title: Advantage of metropolis hastings or MonteCarlo methods over a simple grid search?
body: <p>I have a relatively simple function with three unknown input parameters for which I only know the upper and lower bounds. I also know what the output Y should be for all of my data. </p>
  
  <p>So far I have done a simple grid search in python, looping through all of the possible parameter combinations and returning those results where the error between Y predicted and Y observed is within a set limit.  </p>
  
  <p>I then look at the results to see which set of parameters performs best for each group of samples, look at the trade-off between parameters, see how outliers effect the data etc.. </p>
  
  <p>So really my questions is - whilst the grid search method I'm using is a bit cumbersome, what advantages would there be in using Monte Carlo methods such as metropolis hastings instead?</p>
  
  <p>I am currently researching into MCMC methods, but don’t have any practical experience in using them and, in this instance, can’t quite see what might be gained.</p>
  
  <p>I’d greatly appreciate any comments or suggestions</p>
  
  <p>Many Thanks</p>