Pixel samples is all about anti-aliasing. 3 means that a single pixel in the render is derived from a 3x3 subpixel matrix, which actually quadruples the amount of pixels to be rendered. 1 means: no AA, and personally I don't like the even values as they don't take the main pixel itself into account. 5x5 might be fine for high end printing but in my opinion printing at 300dpi does some AA itself, so I tend to stick with 3x3 and go for larger image dimensions when I'm into fine print.

Min Shading Rate is meant to stop Poser from subdividing object poys into micro-polys, the value tells you how many render-pixels are at least (!) covered by a single micro-poly. So, 4 means; 1 micro-poly covers at least 4 pixels in the final result. As said in the Poser manual.
In my opinion, if I want to do AA in a 3x3 matrix, I'd like to hit at least 1 micro-poly per subpixel because otherwise I cripple the AA process. So, 10 micro-polys per render-pixel would not be too bad, and given the minimum / at least clause in this I even might think 20. This gives the MSR = 0.05 value as Vilters presented (my earlier post was slightly off, sorry for that).

Note that a Pixels Sample = 5 would imply a MSR = 0.01 to make the microplys support the AA process.

Next to that, the micropoly / AA process should be supported by the object texture map as well. Say, I'm portraying a head which takes 50% of a 1000 pixels wide render. So the head is showing 500 pixels texture, and the complete map around it requires 1000 pixels. Accoring to information theory (Nyquist...) I'd better double that resolution, requiring 2000 pixels at least for the texture map. 4000 would be overkill.
But when I take a closeup, the render takes 50% of (one side of) the head. That's 2000 pixels for one side full, 4000 for all around and 8000 for decent quality according to Nyquist. Note; this is already the Poser limit, and for a 1000 pixel wide closeup, not for a 16"wide 300dpi magazine centerfold. This is why photoreal characters in cinema come with Gb's of textures.

Nyquist puts at least 2x2 texture map pixels per render pixel, this is barely enough to support 3x3 antialiasing and actually too coarse to support 20 micropolys per renderpixel. So, in order to balance render resolution, texture map resolution, AA and Shading Rate one might double the texture map resolution once more. Once, not twice.
There are no "best values" for any of these, but in my opinion it's worthwhile to watch the balance between them. Once one of them becomes the weakest link in quality, the others only add rendering time and resource consumption without further benefits.

Last but not least: Min Displacement Bounds. It has to do with buckets. Each bucket considers the objects within the bucket area, but displacement might push objects into such an area while the object itself is not. Poser is quite good in guessing about that (and buckets have overhead edges as well!), but might go wrong in complex material trees. In that case some details of an object with displacement are cut off in a neighboring bucket, as the object is incorrectly not taken into consideration. The risk grows larger at smaller buckets.

The cure is to tell Poser to consider objects with displacement a bit bigger in size, to blow them up a bit just for proper bucket allocation. This blow-up is the displacement bound, and it's measured in Poser Native Units. 1 PNU = 262cm, or: 1mm = 0.00035.
It's up to you to manually override Poser, and small values just put a small time and resource burden on the rendering. But MDB = 0.5 blows up all objects 131 cm in all directions, which means about every object will be considered in every bucket, as a manual override to Poser which does quite a good job by itself. Well, it would not be my choice. The memory consumption that comes with that might force you into smaller buckets, and so on.

Shading Rate as well as Displacement Bounds can be set at the object level as well. Poser takes the largest value of the one set in Render Settings and the objects' one. So depending on the object settings, you might get less (!) micro-polys and/or more blow-up than set in Render Settings.

all the best, comments are very welcome.

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Usually I'm wrong. But to be effective and efficient, I don't need to be correct or accurate.

visit www.aRtBeeWeb.nl (works) or Missing Manuals (tutorials & reviews) - both need an update though