Hello, AI researcher here!

We borrow the term "prior" or "prior probability" from Bayesian statistics, and in simple language you can think of a "prior" as being "what we believed before we saw the evidence". Prior just means "former" or "before" in Latin. After we see some evidence we update our beliefs, and that becomes our new "prior" for any further reasoning. We use a calculation called Bayes Rule to find our current belief (posterior probability) from our previous belief (prior probability) and some evidence.

The least informative prior, and also the default if we have no information at all, is "I know nothing". If you know nothing about the probability of some event occurring then you regard all outcomes as equally likely. For example, when I roll a fair die I am completely ignorant about the outcome, so my prior is that any outcome has a probability of 1/6.

I can say I have a more informative prior when I know something about the probability of an outcome. If I want the probability of it raining tomorrow, I could say "I know nothing", or I could think about it and actually, the weather today is probably similar to the weather tomorrow, and it was sunny today, so actually my prior is that it's a bit more likely than not to be sunny tomorrow - let's say 65% or so.

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Your first example is saying that it's silly to spend effort finding a good prior and then forgetting to take into account the actual evidence. For example, if i want to know if it will rain today, it is silly to think about yesterday's weather and forget to just look out the window.

Your second example is talking about how "extreme" a prior is. In Bayesian calculations, if you believe a probability is at 100% or 0% then there is no mathematical way to change it. This is an extreme prior. The more confident you are something will or won't happen, the harder it is to change your mind. The example, then, is saying that it is strange to talk about a "high-uncertainty" prior (one which is nearer to the "I know nothing" default position) as being extreme - without context I cannot tell you why they are saying that.

It probably is using the term in context of Bayesian statistics, where it is a measure of how likely you estimate changes of something happening (the probability distribution), before you have any evidence on the phenomenon.

Also, in medicine it's used to mean "a previous study". If a radiologist needs to see a prior, then they're looking at a previous exam in order to compare it to a current exam.

It means an incident in a person's past. It's most often used in law enforcement as a short term for prior conviction or arrest

If they are talking about "evidence", usually it's in regards to a prior conviction or a prior charge that a person faced. Like, "the judge went easy on the sentencing because the defendant had no priors" - they had a clean criminal record.

noun. plural priors. : the superior ranking next to the abbot of a monastery. : the superior of a house or group of houses of any of various religious communities. US law enforcement, informal : a previous instance of arrest or conviction for a crime. Thanks to Google