You gave Shackleton v. Science in response to religion v. science.
All of science involves the application of all human experience to explain the particular experience.
Except for all events which have a zero probability. For example, what is the probability that a hand will reach through this screen and hand each of us a pot of gold with a note attached that says: "Shut up and I'll double your money." Some things are just flat impossible.
I would enjoy following up on IPUs with you, but first we need to decide what "probability" means. Under probability theory, we understand that it only applies to random events. I'm not sure how "invisible pink unicorn" categorizes as "random event".
Now we're getting somewhere. You only need to cross one more barrier, but I'm not sure if you're willing or able. You now need to clearly distinguish the characterization "rogue". Scientists were looking for a specific phenomenon in which the sum of all amplitudes of randomly propagating surface waves could reach a particular value (say 30 m). Shackleton had no such categorization or characterization in mind, just the harrowing experience of it. Shackleton did not care if it was a random sum, or a wave whipped up by a hurricane, or a tsunami. He merely experienced it. You need a way to overcome the fact that if Shackleton had said "I was hit by a monster wave" (which is close to his actual reamarks) most scientists probably would have assumed he was talking about a storm wave or a tsunami. So information is missing here, information needed to complete your thesis.
The light house is cited as early evidence that such waves were already documented in the literature.
Above I posted the picture of a ship struck by a rogue wave. You appear to be saying that scientists deny the evidence presented in the picture. That makes no sense. As for scientists working on rogue wave analysis, I can refer you to the following sources.
You can start with Shackleton's own book. I find no discussion of any scientists discrediting him. Since there were scientists on board, it's hard to understand which scientists are claiming the existence of rogue waves and which are not:
http://books.google.com/books?id=EICKclfgBPYC&pg=PA177
Here is a reference to the lighthouse I mentioned
http://www.commissionersofirishlights.com/cil/aids-to-navigation/lighthouses/eagle-island.aspx
For scientific work regarding rogue waves
http://www.opc.ncep.noaa.gov/perfectstorm/mpc_ps_rogue.shtml
http://folk.uio.no/karstent/waves/index_en.html
http://www.photolib.noaa.gov/htmls/wea00800.htm
http://www.tos.org/oceanography/issues/issue_archive/issue_pdfs/18_3/18.3_muller_et_al.pdf
http://www.theregister.co.uk/2005/08/05/hurricane_prompts_wave_rethink/
http://earth.esa.int/workshops/seasar2006/proceedings/papers/s1_5_jan.pdf
OK now you can put the above source material in your pipe and smoke it.
I'm waiting for you to establish what probability means.
You still are outside of the domain of probability theory.
I doubt you have any evidence of this. Shackleton and his crew report a frequency of zero. I still can't find any evidence that any scientist denied anything. So far I have a dozen or so sources, referencing others, and going back to the 19th century, in which scientists appear to be taking notice that these "freak waves" do in fact occur. Shackleton's science officers probably are the only scientists who we are going to find who have anything to say about Shackleton's experience, which they shared with him, and would have no reason to deny.
You assume he never wrote a book about it.
I make no such assumption. I'm quite certain a lively discussion went on among the scientists in his party concerning the wave, and whether or not it was from a gale or a tsunami, since they had no reason to suspect that amplitudes might randomly add in constructive coherence. I doubt seriously that they concluded it was the thing which has come to be known as a rogue wave, which is why I do not connect their ideation with the ideation of scientists at large who you say disputed him.
This is incorrect. The fact of an occurrence does not affect the expected value. For example, shuffle a deck of cards. The probability of drawing any particular card is 1 out of 52 (1/52, or 1.923%). Each time you draw a card you are experiencing an event that has only 1.923% chance of occurring. Note how easy it is to alter the expected value. Take a red deck and a blue deck (to differentiate them into 104 distinct species) and shuffle them and repeat the test. Your odds of drawing each particular card is reduced to 0.9165%. Now take 10,000 cards numbered 1 to 10,000. Shuffle them and draw. The odds of drawing that particular card is 0.01%. Draw another. Still 0.01%. The draw of a specific card has no bearing on the odds.
I think there was enough validation from among his crew. Again, you have not explained if Shackleton was concerned with categorizing the wave as a rogue wave, or a soliton from another source, such as a storm or seaquake. Without that information, the question of how other scientists may have estimated the odds, based on the specific probabilistics of rogue wave formation, is moot.
So far I only see the problems in yours as I have noted.