Though I don't think I'd claim to have strong convictions about any particular interpretation of physical reality, the idea that it is potentially deterministic has long been attractive to me for some reason. The idea that there might actually be some pervasive order underlying the apparent chaos just appeals to me.
Then quantum phenomena and Bell's inequality come along and mess things up, with most people interpreting these as implying that god does play with dice, and no hidden variables--no underlying deterministic set of rules--can account for easily observable quantum effects. The 1935 gedanken experiment known as the Einstein-Podolsky-Rosen paradox concludes that we either have to accept quantum theory's fundamental randomness or a "nonlocal" deterministic reality beneath it, and modern physics seems to have concluded that the former is the only viable truth. How untidy.
But, amongst other things, Bell's theorem depends upon locality--nothing can take place, no information can be transferred between two points faster than the speed of light. And nonlocality was the other solution to the EPR paradox (though EPR thought of the impossibility of this as proof that hidden variables must exist). Yet experimental evidence of nonlocality has been with us since Aspect's experiments in the 1980s (which have been reproduced and confirmed a number of times since).
Now, normally nonlocality is thought of as contrary to hidden variables and determinism. But if there are actually more dimensions than 4 (3 space plus time), then two points that are nonlocal in our limited view of space-time may very well be local in a higher-dimensional space-time. Problem solved. Reality can be deterministic, as long as it has dimensionality greater than 4, and provided the hidden variables appear local in that higher dimensional space and non-local in our 4-D view of space-time. The nonlocality in normal space-time sidesteps the limitations of Bell's inequality and the locality in higher dimensions satisfies the EPR paradox. Et voila, a deterministic universe.
Disclaimer: I am not a physicist, but I do look like one. :)