Conditional density estimation using population Monte Carlo based approximate Bayesian computation

Faiza Afzaal

Article Details

Conditional density estimation using population Monte Carlo based approximate Bayesian computation

Authors:

Faiza Afzaal

Publisher:

Hacettepe University

Main Topics:

Statistics

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.52 Issue 4, pp.1120-1134

Document Type:

Article

Publication Date:

8/2023

Document Language:

English

Document ID (Org No.):

2001293856

pISSN:

2651-477X

Keywords:

Abstract:

 Most statistical methods require likelihood evaluation to draw a statistical inference. However, in some situations, likelihood evaluation becomes difficult analytically or computationally. Different likelihood-free methods are available that eliminate the need to compute the likelihood function. Approximate Bayesian Computation ABC is a framework that implements likelihood-free inference and replaces the likelihood evaluation with simulations by using forward modeling. The goal of ABC methods is to approximate the posterior distribution. However, posterior approximation via ABC methods is still considerably expensive for high dimensions. ABC requires many simulations that become computationally infeasible for complex models. Here, a technique is proposed that combines a somewhat more efficient form of ABC Population Monte Carlo, PMC with a Conditional Density Estimation CDE approach. The proposed framework provides an estimation of the posterior distribution which is referred to as PMC-CDE. A simulation study is performed that provides empirical evidence to show the efficiency of PMC-CDE in terms of integrated squared error loss. Furthermore, real-life datasets manifest the application of the proposed method.

 Most statistical methods require likelihood evaluation to draw a statistical inference. However, in some situations, likelihood evaluation becomes difficult analytically or computationally. Different likelihood-free methods are available that eliminate the need to compute the likelihood function. Approximate Bayesian Computation ABC is a framework that implements likelihood-free inference and replaces the likelihood evaluation with simulations by using forward modeling. The goal of ABC methods is to approximate the posterior distribution. However, posterior approximation via ABC methods is still considerably expensive for high dimensions. ABC requires many simulations that become computationally infeasible for complex models. Here, a technique is proposed that combines a somewhat more efficient form of ABC Population Monte Carlo, PMC with a Conditional Density Estimation CDE approach. The proposed framework provides an estimation of the posterior distribution which is referred to as PMC-CDE. A simulation study is performed that provides empirical evidence to show the efficiency of PMC-CDE in terms of integrated squared error loss. Furthermore, real-life datasets manifest the application of the proposed method.

 Most statistical methods require likelihood evaluation to draw a statistical inference. However, in some situations, likelihood evaluation becomes difficult analytically or computationally. Different likelihood-free methods are available that eliminate the need to compute the likelihood function. Approximate Bayesian Computation ABC is a framework that implements likelihood-free inference and replaces the likelihood evaluation with simulations by using forward modeling. The goal of ABC methods is to approximate the posterior distribution. However, posterior approximation via ABC methods is still considerably expensive for high dimensions. ABC requires many simulations that become computationally infeasible for complex models. Here, a technique is proposed that combines a somewhat more efficient form of ABC Population Monte Carlo, PMC with a Conditional Density Estimation CDE approach. The proposed framework provides an estimation of the posterior distribution which is referred to as PMC-CDE. A simulation study is performed that provides empirical evidence to show the efficiency of PMC-CDE in terms of integrated squared error loss. Furthermore, real-life datasets manifest the application of the proposed method.

 Most statistical methods require likelihood evaluation to draw a statistical inference. However, in some situations, likelihood evaluation becomes difficult analytically or computationally. Different likelihood-free methods are available that eliminate the need to compute the likelihood function. Approximate Bayesian Computation ABC is a framework that implements likelihood-free inference and replaces the likelihood evaluation with simulations by using forward modeling. The goal of ABC methods is to approximate the posterior distribution. However, posterior approximation via ABC methods is still considerably expensive for high dimensions. ABC requires many simulations that become computationally infeasible for complex models. Here, a technique is proposed that combines a somewhat more efficient form of ABC Population Monte Carlo, PMC with a Conditional Density Estimation CDE approach. The proposed framework provides an estimation of the posterior distribution which is referred to as PMC-CDE. A simulation study is performed that provides empirical evidence to show the efficiency of PMC-CDE in terms of integrated squared error loss. Furthermore, real-life datasets manifest the application of the proposed method.

Article Details

Conditional density estimation using population Monte Carlo based approximate Bayesian computation

Authors:

Faiza Afzaal

Publisher:

Hacettepe University

Main Topics:

Statistics

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.52 Issue 4, pp.1120-1134

Document Type:

Article

Publication Date:

8/2023

Document Language:

English

Document ID (Org No.):

2001293856

pISSN:

2651-477X

Approximate Bayesian computation

sequential Monte Carlo

population Monte Carlo

conditional density estimation

Issues

Article Details

Conditional density estimation using population Monte Carlo based approximate Bayesian computation

Authors: Faiza Afzaal

Publisher: Hacettepe University

Main Topics: Statistics

Journal: Hacettepe Journal of Mathematics and Statistics Vol.52 Issue 4, pp.1120-1134

Document Type: Article

Publication Date: 8/2023

Document Language: English

Document ID (Org No.): 2001293856

pISSN: 2651-477X

Approximate Bayesian computation

sequential Monte Carlo

population Monte Carlo

conditional density estimation

Issues

Authors:

Faiza Afzaal

Publisher:

Hacettepe University

Main Topics:

Statistics

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.52 Issue 4, pp.1120-1134

Document Type:

Article

Publication Date:

8/2023

Document Language:

English

Document ID (Org No.):

2001293856

pISSN:

2651-477X