Is it ever objective to guess about the future? I'm not smart enough to answer my own question. But among the words you listed, I think "predict" and especially "forecast" are more often used when discussing future events based on scientific methods. For example if a scientist was saying that the earth's temperature would rise by one degree in the next 10 years, you would often see those terms being used, especially since as Sheldon pointed out, "forecast" is often used in relation to weather. Another very common verb used in this (scientific) way is "project". Here's an example: "Based on this, the UN Population Division projects the world population, which is 7.8 billion as of 2020, to level out around 2100 at 10.9 billion." Another useful verb is "expect". ("Economists expect this trend to continue into the near future.") So they think it will happen, though often we aren't told what that expectation is based on. "Anticipate" and "foresee", might sound more subjective or less certain, like an educated guess. You can also use "estimate" similarly. Or you can say "guesstimate" which is informal, but really communicates that you are unsure and may well be wrong.

We usually use forecast for the weather. Predict tends to be used objectively as tends to involve some form of analysis. Foresight is similar to predict but it is used more similarly to hindsight. As in he had the foresight to see this coming after the fact. This could be used subjectively a bit more than the others.

Anticipate is similar to predict as well.