In Bayesian inference, likelihood function may be unable to obtain posterior distribution in some cases. In this cases, is there any alternative approach (apart from MCMC-alternative methods) as alternative to likelihood function for bayesian inferences ?
I think you can use the dependent simulations of Gibbs sampler in complicated case such as hierarchical Bayesian models
You can dear brother, Çağatay Çetinkaya use the Approximative bayesian methods like: Integrated Nested Laplace Approximation developped bay Rue, H. and Martino, S. and Chopin, N. (2009). a package named "INLA" is available in R cran , or simply you will find a lot about it in http://www.r-inla.org
I recommend the handbook of Approximate Bayesian Computation. A great source for theory and application. Some of the chapters are available on ResearchGate.
https://www.crcpress.com/Handbook-of-Approximate-Bayesian-Computation/Sisson-Fan-Beaumont/p/book/9781439881507
Dear Nuha abdulrazzaq Yahya , Chellai Fatih and Kevin McNally ,thanks for all your valuable contributions. I already solved my problem using Gibbs sampler and modifying the distribution with talent variables. However, INLA seems a good alternative to improve my work. It seems considerable. Proposition
of dear Kevin McNally seems a good source. Thanks all of you, again. Best wishes.
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