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airlineecon
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

I disagree.

Bayesian updating. If the initial prior was 50%, after searching 80% of the area with nothing found, the posterior should be lowered.

As for the fair coin analogy. We don't know with certainty that the coin is fair 50/50 flip. We only start with a prior that it is a fair coin.

airlineecon
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

Your point about Bayesian updating is correct. They've been following that principle since day 1 with search off the coast of Vietnam, proceeding now to the Indian Ocean.

Be careful with your definition of TOTAL search area. Strictly speaking the total search area encompasses every square inch of the globe. This small area defined by the pings is not the total search area, in which case Bayesian updating implies the probability of it being in this area shrinks with each passing day.

nupogodi
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

With the Bayesian method, what I said still makes sense except as airlineecon pointed out your "search area" is, well, everywhere you have a non-zero chance of finding it. So by searching one part of it, your probability of finding it in the whole does not change ... But if you apply the method, it depends on what your hypothesis is ... how you determined how probable it is to find it in a particular area anyway. In this case I suppose it would be based on the strength of the pinger signals? Once you search an area and effectively reduce the probability of finding it in that spot to 0, to maintain the same probability of finding it across the entire area, your model needs to compensate, so there would need to be a higher probability of finding it in other yet-unsearched areas. In our cases I guess the next highest probable areas will be adjacent ones where the pinger signal was strong but not quite as strong, etc.

Your chance of finding it doesn't decrease. All you can really say is that if you've searched a place, your chance of finding it there is zip. But if you apply this method properly, then theoretically your chance of finding it 'a few blocks down' just got better ...   But no better in general than if you hadn't taken a systematic approach. You could have just searched everything. This is just for efficiency and cost-estimation purposes. It's imperfect since it does rely on probability models, and that's not a hard science, it's quite hand-wavy. You could create a probability gradient based on the pinger signal, but how do you assign meaningful values to all the other areas in the plane's range in the absence of data?

[Edited 2014-04-23 20:02:20]
A man must know how to look before he can hope to see.

nupogodi
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

I still feel I haven't explained myself correctly... We know it's somewhere within a reasonable range of that final ping arc. We also have the ULB (or ULB-like) signals in a particular area, so we can say it's most likely there and search there. If you search that entire area and come up with nothing, in the absence of extra data, you are equally likely to find it in any area within range of that ping arc except the areas you've already searched.

Fancy way of saying "back to square one".
A man must know how to look before he can hope to see.

Posts: 322
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting nupogodi (Reply 53):I still feel I haven't explained myself correctly... We know it's somewhere within a reasonable range of that final ping arc. We also have the ULB (or ULB-like) signals in a particular area, so we can say it's most likely there and search there. If you search that entire area and come up with nothing, in the absence of extra data, you are equally likely to find it in any area within range of that ping arc except the areas you've already searched.

question…what is considered (by you, experts, investigators et al) to be a reasonable range of the final ping arc?

Struggling to understand how they heard 2+ hours of constant ULB signaling, and, given the stated range (yes, I'm aware of all the variability by way of conditions) of detection, have seemingly come up empty-handed?? Just heard on NPR that "well over 90% of area has been covered".

Stats, Bayesian method, probabilities etc…In a given area of search which begins with a probability of anything less than 100%, the corresponding likelihood (probability) of finding said object decreases in probability proportionally with the diminishment of the search area…so, this area is almost certain to be unproductive.

Theoretically we have 3 more areas of ascertained (assumed) lesser probability still to search. If they yield nothing, presumably back to the range of the final ping. But to have 2+ hours and to then NOT be able to re-aquire signal seems to almost be irrefutable evidence. If they were able to re-aquiure the signal (like, it's still signaling now, great skepticism would be in order), but the timing CANNOT just be coincidental, no? Anyone with any thoughts?

Finn350
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting MarkAK (Reply 42):The current underwater search is being conducted in a 10km radius around Ocean Shield's Pinger Detectiion #2. I'm presuming that's because it was roughly in the centre of the four separate detection locations. The logical step would be to make the next search either around one of the other three pinger detection locations or immediately adjacent to the first search area.

The problem is that if we assume the acoustic pings are from a single source and the maximum range of the acoustic signal is no more than 15 km, they have already covered the area defined that way. They can start searching around the other pinger detections, but it would inevitably contain only places that are at least 15 km away from some of the other pinger detections.

nupogodi
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting sipadan (Reply 54):question…what is considered (by you, experts, investigators et al) to be a reasonable range of the final ping arc?

Well, I can only give you maximums. If you take the 0011Z complete handshake as the ping ring, then it could have flown powered for ~63 minutes or so, lost power, and then glided from whatever altitude it was at. Quite a distance. The important thing is that it didn't handshake at 0115Z (when the next handshake was requested by the ground station).

There is evidence of a partial handshake at 0019Z, and a lot of people here and elsewhere seem to think this is consistent with power failure (running out of fuel), the terminal coming back online briefly (perhaps the APU briefly started), and then being shed as electrical power is conserved. In that case, it couldn't have gone too far from the 'ping ring' at 0019Z... I'm too lazy to look up the glide ratio of a 772 but if you do, and assume best glide from its service ceiling, that's the maximum possible range from the partial handshake arc IF the power-out scenario is what caused it.

Either way, those 'ping rings' are pretty fat.

[Edited 2014-04-23 21:17:01]
A man must know how to look before he can hope to see.

cat3appr50
Posts: 185
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

Responding to Nupogodi response #52:
Sorry, I can’t resist:

Nearly \$ 300 Million spent to date (as reported) on search and rescue costs spanning over 20 nations for this MH370 search with no end in sight, and after nearly two months of search time with (beyond comprehension) not even a single piece of floating debris, complex calculations for a few satellite “pinger” points…and no successful sonar data…nothing.

And forty nine years after the USA landed a man on the moon with navigation, communication, etc. technology much antiquated compared to the technology today, and despite the obvious lessons that should have been learned from the past Air France incident in the Atlantic, it’s still an unbelievable SAR game of effectively trying to find a needle in a haystack. The available technology to make all of this currently archaic method of finding a lost aircraft via reactive technology a thing of the past, with instead using proactive, real time, constant position reporting technology continues to be ignored (and not “required”) due to so called “bandwidth costs.”

Technology currently exists, as well as the methods to make it secure and foolproof, utilizing ACARS, etc. transmissions to constantly report at necessary and appropriate (and affordable) intervals altitude, lat./long., and speed data to assure that every aircraft transiting large bodies of water at significant flight times, if encountering emergency situations, can be quickly found. That would take the ICAO to declare that as a requirement for transiting such over water flight paths. But it’s not happened, supposedly because of the ‘ol “bandwidth costs.”

So, if this search takes \$ 500 Million or more to find this aircraft, and it very well could much exceed that, what’s the ROI of the real time, proactive ACARS type solution (and obvious 2014 technology solution) instead of this archaic, reactive, and non-real time method currently being used? “Bandwidth costs”? If it’s too expensive to require constant ACARS reporting, then make it a requirement for all aircraft to trigger the ACARS transmissions to automatically report 3D position data only upon unusual (abnormal) flight situations and flight emergencies to save on the…”bandwidth costs.”

777Jet
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting airlineecon (Reply 50): I disagree.

If they are not even searching in the right place to begin with it doesn't matter anyway...
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KIAS
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting sipadan (Reply 54):Bayesian method, probabilities etc…In a given area of search which begins with a probability of anything less than 100%, the corresponding likelihood (probability) of finding said object decreases in probability proportionally with the diminishment of the search area…so, this area is almost certain to be unproductive.

1) That statement is mathematically incorrect. Your chances of finding an object do not decrease in probability proportionally with the diminishment of a search area, whether the probability of finding it is less than 100% or not.

For example, If I have 10 boxes, and know a penny may or may not be inside one of them, and I search 8 and don't find it, the statistical chance of me finding it in the last 2 boxes is the exact same as the first 8.

2) This is actually the opposite of how you would use Bayes theory in this type of search operation. In this case - and what was done while searching for AF447 - is that you define a search area, and if you don't find the wreck, you recalculate and treat other areas of the current search area as more likely to contain it. You continue until you 100% complete the defined area.

The point here is that you are first determining a probability of finding the wreck if you assume that the wreck is indeed there. From this, you determine which cells of your grid-based search area you will begin searching. As you go along, and don't find the wreck, other remaining cells are treated as being more likely to contain it, following the computation.
"We fly, but we have not 'conquered' the air. When we presume mastery, we are often startled by our ignorance." - DHW

YoungMans
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

As repeated by Finn350..:

The current underwater search is being conducted in a 10km radius around Ocean Shield's Pinger Detectiion #2.

If this is the case, then Pinger Detection location #1 would be just outside that search area and locations #3 & #4 would be well and truly outside.

They would probably need at least another two or three (or even four) search efforts like the one we just had or still having now.
In other words, it'll be quite a while yet before we'll know anything for sure.

nupogodi
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting cat3appr50 (Reply 57):And forty nine years after the USA landed a man on the moon with navigation

49 years? 1965? Ouch, you're an American, that's a bad date to get wrong in a rant. It's July 20th 1969 they landed, July 21st they took the first steps.

Yep, there is a way to do better position tracking without jamming the global airwaves, SATCOM solution is one of them, 406 ELT test messages maybe another, space-based ADS-B is another good one. They can all be shut off, so... Depends on what you think caused this accident whether this would have helped. But, the transponder was off, and the transponder is pretty darn useful except in the middle of nowhere.
A man must know how to look before he can hope to see.

777Jet
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting KIAS (Reply 59):1) That statement is mathematically incorrect. Your chances of finding an object do not decrease in probability proportionally with the diminishment of a search area, whether the probability of finding it is less than 100% or not. For example, If I have 10 boxes, and know a penny may or may not be inside one of them, and I search 8 and don't find it, the statistical chance of me finding it in the last 2 boxes is the exact same as the first 8.

Correct! Regarding your example, sometimes you might find it in the first box you search and sometimes you might find it in the last box you search. But, like you said, the statistical chance of finding it does not change after starting your search and not finding it in the first few boxes.
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nupogodi
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting 777Jet (Reply 62):Correct! Regarding your example, sometimes you might find it in the first box you search and sometimes you might find it in the last box you search. But, like you said, the statistical chance of finding it does not change after starting your search and not finding it in the first few boxes.

The idea is that if you *know* there's a penny in one of the boxes, with each one you search, your probability of finding it in the next one increases.

Effectively we are all saying the same thing though. 80% of a specific area searched with nothing found does not mean it is not there. It doesn't mean it's less likely to be there. It just means it's not where you searched.

The Monty Hall Problem illustrates this - but isn't terribly relevant here.

[Edited 2014-04-23 21:55:25]
A man must know how to look before he can hope to see.

Backseater
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quote: DTW2HYD thread 56, post #288Pundits gave several explanations for 33.5 Khz pings, ranging from weak battery, buried in silt, damage, ocean temperature...
 Quoting Finn350 (Reply 55): if we assume the acoustic pings are from a single source and the maximum range of the acoustic signal is no more than 15 km,

This investigation has been powered by many (too many?) assumptions and too few pieces of "corroborated" hard data.
Rather than enlarging the current 'sweet spot" or rushing to the next one, It night be worth taking a step back and doing a little bit of science to reduce the number of assumptions and consolidate the data at hand (the " clean your test tubes and calibrate your instruments before making any more experiments!").

I already proposed that in thread 56, post #13 but if I may, I'll rephrase it here:
- determine the operational characteristics of the MH370 pinger at end of battery life at great depth
- firm up the understanding of sound propagation in that area and as those depths:
--- bring HMS Echo to lower a test pinger with a weak battery right where Ocean Shield believes is the most likely location of MH370's pinger
--- have Ocean Shield drag the towed pinger locator along the tracks where the original pings were heard
--- repeat by positioning the test pinger
------ on the bottom (approx. depth 4,500m)
------ deeper in a trench nearby
------ at max depth of a navy submarine (to rule out any possibility of emulation by an active sonar)
--- compare actual recorded pings with the new ones, adjust strategy and schedule next experiment
--- move HMS Echo to other locations nearby (or further away) as dictated by the cumulative results

Some of you are probably going to tell me that there is no need for the experiments I am proposing as investigators for sure already know all the expected results. Maybe. But that is just one more assumption!

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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting nupogodi (Reply 56):There is evidence of a partial handshake at 0019Z, and a lot of people here and elsewhere seem to think this is consistent with power failure (running out of fuel), the terminal coming back online briefly (perhaps the APU briefly started), and then being shed as electrical power is conserved. In that case, it couldn't have gone too far from the 'ping ring' at 0019Z... I'm too lazy to look up the glide ratio of a 772 but if you do, and assume best glide from its service ceiling, that's the maximum possible range from the partial handshake arc IF the power-out scenario is what caused it.

thanks, just to pick your brain (or any others), what else could possibly be emitting 33-37MHz every 1.06 seconds for a continuous 2 hour period and then NOT be able to be re-aquired, other than SOMETHING that would have had to have failed around the predicted failure time?? The coincidence of NOT being able to re-aquire said signal seems to be astronomical if the pinger locater was detecting something else man-made. And some aquatic life, for 2 hours per seconds, think rather not.

 Quoting KIAS (Reply 59):1) That statement is mathematically incorrect. Your chances of finding an object do not decrease in probability proportionally with the diminishment of a search area, whether the probability of finding it is less than 100% or not.
 Quoting KIAS (Reply 59):For example, If I have 10 boxes, and know a penny may or may not be inside one of them, and I search 8 and don't find it, the statistical chance of me finding it in the last 2 boxes is the exact same as the first 8.
 Quoting 777Jet (Reply 62):Correct! Regarding your example, sometimes you might find it in the first box you search and sometimes you might find it in the last box you search. But, like you said, the statistical chance of finding it does not change after starting your search and not finding it in the first few boxes.

No, but the probability does. Say you have a billion boxes, and a penny may or may not be in one of the billion boxes. You have opened 999,999,999 and found no penny. The probability that you will now find a penny in the last possible box is a probability that has been continuously decreasing from the moment you began opening boxes and not finding the penny.

[Edited 2014-04-23 22:23:09]

nupogodi
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting sipadan (Reply 65):No, but the probability does. Say you have a billion boxes, and a penny may or may not be in one of the billion boxes. You have opened 999,999,999 and found no penny. The probability that you will now find a penny in the last possible box is a probability that has been continuously decreasing from the moment you began opening boxes and not finding the penny.

But we have millions of 'boxes' and we know for sure the penny is under one of them.

In your scenario, we can hypothesize that the penny exists and with each box we open the probability of our hypothesis being true falls.

In the plane scenario, we *know* the plane exists. With each box we open - each km^2 searched - even if you naively assume it could be absolutely anywhere in the indian ocean - the probability of finding it in the other ones increases. Reality of course is not so simple and we know where it would more likely be, hence the Bayesian search.
A man must know how to look before he can hope to see.

comorin
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

The Monty Hall Problem illustrates this - but isn't terribly relevant here.

Great. So why bring it up?

scbriml
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting 777Jet (Reply 62):Correct! Regarding your example, sometimes you might find it in the first box you search and sometimes you might find it in the last box you search

This is interesting, because (although I'm not a statistician) in my experience, whenever I'm looking for something, I always find it in the very last place I look! What are the odds of that?
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777Jet
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

I can see the other side of the argument, however. Let's apply such theories to the game show 'Deal or No Deal' when trying to pick the suitcase out of 26 with the \$250,000 in it and then knocking out the others in order containing the least amount of money. Let's say you pick case 1 and there is only 1 case left to select to knock out - you are almost to the end! One of the cases has the \$250,000 and the other has .50 cents - but you don't know which one has which. So, do you: now have a 1 in 2 or 50% chance of having the \$250,000 in your suitcase or (even though there are only two cases left so the 250k is either in your case or the other case) do you still only have a 1 in 26 chance of having the \$250,000 as those were the odds when you started? I believe your odds have increased from 1 in 26 to 1 in 2! However, you at least know that the 250k is in one of the cases. I guess with MH370 this theory could be twisted because they don't know if what they are looking for is in one of the areas they are looking...
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nupogodi
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting comorin (Reply 67):Great. So why bring it up?

It's relevant for understanding how probabilities work in non-intuitive ways.

It's not relevant to the airplane search since there are no goats.
A man must know how to look before he can hope to see.

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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting nupogodi (Reply 70):It's relevant for understanding how probabilities work in non-intuitive ways. It's not relevant to the airplane search since there are no goats.

It did bring some humor to those of us that got the reference...which this thread does need a little bit of, from time to time.

lancelot07
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting scbriml (Reply 68):This is interesting, because (although I'm not a statistician) in my experience, whenever I'm looking for something, I always find it in the very last place I look! What are the odds of that?

100%. You stop looking after you found it.

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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

Well... I really doubt the plane is there.... For all I know, they don't know where the plane is, am I correct or not?
Where is the solid proof that says the plane went down in near by Australia? We can't find the plane when we have no idea where the plane is. For all i Know, all parts of ocean within the range of MH 370 is the whole area we have to search! which is impossible to do.

if an unknown Boeing 777 entering Australian airspace, won't the australian will scramble their jets to look for the plane at first place?

UALWN
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting 777Jet (Reply 69):Let's apply such theories to the game show 'Deal or No Deal' when trying to pick the suitcase out of 26 with the \$250,000 in it and then knocking out the others in order containing the least amount of money. Let's say you pick case 1 and there is only 1 case left to select to knock out - you are almost to the end! One of the cases has the \$250,000 and the other has .50 cents - but you don't know which one has which. So, do you: now have a 1 in 2 or 50% chance of having the \$250,000 in your suitcase or (even though there are only two cases left so the 250k is either in your case or the other case) do you still only have a 1 in 26 chance of having the \$250,000 as those were the odds when you started? I believe your odds have increased from 1 in 26 to 1 in 2!

No. unfortunately, you still only have a 1/26 chance of having chosen correctly (the money hasn't changed from one suitcase to another in all this process, right?). Which means that there's a 25/26 chance that the money is in the other suitcase. Which means that if you're given the opportunity to now select the other suitcase, you have to a) thank God for the lack of statistical knowledge of the show host; and b) choose immediately the other suitcase.

(I have to admit that I don't know the exact details of this show, though.)
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YoungMans
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting BackSeater (Reply 64):It night be worth taking a step back and doing a little bit of science to reduce the number of assumptions and consolidate the data at hand
 Quoting BackSeater (Reply 64):firm up the understanding of sound propagation in that area and as those depths

That's a good idea ...
It probably would take only a few days to get some initial results; which in turn would be quicker than having the Bluefin AUV covering all the areas in question.

The test(s) you are suggesting would give them a much better understanding on which to make decisions.

Such tests ought to have been carried out by various oceanic institutes already.

Backseater
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

All the statistical back and forth is simply a conditional probability:
Prob(finding the wreck at the next step) =
Prob(wreck in in the zone) X Prob(finding wreck at next step when wreck is in the zone)

If the zone can be searched in 10 steps, after 9 unsuccessful steps you have a prob 1. to find it at the next step, provided it is in the selected zone! That's the catch.
For the search, the only interesting factor is the value of: Prob(wreck is in the zone)!

Backseater
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

The safety bureau: who they are and how they work in KL and on Ocean Shield

Excerpts from:
http://edition.cnn.com/2014/04/22/wo...ats-next/index.html?iref=allsearch

 Quote:Crucially, the safety bureau chief commissioner said he expects ongoing data analysis by an international team of experts in Kuala Lumpur to result in further refinement of the search area within the next couple of weeks. "The area for focus of the search ... has already been moved twice, and there's always a possibility that further work will move it again," Dolan said. The safety bureau has three investigators who have been working as part of that team in Malaysia since early April. They continue to study satellite communications data from Inmarsat and details about aircraft performance to determine the most likely area where the Boeing 777-200ER may have entered the water, Dolan said. "They are literally sitting around a big table with their own computers having conversations with a team leader," he said, prefacing his remarks by acknowledging that he was commenting on a Malaysian-led investigation. The safety bureau also has three investigators aboard the Ocean Shield, the Australian ship carrying the U.S. Navy and Phoenix International teams responsible for deploying a submersible, the Bluefin-21. The bureau investigators have expertise in flight data recorders, materials and aerospace engineering, and maritime operations.

Do they have a suggestion box, just in case???

777Jet
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting UALWN (Reply 74):No. unfortunately, you still only have a 1/26 chance of having chosen correctly (the money hasn't changed from one suitcase to another in all this process, right?). Which means that there's a 25/26 chance that the money is in the other suitcase. Which means that if you're given the opportunity to now select the other suitcase, you have to a) thank God for the lack of statistical knowledge of the show host; and b) choose immediately the other suitcase. (I have to admit that I don't know the exact details of this show, though.)

You get bank offers along the way depending on what figures you have not yet knocked out. Ideally, you get to the last two cases and 1 is worth, let's say, \$200,000 and the other \$100,000. You might get an offer of \$150,000 cash to stop playing. You either take the offer or play on thinking you have the 200k and keep whatever is in that case. You could get to the last two cases and have 200k and \$1 remaining thus probably getting an offer of about 100K, or, you might get down to the last three cases and there is \$1, \$2 and \$50,000 remaining so you might take a deal of something like \$15,000. But, I like your thinking - if you get to that last two situation you could assume, using your logic, to take the offer in between instead of keeping your case because you only had a 1 in 26 chance of picking the case with the most when you started whereas the other case was one of the other 25/26
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lancelot07
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### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting asetiadi (Reply 73):if an unknown Boeing 777 entering Australian airspace, won't the australian will scramble their jets to look for the plane at first place?

it did not enter Australian airspace, not even close, and it was not threatening in any way.
Why would they "scramble their jets" for a civilian plane flying 1000 miles away parallel to the coast?

Lizzie
Posts: 130
Joined: Wed Apr 02, 2014 11:18 am

### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting KIAS (Reply 59):1) That statement is mathematically incorrect. Your chances of finding an object do not decrease in probability proportionally with the diminishment of a search area, whether the probability of finding it is less than 100% or not.

No, it isn't incorrect, which is why I've been banging on about Bayesian probabilities since I joined this thread!

If, and only if, you know for sure that an object is within a given search area, does your probability of finding it go up with every [subsection of that] area you reject as not containing it.

To simplify the question, let's assume that you have 101 possible search areas (e.g. solutions to the satellite data), and some other data (e.g. hearing possible black box pings) tells you that it has a 90% probability of being in the area at the top of your list, Area1, and 1% in each of the remaining 100areas (Area2-Area101) . So obviously you start with Area1. Let's say you divide it into 100 subdivisions, searching 1 each day. Let's compute the probability that the plane is in Area1, given that information. Let A1 stand for "plane in Area1" and NFY stand for "Not Found Yet".

P(A1|NFY)=P(NFY|A1)*P(A1)/[P(NFY|A1)*P(A1)+P(NFY|¬A1)*P(¬A1)]

P(NFY|A1)=1-proportion of A1 searched so far, i.e. the proportion of Area1 unsearched, so, if it's there, and 80% has been searched, the probability of not having found it yet is 20%.

P(A1) = 90% (prior probability)
P(¬A1)=10% (from prior probability)
P(NFY|¬A1) = 100%(Areas2-Area101 haven't been searched yet).

P(A1|NFY)=Proportion of Area1 unsearched *.9/[Proportion of Area1 unsearched *.9)+.1]

This means that the smaller the proportion of Area1 still unsearched, the smaller will the numerator be in relation to the denominator, and therefore the smaller the probability that the plane is in Area1.

Note also that the smaller the probability that the plane is anywhere other than Area1, the more slowly does the probability that it is in Area1 decrease as Area1 is searched, and vice versa.

The Bayesian take-home message here, it seems to me, is that given that there is so little hard data, and so many potential solutions to satellite data (not all of equal probability of course), and that even near-hard data may come with confidence limits (did the military Radar really track this plane, not another? Did the Chinese search ship really hear the box? Did Ocean Shield really hear the box?), every search that comes up blank alters the posterior probabilities that some other inference from other data is correct. Eventually, it may turn out that a northern route has higher posterior probabilities, given new data.

It's a more rigorous version of Sherlock Holmes's "When you have eliminated the impossible, whatever remains, however improbable, must be the truth." Or rather "As you eliminate the more probable, whatever remains, however initially improbable, becomes more likely".

[Edited 2014-04-24 02:58:18]

Lizzie
Posts: 130
Joined: Wed Apr 02, 2014 11:18 am

### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting Gennadius (Reply 71):It did bring some humor to those of us that got the reference...which this thread does need a little bit of, from time to time.

Yes indeed! And letting the mind run loose a little sometimes brings enlightenment

Sandgroper
Posts: 66
Joined: Tue Mar 04, 2008 8:40 am

### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

Interesting to see photos just released not sure if they come from a 777:

Sandgroper

LandSweetLand
Posts: 185
Joined: Sat Mar 08, 2014 10:47 pm

### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting Lizzie (Reply 80):It's a more rigorous version of Sherlock Holmes's "When you have eliminated the impossible, whatever remains, however improbable, must be the truth." Or rather "As you eliminate the more probable, whatever remains, however initially improbable, becomes more likely".

So essentially we're assuming it's somewhere on planet earth and now determining where it isn't
 Quoting Sandgroper (Reply 82):Interesting to see photos just released not sure if they come from a 777: http://www.watoday.com.au/national/m...d-about-debris-20140424-376li.html

Not sure, it almost looks like some kind of kayak shell to me.

[Edited 2014-04-24 04:15:13]

[Edited 2014-04-24 04:16:54]

YoungMans
Posts: 432
Joined: Sat Mar 15, 2014 10:31 am

### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting Sandgroper (Reply 82):Interesting to see photos just released not sure if they come from a 777

Interesting indeed; finally we have a few photos of at least one item from all the debris they are talking about.

It would seem this could be part of an aluminium dinghy. The white parts look like aluminium and could be the right thickness. The brown stuff doesn't look like timber. Instead it looks like the floatation foam under the seats and various other places in aluminium dinghies. It's hard to place, though, where exactly this piece would fit, without being able to have a really good look at it.

Whatever it comes from, there must have been fairly strong forces acting on it, tearing the material just like that.

Maybe this will solve a totally different case that the WA police has been working on..!?

Is there a fisherman on the thread who can expand on this..??

Lizzie
Posts: 130
Joined: Wed Apr 02, 2014 11:18 am

### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting LandSweetLand (Reply 84):So essentially we're assuming it's somewhere on planet earth and now determining where it isn't

More or less - Calculatus Eliminatus.

But this is (IMO) a serious point, and applies to all aspects of this mystery. What happened was a very low probability event, and the factors that contributed to it were very low probability events. But it happened, and so some of those causal low probability events must have occurred, and in the absence of anything other than frequency distributions for such events to go on, then a Bayesian approach is one way of getting one's intuitions straight.

YoungMans
Posts: 432
Joined: Sat Mar 15, 2014 10:31 am

### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting Lizzie (Reply 86):More or less - Calculatus Eliminatus.

This reminds me of a German saying, which of course is getting away completely from the subject we are discussing here.

"Being organised means:
You know where you don't have to look..!!"

WarrenPlatts
Posts: 517
Joined: Wed Mar 26, 2014 6:03 pm

### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting nupogodi (Reply 47):From a mathematical perspective (although I hated stats as almost everyone does), searching 80% of the search zone says absolutely nothing about the probability of whether the wreck is in the search zone. .... we can't say "because we haven't found it, it's probably not there". What we can say is that, if we figured we'd have 50% chance to find it in 100km^2, but we've searched 80km^2, now all we can say is that we have a 50% chance to find it in the remaining 20km^2. I hate stats. ... (In a very basic example, if you are sure you have a fair coin, getting 5 tails in a row does not mean your chance of getting heads on the 6th flip is worse than 50%)

Right analogy--wrong interpretation. If it takes 10 missions to search the entire area, but the prior probability of finding anything at all in the entire search area is 50%, then there is a 5% chance of finding something on any particular mission.

After 9 missions, 90% of the search area has been searched. The probability of finding something does not go up with each mission: i.e., it is not the case that the 1st mission had a 5% chance of finding something, but the 10th mission has a 50% chance of finding something.

Nor does the probability of finding something go down per mission: that is not what we are saying. We are saying the probability of finding something is the same on the 1st mission versus the 10th mission: 5% each. It's just that before the 1st mission, if we can say there is a 50% probability that something is in the entire search area, then after 9 missions, the overall probability that something in the search area is no longer 50%, as it was before the 1st mission: it is now only 5%.

Assuming, of course, that other area it could be in (e.g., half the entire Indian Ocean) is sufficiently large.

On this last point, if you had definitively narrowed the search to two equal sizes (say 100 km^2 each), with a 50% prob that it would be in one or the other, after having searched 90 km^2 of the first patch after 9 missions, you have narrowed the search to 110 km^2, so your chance of finding something does in fact go up: 10 km^2/110 km^2 = ~9%.

But in our case, if the wreck is not in the current search area, then there's no telling where it might be--excluding the current search area does not narrow down much the entire possibilities that include practically half the Indian Ocean.

aviators99
Posts: 54
Joined: Mon May 19, 2008 6:41 pm

### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting UALWN (Reply 74):No. unfortunately, you still only have a 1/26 chance of having chosen correctly (the money hasn't changed from one suitcase to another in all this process, right?). Which means that there's a 25/26 chance that the money is in the other suitcase. Which means that if you're given the opportunity to now select the other suitcase, you have to a) thank God for the lack of statistical knowledge of the show host; and b) choose immediately the other suitcase. (I have to admit that I don't know the exact details of this show, though.)

The Monty Hall mechanism doesn't apply to the Deal or No Deal show. The boxes are not being intentionally eliminated with knowledge of the higher valued box, unlike Monty Hall (almost abbreviated MH there). When down to 2 boxes, the odds are 50/50, as opposed to 25/26 for switching, as would be with Monty Hall. Google to read about Monty Hall vs Deal or No Deal. There are good explanations that are too long to post here. The Monty Hall problem is my favorite math topic.

bond007
Posts: 4428
Joined: Mon Mar 14, 2005 2:07 am

### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting Lizzie (Reply 44): if there is a chance it's not in the search area at all, then with every additional portion searched it becomes less likely it's there at all

That all depends on the what you think the chance of it not being in that area is, and how big the total possible search area is. We are hoping that at least they thought this had a high chance of being the correct area to start with.

The more likely you think it is in the search area, then as you said ...

 Quoting Lizzie (Reply 44):... it becomes increasingly probable that you'll find it on the next pass you take.

Jimbo
I'd rather be on the ground wishing I was in the air, than in the air wishing I was on the ground!

YoungMans
Posts: 432
Joined: Sat Mar 15, 2014 10:31 am

### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

This play with words about percentages is intriguing ....

At the onset of this particular search operation, with the AUV, it was surmised (assumed, believed) that the missing A/C could be in that area because that is where the pings were detected.

From what we now know, they have done 9 separate sweeps. What did they find? Nix..!

They have one more sweep to go to complete this area.

What are the chances they will find something this time? 50:50..; no better no worse.

If they find nothing again this time, they'll have to rethink.

[Edited 2014-04-24 06:25:07]

markak
Posts: 43
Joined: Thu Mar 20, 2014 1:14 am

### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

If the object is located in 1 of 100 boxes and my search area consists of 10 boxes selected at random then the odds of finding the object at the beginning of the search is obviously 10/100 = 10%. After I search 1 box and do not find it, the odds of finding it are now 9/99 = 9.091%. After 2 boxes 8/98 = 8.163%. etc... After 9 boxes (1 left) 1/ 91= 1.099%.

Another interesting example If my search area is 99/100 boxes the odds at the start are 99/100 = 99%.
When I have 1 box remaining and still have not found it the odds of finding it are 1/2 = 50%.

As the search continues, the odds of finding it in ANY of the remaining boxes goes down.
As the search continues, the odds of finding it in ONE PARTICULAR remaining box goes up.

In the special case where the search area includes all 100 boxes, the odds are obviously constant at 100%.

Unfortunately this is the pure world of math.
Reality is always a bit more messy and we don't know for sure that the A/C is even really in the search area or not. We don't even really know for sure what the entire "universe" of possible locations is i.e. what is the area that corresponds to 100 boxes in the analogy.

My comment about always finding an item in the LAST place you look was tongue in cheek. I should have included a smiley.

Mark

bond007
Posts: 4428
Joined: Mon Mar 14, 2005 2:07 am

### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting MarkAK (Reply 91):If the object is located in 1 of 100 boxes and my search area consists of 10 boxes selected at random

But we are hoping that's not how this search area was determined. They didn't look at the whole ocean and randomly decide to search this box first...and then the next. This was the search area that they thought had the highest probability...I'm assuming.

Jimbo
I'd rather be on the ground wishing I was in the air, than in the air wishing I was on the ground!

YoungMans
Posts: 432
Joined: Sat Mar 15, 2014 10:31 am

### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

My comment about always finding an item in the LAST place you look was tongue in cheek.

But still very interesting; and it makes sense ....

[Edited 2014-04-24 06:41:32]

lancelot07
Posts: 1078
Joined: Mon Apr 21, 2014 8:22 pm

### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting YoungMans (Reply 90):At the onset of this particular search operation, with the AUV, it was surmised (assumed, believed) that the missing A/C could be in that area because that is where the pings were detected.

only a very small part of the area of the pings is being searched now, actually it is a circle of 10 km around ping #2.
This area was almost certainly chosen because of fancy probability calculations.

Lizzie
Posts: 130
Joined: Wed Apr 02, 2014 11:18 am

### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting YoungMans (Reply 90):This play with words about percentages is intriguing ....

It isn't a play with words, it's real math, and it would have been the math used to narrow down the search area in the first place, so it's worth understanding
 Quoting YoungMans (Reply 90):What are the chances they will find something this time? 50:50..; no better no worse.

No, the chances they will find something this time is not "50:50".

If they were 100% sure that the had the right search area, then the probability that they will find it on the next sweep is higher than ever before. If they are not sure they have the right search area, then the probability will find it on the next sweep is lower than ever before.

Check the math in my Reply 80

abba
Posts: 1385
Joined: Mon Jun 06, 2005 12:08 pm

### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting MarkAK (Reply 91):If the object is located in 1 of 100 boxes and my search area consists of 10 boxes selected at random then the odds of finding the object at the beginning of the search is obviously 10/100 = 10%. After I search 1 box and do not find it, the odds of finding it are now 9/99 = 9.091%. After 2 boxes 8/98 = 8.163%. etc... After 9 boxes (1 left) 1/ 91= 1.099%.

If you KNOW the object is located in one of the boxes - then the chances are 100% when you get to to the last box and haven't found it in the previous. The chances of finding the object grow as more and more boxes are eliminated.

At first it is 10/100 - 10%. Then you eliminate 10, go on with the next 10 of the 90 now remaining. You then then get 10/90 11%. Then you take away another 10 and get 10/80 12,5 ...... In the end you have excluded 90 boxes and you still have 10 boxes to look in - and you will know it is there.

[Edited 2014-04-24 07:07:25]

[Edited 2014-04-24 07:09:49]

Trin
Posts: 167
Joined: Mon May 02, 2011 4:45 pm

### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting nupogodi (Reply 47):What we can say is that, if we figured we'd have 50% chance to find it in 100km^2, but we've searched 80km^2, now all we can say is that we have a 50% chance to find it in the remaining 20km^2.

But surely the probability percentage of finding it in the remaining 20km^2 would depend on our baseline confidence probability that the aircraft was IN the overall search area in the first place, wouldn't it?

I love all this probability mathematics - VERY interesting!

Trin
Posts: 167
Joined: Mon May 02, 2011 4:45 pm

### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting abba (Reply 96):If you KNOW the object is located in one of the boxes - then the chances are 100% when you get to to the last box and haven't found it in the previous. The chances of finding the object grow as more and more boxes are eliminated

I don't think you read his post fully. He was beginning with only a 10% sample of the available boxes.

abba
Posts: 1385
Joined: Mon Jun 06, 2005 12:08 pm

### RE: MH370 Malaysia Airlines B772 Missing Enroute KUL-PEK Part 57

 Quoting Trin (Reply 98):I don't think you read his post fully. He was beginning with only a 10% sample of the available boxes.

Yes - but as as his primes is, that an object is located in one of the boxes - and as he goes on elliminateing boxes - the chances increases.

However, if he does not know if there is an object in any of the boxes, then it is different. Then it is like having lottery tickets and opening them. If there are 100 tickets and you have got 10 - your chances at the beginning of getting the prize is 10/100. After opening the first ticket it is 9/99 then 8/98, 7/97 and so on.

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