and their values

q\left({\boldsymbol{\theta}}_i\right)

.…”

Section: Ess For Priors With the Exponential Family Sampling Models W...mentioning

confidence: 99%

“…Finally, we search 𝛼 and (t 1 , … , t K ) that minimize KL(𝛼, t 1 , … , t K ) using the Nelder-Mead method, which is the algorithm for the optimization problem proposed by Nelder and Mead [21]. This method is still used today when the gradient function cannot be computed [12,28]. In a series of programs, the user only needs to provide the prior samples (𝜽 1 , … , 𝜽 N ) and their values q(𝜽 i ).…”

mentioning

confidence: 99%

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Prior effective sample size for exponential family distributions with multiple parameters

Tamanoi

2024

Statistical Analysis

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The setting of priors is an important issue in Bayesian analysis. In particular, when external information is applied, a prior with too much information can dominate the posterior inferences. To prevent this effect, the effective sample size (ESS) can be used. Various ESSs have been proposed recently; however, all have the problem of limiting the applicable prior distributions. For example, one ESS can only be used with a prior that can be approximated by a normal distribution, and another ESS cannot be applied when the parameters are multidimensional. We propose an ESS to be applied to more prior distributions when the sampling model belongs to an exponential family (including the normal model and logistic regression models). This ESS has the predictive consistency and can be used with multidimensional parameters. It is confirmed from normally distributed data with the Student's‐t priors that this ESS behaves as well as an existing predictively consistent ESS for one‐parameter exponential families. As examples of multivariate parameters, ESSs for linear and logistic regression models are also discussed.

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“…Finally, we search