# Ships With Multiple Fates

1. Apr 19, 2012

### John Hailey

I belong to a group of people who, inter alia, (try to) apply Bayesian Theory to miscarriages of justice eg the recent spate of medical staff arrested when rare (but to be expected eventually) clusters of deaths occur in hospitals. A somewhat opposite case has recently arisen which has generated statistical questions that are beyond our ken but may be within some of yours.

The problem has a number of stages but the first, and perhaps easiest, question is this: what is the probability that a ship that has been hijacked will subsequently sink from an unconnected misadventure?

To save time, here are the assumptions we are working with (but feel free to vary them if you prefer):
'ships' : means all vessels over 1000 tons
'hijack' : means in the last hundred years (and includes modern pirates)
'misadventure' : means accident, insurance scam etc but not for instance a ship captured by the British in the war and subsequently sunk by a German U-boat.

We have been working with a figure of 100,000 ships that qualify (but feel free to vary this if the figure is unrealsitic). You are invited to use either gut feeling or available statistics to judge hijacking and sinking rates.

As a mathematical ignoramus myself I'd very much appreciate answers that are mainly in English rather than integers, Greek letters and suchlike. Anybody who thinks they recognise the source of the problem (it has had some publicity recently) is kindly requested not to blurt it out at this stage since such knowledge may interfere with the science.

2. Apr 19, 2012

### Stephen Tashi

Do you expect someone to answer this question for you? Or is your real question how to analyze the data that you have in order to get an answer? If the question is how to analyze the data, then you'd best described the data. If you want someone to answer the question for you... well, good luck.

3. Apr 20, 2012

### John Hailey

Since I can't even follow the logic of your request, Stephen, and nobody else has responded, I will go elsewhere. Sorry to have trespassed on your time.

4. Apr 20, 2012

### StatGuy2000

John Hailey,

In order to answer your question, there are several pieces of information that are missing, including the probability of a ship being hijacked, the probability of a ship suffering a misadventure, etc.

Without these pieces of information, you cannot formulate a prior distribution (a probability distribution capturing your subjective belief in the phenomena your interesting in analyzing -- here in this case, your subjective belief in what you think the probability of ships being hjjacked). You also have not provided us with any data indicating the observed number of ships suffering misadventures, etc.

Therefore, as a statistician, there simply is not enough information for me to even assess, using a Bayesian criteria, to even address your problem.

5. Apr 20, 2012

### John Hailey

Sorry, I am used to people who conceptualise these not-exactly-knowable things by other means. However the following would be reasonable figures for ships, during their lifetime:
Probability of hijacking: one in a thousand
Probability of sinking: one in a hundred

6. Apr 20, 2012

### SW VandeCarr

Using Bayes Rule: the marginal probabilities are:probability of hijacking; P(H) and probability of sinking P(S)

You want the conditional probability of sinking given that the ship is hijacked. P(S|H)

Bayes Rule:

$P(S|H) =\frac {P(H|S)P(S)}{P(H)}= \frac{(001)(.01)}{.001}=.01$

In other words, the probability of sinking is unaffected by whether you are hijacked or not since you stated these to be "unconnected" or independent events. If sinking and hijacking were connected you would need to provide the probability that a ship was hijacked given that it sank. Otherwise the presumptive probability is simply the conjunction of two independent events.

Last edited: Apr 20, 2012
7. Apr 20, 2012

### John Hailey

Come off it, Vando, just give us the actual 'presumptive probability'. You know, "Given the numbers you have supplied I would expect approximately x number of ships to have been both hijacked and sunk."

8. Apr 20, 2012

### Antiphon

Wow. With a 'tude like that I'd like to hijack *and* sink whatever ship you're sailing in.

9. Apr 20, 2012

### John Hailey

It is true that I am impatient with mere process.

10. Apr 20, 2012

### phinds

You have already told us that you are a mathematical ignoramus. You don't need to continue to prove it.

11. Apr 21, 2012

### John Hailey

OK, OK, I understand. You (collectively) are neither going to give me the answer nor tell me, in simple terms, what more information I have to provide. I chose your group as being, in so far as I can judge these things, as the best around but as they say, 'the best is the enemy of the good'.