Better word for 'believe' or 'think'

You can use the word deem.

Deem - to come to think or judge; to have an opinion.

We deem that XYZ corp will continue to see an increase in sales in the next quarter.

I deem that this sentence can be persuasive to someone.

How about Foresee - to see (as a development) beforehand

"On the basis of our analysis, we anticipate....." Anticipate: ..."to foresee...to expect..." Webster's New Collegiate. Or, "on the basis of our analysis, we expect.." Expect: "to look for with some confidence" Webster's New Collegiate. Then produce a convincing analysis, which includes consideration of what could go wrong.

If you are confident about the prediction, then maybe you want to say so plainly.

We are confident that XYZ corp will continue to see an increase in sales in the next quarter.

If you know for certain then you could say that too.

We are certain that XYZ corp will continue to see an increase in sales in the next quarter.

Somewhat more flowery, possibly a little softer:

We have no doubt that XYZ corp will continue to see an increase in sales in the next quarter.

Somewhat more stern:

We are firm that XYZ corp will continue to see an increase in sales in the next quarter.

or

We are firm on XYZ corp continuing to see an increase in sales in the next quarter.

If you want to use something more specific to the business world, you could try "to project", which is defined by oxforddictionaries.com as "[to] estimate or forecast (something) on the basis of present trends".

You could use Understand or Understanding.

"We understand that XYZ corp will continue to see an increase in sales in the next quarter."

"It is our understanding that XYZ corp will continue to see an increase in sales in the next quarter."

Either case would need to be backed by additional reasons why you have that understanding.

Your analyst had the right idea but the wrong solution. "Think" may imply a more rational approach, but it is no better than "believe" in terms of implying an empirical (evidence-based) approach. If you have evidence, you can say so while still using comfortable language by using the idiom:

"We have reason to believe that XYZ corp...."

This retains the natural flow of your original sentence while explicitly establishing that your prediction is supported by evidence and is neither a matter of pure belief nor subjective thinking.

If you want synonyms of think or believe with better persuasive power, then you could use hold or maintain.

"We hold that XYZ corp will continue to see an increase in sales in the next quarter."

"We maintain that XYZ corp will continue to see an increase in sales in the next quarter."

Google defines maintain as "state something strongly to be the case; assert." Usage example: "he has always maintained his innocence."

Google defines hold as "have or adhere to (a belief or opinion)." Usage examples: "the court held that there was no evidence," "I feel nothing but pity for someone who holds such chauvinistic views."

Because both words have other definitions that have to do with physically keeping something in place, I feel that the above "figurative" (at some point, I guess, they were figurative, but probably no longer) senses have connotations of you "holding your ground" in an argument, not being easily "moved" from your point of view.

Plus, because they are not frequently used, they should have some additional power to impress readers of your analytical reports.

To reckon

1. establish by counting or calculation; calculate.

"his debts were reckoned at $300,000"

synonyms: calculate, compute, peg, work out, put a figure on, figure;

2. informal, conclude after calculation; be of the opinion.

"he reckons that the army should pull out entirely"

synonyms: believe, think, be of the opinion/view, be convinced, dare say, imagine, guess, suppose, consider, figure;

"I reckon I can manage that"

If the prognostication is encouraging, explain why at the beginning of the sentence, and leave will as it is. The auxiliary verb, will, expresses probability and expectation.

“According to our analysts/to the latest figures in our possession, XYZ corp will continue to see an increase in sales in the next quarter.”

“… XYZ corp will see an increase in sales etc.

OR

We are [cheerfully] optimistic that XYZ corp will continue....

contend

: to argue or state (something) in a strong and definite way

also

maintain or assert “He contended that Communism had no future”

or

assert

: to state (something) in a strong and definite way

Depends on where you want the power of your statement to reside and the context within which the word resides.... you could use....

"A confluence of research leads us to support..." - uses confluence, which is nice, and implies that many people have worked to find this solution....

Reserve the words 'believe' and 'think' for statements from which you want to be able to distance yourself. The next level up of personal removal would be 'research indicates,' 'independent study shows,' because the burden (and support) rest on said research....

But you want to sell the security and I believe ;) that your legal people would probably like you to 'print' as weak a term as possible, so that you sales person can us the force of his/her charisma to imply more than the words hold you liable for.

I agree that saying "We believe..." sounds a bit like wishful thinking. Economists are fond of saying "should" a lot, as in "Things should pick up in Q4..." But then again, you probably don't want to sound like an economist.

If it's truly the case that you have evidence or experience to support your position, then perhaps that's what you should say. Consider:

"Our evidence points to XYZ outcome based on the following: ...."

or

"Situation XYZ resembles our experience with PDQ. The outcome for PDQ was QRS and therefore we predict a similar outcome for XYZ."

You seem to be asking several questions more than just the single word request and with the word-usage tag, I am somewhat inclined to believe they are not implicative rhetoric.

How Believable

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If we have evidence or experience to support our position, then isn't it more than a belief?

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It is not. First there isn't anything strictly "more" than a belief because it covers the entire range of acceptance from the probable truth to irrefutable confidence. Before reading the following, keep in mind that Noah Webster was a doubtless Christian from a bygone era:

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1: A persuasion of the truth, or an assent of mind to the truth of a declaration, proposition or alleged fact, on the ground of evidence, distinct from personal knowledge; as the belief of the gospel; belief of a witness. Belief may also by founded on internal impressions, or arguments and reasons furnished by our own minds; as the belief of our senses; a train of reasoning may result in belief. Belief is opposed to knowledge and science.

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4: In some cases, the word is used for persuasion or opinion, when the evidence is not so clear as to leave no doubt; but the shades of strength in opinion can hardly be defined, or exemplified. Hence the use of qualifying words; as a firm, full or strong belief.

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In Webster's Revised Unabridged Dictionary 1913, we also have this example quote, which I slightly disagree with but illustrates that the range can be absolute:

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" Belief admits of all degrees, from the slightest suspicion to the fullest assurance." ~ Reid. "

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Second, as sense No. 1 mentions, the range of believability includes what is believed due to a foundation in evidence. The best beliefs usually are. "Do you believe me now?" is something somebody might smugly ask after their point has been proven, to which the response is often something to the effect of "Yes, I do. I believe you!" if not awed silence.

However, it should be noted that more specific words might be stronger or weaker on average, depending upon their particular meaning.

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But the word "believe" seems like a somewhat flimsy way of persuading someone.

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Any one word would have that problem unfortunately. I do not want to go too much into the philosophical aspects but it is always up to the recipient of a message to decide the degree of skepticism applied to it, since the only possibly undeniable thing is perhaps Descartes' creed: Cogito Ergo Sum (I think therefore I am). If believe has any problem, it is that people have used it too much to lend unwarranted credibility to their claims, which would also be a problem that is virtually inevitable for any word concocted to replace it. Try too hard to convince by the power of rhetoric alone and you might damage your credibility by leading your client to suspect your claims are pushy, fraudulent or unrealistic, with nothing to back them up.

This is Not in Conclusion

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What about "concluded"?

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It would be unfortunate if you used the word "concluded" if you are unwilling to use confident, since this word effectively means the same thing in this context, albeit in a roundabout way. "We have finished making our determination, there is nothing more to be done regarding this matter, except sit and wait to see it unfold."

pp. Shut; ended; finished; determined; inferred; comprehended; stopped, or bound.

If this does not lend itself to the unsavory implications I mentioned above, it minimally edges too close to a guarantee.

Word Choices

Since you have mentioned that you want to indicate that your beliefs are founded on external factors, in the hope that this will add to your credibility, there are at least a few few words words that can fit the bill.

Infer isn't so bad of a word from the definition of concluded but I still think it is stronger than what you are looking for now.

2. To deduce; to draw or derive, as a fact or consequence. From the character of God, as creator and governor of the world, we infer the indispensable obligation of all his creatures to obey his commands. We infer one proposition or truth from another, when we perceive that if one is true, the other must be true also.

This basically makes you beholden to the standards of formal logic. If your predictions are wrong, it must because your premises were false/incomplete or your rationale was faulty. This is technically true regardless but I doubt you want to draw attention to the fact:

Convinced is better since it focuses a little more specifically on the evidence. It also sounds somewhat like "concluded" except with a more fitting meaning:

pp. Persuaded in mind; satisfied with evidence; convicted.

However, I think persuaded fits best since it can be based upon a number of external factors, like the experiences you have mentioned:

pp. Influenced or drawn to an opinion or determination by argument, advice or reasons suggested; convinced; induced.

Normally I'd explain in further detail but I think the definitions speak for themselves in this case.

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All quoted definitions reference The American Dictionary of the English Language by Noah Webster in 1828.

If you have actual evidence that comes from experience, consider saying it directly - "in our experience," or "our tests show."

Does it have to be single word? If not, I think saying "presume true" fits quite nicely.

Here is quite helpful list http://www.positivethesaurus.com/2016/02/positive-synonyms-for-believe.html

How about, "our projection"is that....

I am also seeking a better word than "believe" to use when speaking to theists about evolution, because the next thing you know they're saying things like, "well, if you can believe in evolution, I can believe in yada, yada, yada."