Subject:
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Re: Any experience with measuring rotations?
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Newsgroups:
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lugnet.robotics.nxt
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Date:
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Sun, 21 Jan 2007 01:34:09 GMT
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Viewed:
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11607 times
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In lugnet.robotics.nxt, Rafe Donahue wrote:
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So, I guess I need a force sensor, ie, an NXT scale, but something more
than just the binary on/off of a (not sensitive enough) touch sensor.
Can you say Posterior Bayes Estimate?
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Well put quite simply...
The probability of some event A occurring given that event B has occurred
is equal to the probability of event B occurring given that event A has
occurred, multiplied by the probability of event A occurring and divided by
the probability of event B occurring.
P(A | B) = P(A) x ( P(B | A) / P(B) )
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Let’s look at a collection of red and white balls, some of which are large and
some small. Let us say there are more small white than large white. Then by
measuring the size of the ball we can improve our chances of correctly guessing
whether the ball is red or white. Now start with 50 red and 50 white. Without
knowing how the colors are distributed between the large and small balls we have
a probability of 0.5 picking a white ball. (Prior probability) If we are told
that all the small balls are white (the equivalent of a likelihood ratio), then
knowing the size will allow us to determine whether or not we have picked a
white or red (posterior probability). Imagine now that the correlation between
small and white is not perfect. Knowing how the size and color is distributed in
the population of balls, and the size of the ball we have picked, will give us a
better estimate of the color of the ball.
Bayes stated that the probability of a white ball in a population of small
balls is equal to the probability of white balls in the total population
multiplied by the probability of a small ball within the white population
divided by the probability of a small in the total population.
(Nah, I had no clue without googling
it, either.)
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Message is in Reply To:
 | | Re: Any experience with measuring rotations?
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| (...) "It's foolproof!" (...) This sounds like a good idea. I'm thinking I'm going to have to work out a sequence of more than just two shades, but that's what weekends are for, right? So, if I could make of sequence of colors that have increasing (...) (17 years ago, 20-Jan-07, to lugnet.robotics.nxt)
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