I think that it is clear that can't do it just splitting existing control group in two parts, as such action could be done in many different ways and researcher could choose most favorable, and also because there could be some interactions inside control group, and also because smaler statistic power.

You can. Cross-validation, the bootstrap, permutation tests - these rely on that sort of procedure. They generate an empirical distribution of differences between groups or effect sizes which replace the assumption of being two normal distributions etc. It would be better to do those with both the experimental and control data, though.

but I only want to do it once, assuming a fixed prior which doesn't update over time.

I still don't understand what you're trying to do. If you're trying to maximize test scores by increasing them through picking textbooks and this is done many times, you want a multi-armed bandit to help you find what is the best textbook over the many students exposed to different combinations. If you are throwing out the information from each batch and assuming the interventions are totally different each time, then your decision is made before you do any learning and your optimal choice is simply whatever your prior says: the value of information is the subsequent decisions it affects, except you're not updating your prior so the information can't change any decisions after the first one and is worthless.

Do you think your monte-carlo Bayesian experimental design is the best way to do this, or can I utilize some of the insights from Thompson sampling to make this process a bit less computationally expensive (which is important for my particular use case)?

Dunno. Simulation is the most general way of tackling the problem, which will work for just about anything, but can be extremely computationally expensive. There are many special cases which can reuse computations or have closed-form solutions, but must be considered on a case by case basis.

You did read the rest of the article right, perhaps looked at the bibliography with over a dozen references?

Checkmate atheists.

(More seriously, you should've posted that to the cognitive science stack where there might actually be someone who knows something about IQ or gifted & talented education.)

You want some sort of adaptive or sequential design (right?), so the optimal design not being terribly helpful is not surprising: they're more intended for fixed up-front designing of experiments. They also tend to be oriented towards overall information or reduction of variance, which doesn't necessarily correspond to your loss function. Having priors affects the optimal design somewhat (usually, you can spend fewer datapoints on the variables with prior information; for a Bayesian experimental design, you can simulate a set of parameters from your priors and then simulate drawing n datapoints with a particular experimental design, fit the model, find your loss or your entropy/variance, record the loss/design, and repeat many times; then find the design with the best average loss.).

If you are running the learning material experiment indefinitely and want to maximize cumulative test scores, then it's a multi-armed bandit and so Thompson sampling on a factorial Bayesian model will work well & handle your 3 desiderata: you set your informative priors on each learning material, model as a linear model (with interactions?), and Thompson sample from the model+data.

If you want to find what set of learning materials is optimal as fast as possible by the end of your experiment, then that's the 'best-arm identification' multi-armed bandit problem. You can do a kind of Thompson sampling there too: best-arm Thompson sampling: http://imagine.enpc.fr/publications/papers/COLT10.pdf https://www.escholar.manchester.ac.uk/api/datastream?publicationPid=uk-ac-man-scw:227658&datastreamId=FULL-TEXT.PDF http://nowak.ece.wisc.edu/bestArmSurvey.pdf http://arxiv.org/pdf/1407.4443v1.pdf https://papers.nips.cc/paper/4478-multi-bandit-best-arm-identification.pdf One version goes: with the full posteriors, find the action A with the best expected loss; for all the other actions B..Z, Thompson sample their possible value; take the action with the best loss out of A..Z. This explores the other arms in proportion to their remaining chance of being the best arm, better than A, while firming up the estimate of A's value.

Still, my question remains - is there real data out there to support the contention that P(elite career|IQ) has a local max and then decreases for higher IQ?

No. As I point out in my comment there, the evidence is strongly the other way: TIP/SMPY. To the extent that measures like wealth hit diminishing returns or even fall (eg Zagorsky), it has as much to do with personal choices & values as ability: the physicist who could make money on Wall Street but chooses to continue studying particles, the person who chooses to become an influential but poor writer, etc. (There are many coins of the realm, and greenbacks are but one.)

von Neumann was noted as being social and extraverted long before he began his lobbying and politicking, and was never described as a second Dirac, so I don't think he was simply acting out of expediency. If high intelligence enabled faking extraversion & social skills, which are useful in almost all contexts*, we would see a noted personality correlation with intelligence and increasing with intelligence, which we don't - extraversion is largely independent of IQ, it's Openness in the Big Five which correlates. High-functioning autistic people are also not noted for easily acquiring psychopath-level skills in imitating & manipulating without feeling.

* see for example the correlation of increasing extraversion with increasing lifetime income in the Terman semi-high IQ sample

My reading of the behavioral genetics literature is that high intelligence being driven by rare autism variants is looking unlikely. DeFries-Fulker extremes analyses like "Thinking positively: The genetics of high intelligence", Shakeshaft et al 2015 aren't consistent with the (relatively) high end being due to rare variants (but are consistent with the low end being due to rare variants) and current attempts to find rare variants enriched in the very high IQ with large effect sizes have turned up nothing: "A genome-wide analysis of putative functional and exonic variation associated with extremely high intelligence", Spain et al 2015. There is also an autism heritability observed in the GCTAs/LD score regression using only common SNPs (>=1% population frequency), along with a positive autism/intelligence genetic correlation, which undermines that idea.

My speculation at this point is that Spearman's law of diminishing returns is - based on all the genetic correlations with intelligence which have piled up and the current trends in brain imaging studies finding brain volume/thickness & global connectivity & white-matter integrity & connection speed to be the best predictors of intelligence - is due to intelligence reflecting a bottleneck between all the regions of the brain communicating to solve problems and that as the global communication becomes closer to optimal due to better health & development, individual specialized brain regions start to become the bottleneck to higher performance and shrinking the g factor.

"Chromatin-modifying genetic interventions suppress age-associated transposable element activation and extend life span in Drosophila", Wood et al 2016 http://www.pnas.org/content/early/2016/09/07/1604621113.long