I don’t think a method is better than other. What exactly do you need? Both methods can give you accurate estimates for the uncertainty in your projections. You need to define your model for the measurement system and then decide according its characteristics which method for the uncertainty assessment is more suitable. MCM is very easy to program using the pseudorandom number generators in MATLAB, while the Bayesian approach will require a lot more analytical development. MCM will provide an approximated result while the Bayesian approach will give you an exact result if it is possible. Sometimes is very cumbersome to propagate the PDF through the Bayesian approach and you will also have to make some approximations/simplifications to accomplish that. In the end it is up to you to decide which method is the one that fits more your needs and skills. I hope you find useful this comment. Good luck!

I forgot to mention that MCM could be very computationally expensive for some models and could also require optimization in the determination of the right/enough number of runs.

Thanks a ton Marco Azpurua

There is no single form of "uncertainty analysis". This term has been stretched and distorted so much in recent years that it no longer has a well-defined meaning. Perhaps this was unavoidable, but it does place the burden of justifiable precision on those of us who claim to quantify uncertainty so that we and others can understand its implications.

You might find it helpful to think of uncertainty analysis as a guiding philosophy, not something you begin, do, and then end. Start with the end state in mind. Focus less at first on what particular method you should use, and more on what you hope to learn by studying the ensemble of model forecasts. Do you want to quantify the sensitivities of certain sample statistics to various model inputs? Do you want to use the output statistics to guide future modeling or data gathering efforts? Do you want to separate the various models into classes of models based on their assumptions and then understand how these assumptions affect the forecasts? Do you want to select the single best model based on comparisons with field data?

Each of these goals calls for different methods. If you can clarify your goals, you'll help us to give you the most effective advice for your needs.

If you have a spreadsheet model in Excel, you can download the free YASAIw add-in for Excel to do Monte Carlo simulation from this link:

http://www.ecy.wa.gov/programs/eap/models.html

Thanks Dr.Greg Pelletier.

Dear Dr. Chris Pettit, first of all thanks a ton for your enlightening discussion. Actually what i try to do is - I have five different GCM outputs, each GCM have different physics option and different mechanism to predict the future under different RCP. A monte carlo simulation for combination of all these (GCMs under RCP 4.5 of AR5 of IPCC) to form an ensemble will put more confidence result of predicted future so that it can be used in impact assessment. As am a beginner in uncertainty assessment i may be a bit different in approach.

Can u suggest me something to make my doctoral thesis a better one?

Thanks in advance.

Recently I published something on the topic; you can find "An exact framework for uncertainty quantification in Monte Carlo simulation" in my publications in RG. If you cannot find I will send you. Let me know your mail

Thanks Dr.Paolo Saracco.

my mail id: [email protected]

Maybe it's too late but I have another paper the related to uncertainty and applications (A framework for propagation of uncertainty contributed by parameterization, input data, model structure, and calibration/validation data in watershed modeling). It was done by watershed simulation model (Soil and Water Assessment Tool, SWAT). Hopefully it helps. 

Thanks a Ton Yen. I am really happy to have your publications.