What is better for a freelancer, who are experienced in different fields (for example: LaTeX typesetting, physicist and statistician) to have multiple accounts (on Elance, oDesk or any other place) for each field, or stick everything for single account?
On Elance - You can have multiple categories and your rating is applied to each category individually. You can be level 10 in one category, and level 2 in another. Each category is paid indeed,
I think on oDesk all is free.
But whatever freelancing site there is, they all have strict policies against multiple accounts. I remember I once tried this on odesk and they blocked both my accounts asking me to send ID for both persons.
Now, if you manage to find the way to be undetected (proxies or similar tricks), the answer to this is two sided. Many times they will choose you because of experience from previous jobs. Clients see 5 jobs and rarely look what kind of jobs they are. On the other hand, if you mess up in one category, it is not reflected to another. I think this is what concerns you, right? If you, give it a try with multiple accounts for a few months, they start using the one with most jobs awarded.
But IMHO you should go with 1 account. You will feel more professional and pressure of not making a mistake will make you be better. We all have 1 brand name and account.