For the first part please see: Can Scientists Pursue Science Successfully Apart From a Robust Epistemology? Part 1

The reason why inferential beliefs are so important is that one’s scientific method cannot be contrary to one’s epistemic method.  With that said, certain models for scientific explanation must have justificatory acceptance.  For example, a deductive form of scientific inquiry cannot be the only means acceptable since one cannot have a deductive form of epistemology since all beliefs would be self-justified and self-preserved (at least this would not account for a robust epistemology).

Such methods are derived from the use of abductive reasoning.  The American philosopher and logician Charles Sanders Peirce first described abduction.  He noted that, unlike inductive reasoning, in which a universal law or principle is established from repeated observations of the same phenomena, and unlike deductive reasoning, in which a particular fact is deduced by applying a general law to another particular fact or case, abductive reasoning infers unseen facts, events, or causes in the past from clues or facts in the present.[1]

A robust epistemology is a sufficient condition for a successful pursuit of scientific inquiry.  There are many other factors and conditions that must be met for science but a vigorous epistemic model for how one pursues scientific inquiry is needed; otherwise, there may be sufficient reasons to doubt not only the conclusions of the scientific inquiry but as well as the pool of data, which must be assessed appropriately.  The scientist is more than welcome to pursue an empiricist model for his epistemology, though strict [naturalistic] empiricism is not very robust, but it must have certain allowances for metaphysical import—perhaps more rationalistic.

I believe the best way to construct a robust epistemology and scientific method is to be a realist.  What I mean by this is that the external reality is how it appears to be to an observer making an epistemic inquiry, the measurements from science accurately depicts reality.  This is in contrast to instrumentalism/anti-realism, which suggests that our inquiry of the world, scientifically, do not accurately depict reality but as useful fictions.  An instrumentalist is more concerned about data fitting theories and predictions than with an accurate depiction of reality.