Re: Markov Chain Monte Carlo and Genetic Algorithms

wojciech@xxxxxxxxx wrote:
Hi everyone,

I'm fairly new to statistics, so I apologize for this question,
either
due to my lack of knowledge and potentially posting in the wrong
place
(this is the closest forum I could find, though!).

I'm currently exploring how to model random graphs based on the
number
of degrees of various nodes. I've come across a model that uses
Markov
Chain Monte Carlo methods to accomplish the task. However, I am also
aware that genetic algorithms could be used to hone in on the proper
parameters for the model. While doing further research (I don't know
much about Markov Chains *or* Monte Carlo methods), I realized that
genetic algorithms could be used to hone in on parameters for many
models using Monte Carlo methods.

So my questions: how do I know which I should choose? Is there any
way
to check, either intuitively or quantitatively, which option should
perform better? Can anyone recommend any reading materials on monte
carlo methods, especially within graph theory?


You need to start from the understanding that the two things are
aiming to do rather different things. By a "Genetic algorithm" I am
assuming you mean one of those search approachs which aim to find the
optimum of a given objective function and which happen to contain
randomised steps in order to work reasonably when the objective
function is discontinuous or multimodal. Still the aim is to find a
single optimum point or perhaps a set of near-eqivalent points (in
terms of the objective function). The objective function being used is
somewhat aribtrary and subject to user choice.

In contrast, the main aim of a Markov Chain Monte Carlo method is to
evaluate a probability distribution representing the uncertainty of
certain model parameters based on available data. While a single "best
estimate" might be derived as an eventual outcome, you should not
think of this as the main aim of MCMC methods. In a sense, the role of
an objective function might be attributed to the likelihood function,
since the main weight of the probability disribution will be given to
parameter values where the likelihood function is high. However, this
"objective function" is not arbitrary and needs to be carefully
formulated.

David Jones


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