I've created a script for my school project that works with data. I'm quite new to working remotely on a server, so this might seem like a dumb question, but how do I execute my script named 

stats.py

so that it continues executing even after I log off PuTTy? The script file is located on the server. It has to work with a lot of data, so I don't want to just try something and then few days later find out that it has exited right after I logged off.
Thank you for any help!
There are many ways you can run a python program after you disconnect from an SSH session.
1) Tmux or Screen
Tmux is a "terminal multiplexer" which enables a number of terminals to be accessed by a single one.
You start by sshing as you do, run it by typing tmux and executing it. Once you are done you can disconnect from putty and when you login back you can relog to the tmux session you left
Screen also does that you just type screen instead of tmux
2) nohup
"nohup is a POSIX command to ignore the HUP signal. The HUP signal is, by convention, the way a terminal warns dependent processes of logout."
You can run it by typing nohup <pythonprogram> &
How to run a python script on a remote server that it doesn't quit after I log off?