Hi @Ramya,
from your config snippet it looks like $kibana_uri is not defined. I guess for your purpose you want to assign that name to the regex capture group as in location ~ /analytics/(?<kibana_uri>.*) {.
To get http://server/analytics to work you probably also need to handle the case of the missing trailing slash. As suggested in Can someone share nginx config for reverse proxying Kibana4.4/4,5, this might do the trick:
location = /analytics {
return 302 /analytics/;
}