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The phrase 'with high confidence' is correct and can be used in written English.
This phrase is used to express strength and certainty in a statement. For example, "We can say with high confidence that the new product will be a success."
Exact(59)
The correction of errors committed with high confidence.
Protein correlation profiles identify lipid droplet proteins with high confidence.
Joint GW + neutrino observations would allow one to make statements with high confidence.
We said in the estimate with high confidence that Iraq had them.
"I came in with high confidence," said Ponder, a wide receiver out of Southeast Missouri State.
The CIA says with high confidence that MBS ordered Khashoggi's killing.
Abnormal operating conditions (faults) could be modeled and predicted with high confidence using software applications.
The estimation of variables was undertaken with high confidence and manageable error.
Eighty compounds were identified with high confidence (>90% of mass spectra similarity).
Digital image correlation at submicron length scales enables mapping of transformation strains with high confidence.
The analysis detected a total of 807 hypothetical proteins with high confidence.
More suggestions(17)
with high reliability
with high credibility
with considerable confidence
with high optimism
with high dependability
with high precision
with substantial confidence
with high faith
with high reliance
with high trust
with high self esteem
with high confident
with highest confidence
with high certainty
with strong confidence
with large confidence
with high level confidence
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com