If you use parity above 2.3.5 and you want to run with docker in a way that your chain is synced on a persistent storage, like under /srv/parity on an ubuntu machine, you can use something similar to the following script:
sudo docker run -ti -d --name parity --network=host --user=root --restart=unless-stopped -v /srv/parity:/home/parity/.local/share/io.parity.ethereum parity/parity:v2.3.5 --chain=ropsten --geth --jsonrpc-apis "web3,eth,net,parity,parity_accounts,traces,rpc,parity_set,personal" --base-path /home/parity/.local/share/io.parity.ethereum
