[SOLVED] 程序代写 AF 447

Case Study: Searching for the
wreckage of Air France AF 447

Copyright By PowCoder代写加微信 assignmentchef

L. Stone, C. Keller, T. Kratzke, J. Strumpfer
“Search for the Wreckage of Air France Flight AF 447”,

to appear in Statistical Science
[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.370.2913&rep=r

ep1&type=pdf] and
L. Stone, C. Keller, T. Kratzke, J. Strumpfer

“Search Analysis for the Underwater Wreckage of Air France Flight 447”
Fusion 2011 – July 7, Chicago, USA

[http://www.sarapp.com/docs/AF447 Slides for INFORMS Jun 2011.pdf]

1 June 2009 – AF 447 disappeared in the Atlantic Ocean
with the loss of 228 passengers and crew

2 June 2009 – Wreckage sighted by search aircraft
May 2010 – Black boxes still not found
July 2010 – U.S. company Metron engaged to use

Bayesian analysis of evidence to redirect search
20 January 2011 – Metron deliver their report on

probability map to guide search
Late March 2011 – Search resumed based on prob. map
3 April 2011 – Wreckage found on ocean floor

Air France Flight AF 447

• We’ll use their work to motivate a very simplified
example of this type of analysis

• At the time of writing, a similar search is underway for
Malaysian Airlines Flight MH 370

• Based on the locations of where “pings” were heard
from the black box flight recorders,
a grid search is being undertaken
in southern Indian Ocean by
Australia, China, Japan, Malaysia,
, South Korea,
United Kingdom and United States

How can we use Bayesian analysis?

Image source: Wikicommons

Consider a grid search is the region of the ocean around the
plane’s last known position

Bij = true iff grid [ij] contains black box flight recorder
Pij = true iff a “ping” is heard

in grid [ij]
Assume a ping can only be caused by

a black box in the same or
adjacent grid cell

Assume only [11, 12, 21]
have been searched
i.e., include only
P11 , P12 , P21

in the probability model

Grid Search for

Observations and Query

We have the following observations:
• Based on active sonar search so far we know

known = ¬b11 Ù ¬b12 Ù ¬b21
• Based on passive acoustic search so far

we know where pings have been heard
p= ¬p11 Ù p12 Ù p21

Suppose we want to evaluate the query:
P( B13 | known, p )

Inference by enumeration

Unknown = Bij’s other than

Query B13 and Known
For inference by enumeration:
P( B13 | known, p )
= α Sunknown P(B13, unknown, known, p)

If|unknown| = 12
then 212 possible combinations of values to enumerate!

Full joint distribution: P(B11, …, B44, P11, P12, P21)
We can rewrite this in terms of causes (B’s)

and effects (P’s) i.e., P( effect | cause )
P(B11, …, B44, P11, P12, P21)

= P(P11, P12, P21 | B11, …, B44) P(B11, …, B44)

Simplify the probability model

Can be simplified:
– Black box can only be in one square
– All squares equally likely (idpt)

Can be simplified:
– Pij’s are independent of each other
– Can exploit conditional independence betweenP’s and B’s

Idea: observations (pings in [11, 12, 21]) are
conditionally independent of more distant squares
given neighbouring unknown squares

Define Unknown = Fringe È Other

P( p | B13, Known, Unknown)
= P( p | B13, Known, Fringe)

Using conditional independence

22 combinations to enumerate
rather than 212 combinations!
Can manipulate query into a form
that uses this expression.

Further details

• Add other types of prior knowledge into
model, such as flight path, ocean currents

• Take account of false positives and
false negatives in detection of pings

• For a detailed derivation of these types of
calculations, see RN Section 12.7

程序代写 CS代考加微信: assignmentchef QQ: 1823890830 Email: [email protected]