General Synonyms:
* Deduction
* Conclusion
* Assumption
* Implication
* Surmise
* Conjecture
* Speculation
* Interpretation
* Extrapolation
* Guess
More Specific Synonyms:
* Logical inference: Deduction, logical conclusion
* Informal inference: Assumption, guess, conjecture
* Statistical inference: Estimation, prediction
* Interpretive inference: Interpretation, analysis
Other options:
* Reading between the lines (implies understanding something unsaid)
* Drawing a conclusion (focuses on the process of reaching an inference)
* Taking a leap of faith (implies a less certain inference)
The best synonym for "inference" will depend on the specific context in which you are using the word.