Nonparametric Bayesian optimal designs for Unit Exponential regression model with respect to prior processes(with the truncated normal as the base measure)

Anita Abdollahi  Nanvapisheh; Soleiman Khazaei; Habib  Jafari

doi:https://doi.org/10.59170/stattrans-2024-032

Nonparametric Bayesian optimal designs for Unit Exponential regression model with respect to prior processes(with the truncated normal as the base measure)

Anita Abdollahi Nanvapisheh Department of Statistics, Razi University, Kermanshah, Iran ORCID:https://orcid.org/0000-0003-3248-0347 , Soleiman Khazaei Department of Statistics, Razi University, Kermanshah, Iran ORCID:https://orcid.org/0000-0003-2537-9232 , Habib Jafari 3Department of Statistics, Razi University, Kermanshah, Iran ORCID:https://orcid.org/0000-0001-5191-2796 Statistics in Transition new series, vol. 25, 2024, 3, pages: 141-154 Published online: 4 September 2024 https://doi.org/10.59170/stattrans-2024-032 Citation: Nanvapisheh A. A., Khazaei S., Jafari H., 2024. Nonparametric Bayesian optimal designs for a Unit Exponential regression model with respect to prior processes (with the truncated normal as the base measure). Statistics in Transition new series, 25(3), pp. 141-154. https://doi.org/10.59170/stattrans-2024-032

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ABSTRACT

Nonlinear regression models are extensively applied across various scientific disciplines. It is vital to accurately fit the optimal nonlinear model while considering the biases of the Bayesian optimal design. We present a Bayesian optimal design by utilising the Dirichlet process as a prior. The Dirichlet process serves as a fundamental tool in the exploration of Nonparametric Bayesian inference, offering multiple representations that are well-suited for application. This research paper introduces a novel one-parameter model, referred to as the ’Unit-Exponential distribution’, specifically designed for the unit interval. Additionally, we employ a stick-breaking representation to approximate the D-optimality criterion considering the Dirichlet process as a functional tool. Through this approach, we aim to identify a Nonparametric Bayesian optimal design.

KEYWORDS

D-optimal design, Bayesian optimal design, Unit Exponential model (UE), Dirichlet process, stick-breaking prior, nonparametric Bayesian.

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