How to search for a lost object

The joke goes, that a drunk searches for lost keys right under the street lightning, because there its easier. But how would a mathematican do it?


John Pina Craven found a lost nuclear bomb  in deep sea.
The method he applied was Bayesian search theory.
In 1866 a US B52 bomber exploded over Spain:

The aircraft and hydrogen bombs fell to earth near the fishing village of Palomares. [...] Three of the weapons were located on land within 24 hours of the accident—two had exploded on impact, spreading contaminated material while a third was found relatively intact in a riverbed. The fourth weapon could not be found despite an intensive search of the area—the only part that was recovered was the parachute tail plate, leading searchers to postulate that the weapon's parachute had deployed, and that the wind had carried it out to sea.

The search for the fourth bomb was carried out by means of a novel mathematical method, Bayesian search theory, led by Dr. John Craven. This method assigns probabilities to individual map grid squares, then updates these as the search progresses. Initial probability input is required for the grid squares, and these probabilities made use of the fact that a local fisherman, Francisco Simó Orts, popularly known since then as "Paco el de la bomba" ("Bomb Frankie"), witnessed the bomb entering the water at a certain location. Orts was contacted by the U.S. Air Force to assist in the search operation.

The method applied in one of the four areas identified as probable target [i]

Scoring, you doing it wrong

Business Schools all over the world seem to teach scoring methodologies.[i] Douglas W. Hubbard[ii] and L. Anthony Cox[iii] have shown that there are fundamental flaws in their application, thus they are valued by the authors as counterproductive. “All of them, without exception, are borderline or worthless. In practices, they may make many decisions far worse than they would have been using merely unaided judgments.”[iv] First I will present the case study of a seminar I attended where their arguments are applied and proven right, second (in a later article) I will present the case of a consumer test, where I propose that the design of scoring led not to “borderline or worthless” results.

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[i] This is anecdotal evidence: I encountered the practice frequently when attending seminars, trainings and workshops in the field

[ii] Hubbard 2009,  http://books.google.at/books?id=e0IoQJcn1-YC

[iii] Cox 2008,  http://www.risksociety.org.nz/file-uploads/risk%20matrix.pdf

[iv] Hubbard 2009, http://books.google.at/books?id=e0IoQJcn1-YC

Hair Salon Simulation now under creative commons

So, as told in my last post I tried hard to argue that immeasurables exist,... and failed miserably. Thats a good reason to start a AIE Group at TIS.

I declare my first Excel Model, the Vienna Hair Salon Simulation as licensed under a Creative Commons Attribution 3.0 Unported License.

Here the Problem and its Solution rawly traduced via Google Translate:

How many salons there are in Vienna?

I put the following considerations:

1. There are approximately 1.8 million "Wiener"
2. Almost all have hair and almost all cut not privately
3. Viennese cut them every one to two months
4. The hairdressers work about 220 days a year, but some part-time
5. Pro Salon work 1-4 Hairdressers
6. A hairdresser needs 20min to 1h for a haircut

From this I calculate the number of salons. Because the calculation is not just simple add up, I make a Monte Carlo simulation.

The result is that the most likely number of hair saloon is between 0 and 2000.

I queried the Yellow Pages after and as of may 9th , 2010 there are 1136 registered salons in Vienna.

The dirty truth is that the model tends to favor slightly the 0-200 salons bin. Of course the Garbage-In/ Grabage-Out Principle says you can't look at the details if your model is that rough. So the result is fairly good.

A Measurement Challenge

Today I postet the following comment to Douglas Hubbards forum:

Mr. Hubbard,

I’ m a Software Developer from Italy with a passion for the ‘uncertainty sciences’ last century gave us so plentiful. I’ve read both your books and I am about to order the second edition of HTMA. In fact I am so intrigued by AIE methodology that I convinced some quantitatively skilled colleagues to set up a workgroup to apply AIE on some relevant problems to us.

I want to say it’s an honor to confront you with a measurement challenge. Let’s start:

The Swiss bank UBS published an article in its ‘UBS investor’s guide’, special edition April 2010, predicting the outcome of the FIFA 2010 Soccer World Cup. http://www.ubs.com/1/e/bank_for_banks/news/topical_stories/edition_10.html

You will agree this is a relevant problem, as the 'uncertainty reduction' on the game’s outcome will give an advantage in sports-betting.

With hindsight, they failed the prediction miserably, claiming:

(1) Brazil is most probable winner – didn’t reach the semis

(2) Germany and Italy likely to go far – true for Germany (3th in Rank) but Italy didn’t survive the first round.

(3) “Spain – favored by many – will likely not do well, and could exit before the semi-final stage” – Spain won the World Cup.

UBS has now an inglorious record of 1 success in 3 attempts - Wordcup 2006 went good, but European Championship 2008 and Wordcup 2010 failed.

I am inclined to argue that you can’t predict the outcome of the game a priori.

1. UBS likely has built a state of the art econometric model but the conclusive verdict about the rightness of the model can only be “it works”. This show: you certainly can make a sound argument about how you measure it, but still failing miserably.

2. But you cannot know if your model is right or you had luck. This is so because the experiment is not repeatable well. The basic dilemma of social sciences: social systems are complex and adaptive. Using a model: the stochastic process is itself complex, if not random. When we cope with induction we can only believe in the stable nature of the stochastic generator. What UBS’ case tells me: there is anecdotal evidence that the underlying principles of “who wins” are not stable. You cannot say if it will work for the next FIFA world championship or not, making it useless.

3. But probably even if you would know the exogenous factors that influence the game, I suspect the endogenous factors in the system are much more important. Making any reasonable forecast before the games started futile.

Mr. Hubbard: can you measure it?

Sincere Regards,

Roland Kofler

Don't have an opinion, build a model

In medicine as in life we have to distinguish emotions and ratio. This is the hardest task ever. Metaphysics succeeds because it simply discounts the problem. So does post-modernism.

But Paul Meehls does not look away.

The machine decides same or better than the intuition. A well ignored secret since 50 years.

http://www.tc.umn.edu/~pemeehl/167GroveMeehlClinstix.pdf

Wieviele Friseursalons gibt es in Wien?

Der berühmte Physiker Enrico Fermi war dafür bekannt, dass er aus einfachen Beobachtungen präzise Abschätzungen (nicht nur) physikalischer Phänomene herleiten konnte. So soll er durch wehende Papierschnipsel die Detonationsenergie des ersten Atomversuchs abgeleitet haben. Seine Studenten mussten knifflige Schätzprobleme lösen, wie durch Gedankenexperiment die Anzahl der Klavierstimmer in Chicago ermitteln.

Fasziniert von der Methodik habe ich mich darangemacht mein eigenes "Fermi Problem" zu stellen und zu lösen:

Wieviele Friseursalons gibt es in Wien?

Ich stellte folgende Überlegung an:

1. Es gibt ca. 1,8 mio Wiener
2. Fast alle haben genügend Haare und fast alle schneiden sie nicht privat
3. Sie schneiden sie alle ein bis zwei Monate
4. Die Friseure arbeiten ca. 220 Tage im Jahr, aber einige Teilzeit
5. Pro Salon arbeiten 1 bis 4 Friseure
6. Ein Friseur braucht 20min bis 1h für eine Frisur

Daraus errechne ich mir nicht die minimale mögliche und maximale Anzahl der Salons, denn die Rechnung besteht nicht nur aus simplen aufaddieren, sondern aus mehreren sich beeinflussenden Variablen. Ich mache eine Monte Carlo Simulation.

Der wahrscheinlichste Anzahl der Friseure liegt immer zwischen 1000 und 2000.

Ich schlage im Herold nach und es gibt 1136 eingetragene Friseursalons in Wien.

Zum nachvollziehen habe ich die ganze Simulation auf Google Docs hochgeladen.

Würde mich freuen wenn jemand Fehler findet.

Unterdurchschnittliche F&E Ausgaben in Suedtirol

Prozentueller Abstand wie folgeneder:

Oesterreich 2x soviel wie Italien, 2x soviel wie Trentino, 2x soviel wie Suedtirol

Aber die Suedtiroler Unternehmen realisieren anteilmaessig das Beduerfniss nach Forschung ueberdurchschnittlich

Bericht Astat