Do Inherited Beliefs and Conjectures Affect Inference?

Yes!

And sometimes the inherited beliefs and conjectures that influence inference are more than 2000 years old:

Ian Fisher, Rome Journal: Some Say His Digging Up of a Legend Is Just a Myth, NYTimes Online Edition (May 6, 2005):

[A]ndrea Carandini ...one of Italy's most renowned archaeologists ... has discovered something extraordinary underneath the tightly packed ruins of the Roman Forum: a palace that he believes belonged to the first king of Rome, who just maybe was actually named Romulus.

...

[I]n the two decades that Dr. Carandini, 68, has excavated in and around the Palatine Hill, the epicenter of successive generations of Roman rulers, he has without doubt attracted a fair share of skeptics.

...

[Dr. Carandini] says his latest discoveries show the myth to be quite possibly true, even if the king's name was not necessarily Romulus ....

Others say that in his two decades at the site, Dr. Carandini has sometimes worked backward from myth to explain what he has found, rather than waiting for evidence to emerge from the finds themselves.

Note, this is not simply an instance in which Dr. Carandini and his critics have different prior beliefs. This is equally a situation in which Dr. Carandini's prior beliefs give the archeological evidence that he finds a different flavor in his mind's eye than it has in his critics' minds' eyes.

"critics minds' eyes"? Now, really, Tillers!