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I am using GA and MCMC for estimating the parameters of a transfer function. GA returns results that each parameter has one value when minimizing the error function, and MCMC returns the whole chain results for each parameter after the burnin, which gives a statistical distribution of the possible values for that parameter.

My first question is: What is the benefit of using MCMC over GA? Which one is better than other in what aspects?

My second question is: Do I get the mean value of each parameter from the distribution of the chain in order to get the fit for the transfer function? If so, do I do that with mean taking the mean value of the distribution? what if the distribution is skewed?

Thank you in advance

sorry I am new here, I didn't know how to tag this question.

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Question 1: What is the benefit of using MCMC over GA? Which one is better than other in what aspects?

As you state, if you are using the Markov Chain Monte Carlo (MCMC) properly, it will give you the complete probability distribution of your estimated parameters. This gives you knowledge about the quality of your estimation, but this is a computationally expensive method.

The Genetic Algorithms (GA) will converge to a minimum of your cost function, which can be local minimum. Furthermore, there is no knowledge about the quality of the estimation, rather than the cost-function value.

Question 2: Do I get the mean value of each parameter from the distribution of the chain in order to get the fit for the transfer function? If so, do I do that with mean taking the mean value of the distribution? what if the distribution is skewed?

If taking the mean-value of the distribution is a good approximation of your parameter depends on the type of distribution. I would state the in general the bin with the highest probability is the best approximation of your parameter. However, if you applied MCMC to estimate your parameters, you can use this technique again to estimate the system response.

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  • $\begingroup$ Thank you very much. This actually confirms what I thought. I just needed another view to be sure. $\endgroup$ – bsn_eng Mar 25 at 14:30
  • $\begingroup$ I'm glad I could help! $\endgroup$ – useless-machine Mar 25 at 16:15

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