anxiety and hosting events

I could use some tips on how to be a better event host when some participants are acting unusually anxious.

Sometimes, when I am hosting an event, there are new participants who demonstrate a level of anxiousness above and beyond standard jitters. Like, it's very common for a first-timer to not initiate conversation and to not move around physically to mingle, to double-check whether it's OK to sit down in a particular chair, and to be unsure of what topics it's ok to talk about.

But I'm talking about stuff like:

• about every 3rd thing they say is laced with self-deprecation
• they respond with uncertainty and "is it ok?" double-checks to pretty standard offers (e.g. a snack from a pile of snacks on a table in front of them)
• their worries take over the ordinary give-and-take of conversation, because when other people mention things they like or new ideas, the anxious person's responses usually include some worry about the thing (not framed as curiosity)

Tips?