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Math Help - Likelihood function, practical use

  1. #1
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    Likelihood function, practical use

    Hi guys,
    Is possible to solve this kind of problem using Maximum Likelihood Estimator?

    Say we have some vector field:

    | x,y,z | 5,5,9 | 2,1,4 |
    | 8,8,4 | 1,2,8 | 5,7,3 |
    | 6,7,2 | 4,7,8 | 9,9,7 |

    And for example we want to find the the location at the field, where the vector would be more or less similar to (9,9,9).
    The possible solution could be two peaks of MLE: |9,9,7| or |8,8,4|

    So is there the way to solve such kind of problems using Gaussian likelihood, or MLE or any other statistical tools?
    Thanks a lot guys
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  2. #2
    Grand Panjandrum
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    Re: Likelihood function, practical use

    Quote Originally Posted by angrykid View Post
    Hi guys,
    Is possible to solve this kind of problem using Maximum Likelihood Estimator?

    Say we have some vector field:

    | x,y,z | 5,5,9 | 2,1,4 |
    | 8,8,4 | 1,2,8 | 5,7,3 |
    | 6,7,2 | 4,7,8 | 9,9,7 |

    And for example we want to find the the location at the field, where the vector would be more or less similar to (9,9,9).
    The possible solution could be two peaks of MLE: |9,9,7| or |8,8,4|

    So is there the way to solve such kind of problems using Gaussian likelihood, or MLE or any other statistical tools?
    Thanks a lot guys
    There is not enough information or context to make this problem likely to recieve a useful reply. Please provide more backgrouns and context.

    CB
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  3. #3
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    Re: Likelihood function, practical use

    Thank you for quick reply!
    Ok, I'll try to explain in different way.
    Say for example we have a fixed array of vectors, i.e.:

    a0{x0,y0,z0}, a1{x1,y1,z1}, a2{x2,y2,z2}, ..., an{xn,yn,zn}

    And say, the vectors are defined as:
    a0={2,6,8}, a1={4,6,1}, a2={7,8,7} and so on...

    I want to find the vector which is closest match to {7,7,7}
    The solution might be a2, as it quite close.

    I know it could be done using Euclidean distance, but just wondering is it possible to use any statistical tool? For example MLE?
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  4. #4
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    Re: Likelihood function, practical use

    Maybe it might help to understand the background of my problem:

    The room is scanned by 3-axis magnetometer at the same height, so I have a matrix of measurements (16 points). Each measurement contain 3 values - magnetic field intensity in each direction (Tx, Ty, Tz). Therefore it could be possible to estimate an object position in the room, by reading the data from magnetometer (which is attached to the object) and comparing that data to the map-data.

    Hope that will make more sence
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