Communities

Writing
Writing
Codidact Meta
Codidact Meta
The Great Outdoors
The Great Outdoors
Photography & Video
Photography & Video
Scientific Speculation
Scientific Speculation
Cooking
Cooking
Electrical Engineering
Electrical Engineering
Judaism
Judaism
Languages & Linguistics
Languages & Linguistics
Software Development
Software Development
Mathematics
Mathematics
Christianity
Christianity
Code Golf
Code Golf
Music
Music
Physics
Physics
Linux Systems
Linux Systems
Power Users
Power Users
Tabletop RPGs
Tabletop RPGs
Community Proposals
Community Proposals
tag:snake search within a tag
answers:0 unanswered questions
user:xxxx search by author id
score:0.5 posts with 0.5+ score
"snake oil" exact phrase
votes:4 posts with 4+ votes
created:<1w created < 1 week ago
post_type:xxxx type of post
Search help
Notifications
Mark all as read See all your notifications »
Q&A

Comments on Search & Probability

Post

Search & Probability

+1
−2

Search Grid

Above is a $2 \times 2$ search grid constructed to search for a lost object.

We begin by not knowing anything and hence if F = finding the object in a particular square, $P(F) = \frac{1}{4}$. Figure A.

We check $1$ square and we don't find the object (that's figure B with one square redded out). We now update $P(F)$ for the remaining $3$ squares: $P(F) = \frac{1}{3}$.

We then search a 3rd square (figure C) and update $P(F)$ accordingly, $P(F) = \frac{1}{2}$

From what I can gather, this is a brute search method and although we can compute the probabilities (vide supra), they don't allow us to refine the search (they do not aid us in any way at all because all the options are equiprobable).

Question: Is there a way we can "remedy" this i.e. (somehow) make $P(F)$ different for each square, which would allow us to shorten the path to finding the lost object (vide infra)

Search Grid 2

History
Why does this post require attention from curators or moderators?
You might want to add some details to your flag.
Why should this post be closed?

1 comment thread

Well, I guess you could find a piece of paper with additional information in the visited square. *Som... (3 comments)
Well, I guess you could find a piece of paper with additional information in the visited square. *Som...
celtschk‭ wrote 4 months ago

Well, I guess you could find a piece of paper with additional information in the visited square. Somewhere the extra information must come from, after all.

Hudjefa‭ wrote 4 months ago

As you can see, the probabilities $P(F)$ do get updated post a null search result, but it doesn't provide clues as to which of the next squares to search.

celtschk‭ wrote 4 months ago · edited 4 months ago

Of course it does. If the top right square now has a probability of $2/3$, then this means it is twice as likely in the upper right square than not. Which is a very strong hint that this square is the one which should be looked at next. Indeed, the probability distribution is exactly that: The information we have about the square in which we will find the object.

Originally, the probability is $1/4$ in each square, which tells us that we know the object is in one of the squares (because the probabilities for the squares add up to 1; if they didn't, there would have to be a fifth option with positive probability, because the sum of all options must be one), but we have zero information about which one it is in (because the probability is equal in all squares).

Searching that square tells us that the object is not there, but gives us zero information in which of the other squares it will be found, therefore the three other squares still have equal probability.