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For example, would "I predict how the Mayans lived for a daily living" be correct?

I'm pretty liberal with the use of words, but you can see from the following definitions that the word "predict" doesn't quite fit what you're saying, that is, if I understand your question correctly.

v.tr. To state, tell about, or make known in advance, especially on
the basis of special knowledge
v.intr. To foretell something.
American Heritage Dictionary

vb (tr; may take a clause as object) to state or make a declaration
about in advance, esp on a reasoned basis; foretell
Collins English
Dictionary

v.t.

1. to declare or tell in advance; foretell.
v.i.

2. to foretell the future; make a prediction.
Random House Kernerman Webster's College Dictionary

: to declare or indicate in advance especially : foretell on the basis
of observation, experience, or scientific reason
Merriam-Webster
Dictionary

verb
to say that an event or action will happen in the future,
especially as a result of knowledge or experience:
Cambridge
Dictionary

verb
[with object]
Say or estimate that (a specified thing)
will happen in the future or will be a consequence of something.
Oxford Living Dictionaries

verb [transitive]
to say what you think will happen in the
future
Macmillan Dictionary

(transitive) To make a prediction: to forecast, foretell, or estimate
a future event on the basis of knowledge and reasoning; to prophesy a
future event on the basis of mystical knowledge or power.
Wiktionary

A prediction (Latin præ-, "before," and dicere, "to say"), or
forecast, is a statement about a future event.
Wikipedia article on prediction

For perspective from answers already answering this question, I provide this Quora link, Is it possible to predict the past

There are search results for "predict the past", I'm unsure what to make of these. Some are phrases like "it's impossible to predict the past" or "predict" is in what are called scare quotes, which shows the writer wishes to draw attention to the word as possibly a misuse. However there seem to many genuine positive results.

For example there is an article on New Scientist magazine online that uses it:

The validity of models can be tested against climate history. If they
can predict the past (which the best models are pretty good at) they
are probably on the right track for predicting the future – and indeed
have successfully done so.
Climate myths: We can’t trust computer models

I would personally use a word like "infer" or "theorise" to describe your hypothesis of how the Maya lived in the past. The word "hypothesise" itself would also fit.

Also an important point, see the first comment to your question by DanBron about the difference between grammar and semantics.