From "Manual of Muad'Dib" by the Princess Irulan

Motives and Purposes
Here follows an excerpt from the Summa prepared by her own agents at the request of the Lady Jessica immediately after the Arrakis Affair. The candor of this report amplifies its value far beyond the ordinary.
Because the Bene Gesserit operated for centuries behind the blind of a semi-mystic school while carrying on their selective breeding program among humans, we tend to award them with more status than they appear to deserve. Analysis of their "trial of fact" on the Arrakis Affair betrays the school's profound ignorance of its own role.
It may be argued that the Bene Gesserit could examine only such facts as were available to them and had no direct access to the person of the Prophet Muad'Dib. But the school had surmounted greater obstacles and its error here goes deeper.
The Bene Gesserit program had as its target the breeding of a person they labeled "Kwisatz Haderach," a term signifying "one who can be many places at once." In simpler terms, what they sought was a human with mental powers permitting him to understand and use higher order dimensions.
They were breeding for a super-Mentat, a human computer with some of the prescient abilities found in Guild navigators. Now, attend these facts carefully:
Muad'Dib, born Paul Atreides, was the son of the Duke Leto, a man whose bloodline had been watched carefully for more than a thousand years. The Prophet's mother, Lady Jessica, was a natural daughter of the Baron Vladimir Harkonnen and carried gene-markers whose supreme importance to the breeding program was known for almost two thousand years. She was a Bene Gesserit bred and trained, and should have been a willing tool of the project .
The Lady Jessica was ordered to produce an Atreides daughter. The plan was to inbreed this daughter with Feyd-Rautha Harkonnen, a nephew of the Baron Vladimir, with the high probability of a Kwisatz Haderach from that union. Instead, for reasons she confesses have never been completely clear to her, the concubine Lady Jessica defied her orders and bore a son.
This alone should have alerted the Bene Gesserit to the possibility that a wild variable had entered their scheme. But there were other far more important indications that they virtually ignored:
1. As a youth, Paul Atreides showed ability to predict the future. He was known to have had prescient visions that were accurate, penetrating, and defied four-dimensional explanation.
2. The Reverend Mother Gaius Helen Mohiam, Bene Gesserit Proctor who tested Paul's humanity when he was fifteen, deposes that he surmounted more agony in the test than any other human of record. Yet she failed to make special note of this in her report!
3. When Family Atreides moved to the planet Arrakis, the Fremen population there hailed the young Paul as a prophet, "the voice from the outer world." The Bene Gesserit were well aware that the rigors of such a planet as Arrakis with its totality of desert landscape, its absolute lack of open water, its emphasis on the most primitive necessities for survival, inevitably produces a high proportion of sensitives. Yet this Fremen reaction and the obvious element of the Arrakeen diet high in spice were glossed over by Bene Gesserit observers.
4. When the Harkonnens and the soldier-fanatics of the Padishah Emperor reoccupied Arrakis, killing Paul's father and most of the Atreides troops, Paul and his mother disappeared. But almost immediately there were reports of a new religious leader among the Fremen, a man called Muad'Dib, who again was hailed as "the voice from the outer world." The reports stated clearly that he was accompanied by a new Reverend Mother of the Sayyadina Rite "who is the woman who bore him." Records available to the Bene Gesserit stated in plain terms that the Fremen legends of the Prophet contained these words: "He shall be born of a Bene Gesserit witch." (It may be argued here that the Bene Gesserit sent their Missionaria Protectiva onto Arrakis centuries earlier to implant something like this legend as safeguard should any members of the school be trapped there and require sanctuary, and that this legend of "the voice from the outer world" was properly to be ignored because it appeared to be the standard Bene Gesserit ruse. But this would be true only if you granted that the Bene Gesserit were correct in ignoring the other clues about Paul-Muad'Dib.)
5. When the Arrakis Affair boiled up, the Spacing Guild made overtures to the Bene Gesserit. The Guild hinted that its navigators, who use the spice drug of Arrakis to produce the limited prescience necessary for guiding spaceships through the void, were "bothered about the future" or saw "problems on the horizon." This could only mean they saw a nexus, a meeting place of countless delicate decisions, beyond which the path was hidden from the prescient eye. This was a clear indication that some agency was interfering with higher order dimensions!
(A few of the Bene Gesserit had long been aware that the Guild could not interfere directly with the vital spice source because Guild navigators already were dealing in their own inept way with higher order dimensions, at least to the point where they recognized that the slightest misstep they made on Arrakis could be catastrophic. It was a known fact that Guild navigators could predict no way to take control of the spice without producing just such a nexus. The obvious conclusion was that someone of higher order powers was taking control of the spice source, yet the Bene Gesserit missed this point entirely!)
In the face of these facts, one is led to the inescapable conclusion that the inefficient Bene Gesserit behavior in this affair was a product of an even higher plan of which they were completely unaware!

Appendix IV: The Almanak en-Ashraf