An empirical Bayes approach for learning directed acyclic graph using MCMC algorithm

Tabar, Vahid Rezaei; Zareifard, Hamid; Salimi, Selva; Plewczynski, Dariusz

doi:10.1002/sam.11430

Cited by 3 publications

(3 citation statements)

References 25 publications

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“…Further the hazard function is extended as

h false(t_{i} false) = ϕ_{i} (t_{i} false| b_{i p}, Y_{i p}, β_{p}) h_{0 p} (t_{i}) \exp (β_{p} Y_{i p} + b_{i p})

where

b_{i p} \sim N false(0, \sum false) .

We have supposed that all unknown parameters in CR model are independent and follow a Poisson distribution. This analysis has been performed through OpenBUGS software [20–22].…”

Section: Methodsmentioning

confidence: 99%

Bayesian competing risk analysis: An application to nasopharyngeal carcinoma patients data

et al. 2021

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Background The Cox proportional hazard (CPH) model is normally used to study the death event data. The presence of competing risk (CR) is often encountered in health data, hence it becomes difficult to manage time to event data in clinical study. Bayesian approach is considered to manage the CR events in clinical data. Objectives The objective of study is to find the predictors associated with overall survival of nasopharyngeal carcinoma (NPC) patients. Further, our purpose is to use a Bayesian model that can analyze time to event data in the presence of CR. Methods Total 245 patients with NPC were taken (https://www.ncbi.nlm.nih.gov/geo/). The sociodemographic and clinical variables were considered for analysis purposes. R software and openBUGS were used to overcome the computational problems of CPH and Bayesian models. The Markov chain Monte Carlo (MCMC) method was used to compute the regression coefficients of Bayesian model. Results The study shows that among NPC patients, the covariates chemotherapy, smoking, N‐stage, and tumor site are associated with the higher risk for the deaths occurring in the cancer patients. The posterior mean estimates of proposed Bayesian model for significant factors have been obtained. The posterior mean and standard deviation estimates help to improve the survival of patients in the presence of CR. Conclusions It is very difficult to use the CR model with Bayesian approach in health research for nonstatistical researcher due to lack of information. This paper is dedicated to the application of Bayesian approach for CR analysis on NPC data.

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“…Further the hazard function is extended as

h false(t_{i} false) = ϕ_{i} (t_{i} false| b_{i p}, Y_{i p}, β_{p}) h_{0 p} (t_{i}) \exp (β_{p} Y_{i p} + b_{i p})

where

b_{i p} \sim N false(0, \sum false) .

We have supposed that all unknown parameters in CR model are independent and follow a Poisson distribution. This analysis has been performed through OpenBUGS software [20–22].…”

Section: Methodsmentioning

confidence: 99%

Bayesian competing risk analysis: An application to nasopharyngeal carcinoma patients data

et al. 2021

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“…Firstly, as can be seen in Figures (3), and (4), we should determine one variable in accordance with the start of a learning algorithm. In previous pieces of literature not only there only assumed variables following the normal assumptions but also they start with an initial number 1 meaning that their algorithms start with the first random variable such as [20,14].…”

Section: Learning Dagsmentioning

confidence: 99%

“…The problem has remained as a gap in literature until providing some investigation in [1,3]. Another applicable strategy for learning DAG, called Markov Chain Monte Carlo (MCMC) procedures has been deeply discussed in [14,12,8,11,7,5]. For all the above methods, the ordering variables does not consider and it is clear that this issue can be regarded in many real world application disciplines like genetics, finance and so on.…”

Section: Introductionmentioning

confidence: 99%

Copula based learning for directed acyclic graphs

Mohsin,

Rezaei Tabar

2023

Stat., optim. inf. comput.

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We provide the learning of a DAG model arising from high dimensional random variables following both normal and non-normal assumptions. To this end, the copula function utilized connecting dependent variables. Moreover to normal copula, the three most applicable copulas have been investigated modeling all three dependence structures negative, positive, and weak kinds. The copula functions, FGM, Clayton, and Gumbel are considered coving these situations and their detailed calculations are also presented. In addition, the structure function has been exactly determined due to choosing a good copula model based on statistical software R with respect to any assumed direction among all nodes. The direction with the maximum structure function has been preferred. The corresponding algorithms finding these directions and the maximization procedures are also provided. Finally, some extensive tabulations and simulation studies are provided, and in the following to have a clear thought of provided strategies, a real world application has been analyzed.

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A Gibbs sampler for learning DAG: a unification for discrete and Gaussian domains

Zareifard

Tabar

Plewczyński

2021

Journal of Statistical Computation and Simulation

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An empirical Bayes approach for learning directed acyclic graph using MCMC algorithm

Cited by 3 publications

References 25 publications

Bayesian competing risk analysis: An application to nasopharyngeal carcinoma patients data

Bayesian competing risk analysis: An application to nasopharyngeal carcinoma patients data

Copula based learning for directed acyclic graphs

A Gibbs sampler for learning DAG: a unification for discrete and Gaussian domains

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