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Estimation

  • Lyric copyright by Jeff Witmer
    may sing to tune of "Let it Be" (Paul McCartney/Beatles)

    When I find myself with normal data,
    William Gosset comes to me
    Speaking words of wisdom, Use a t.

    If my NP plot is linear
    but sigma isn't known to me
    This is not a problem, Use a t.

    Use a t, use a t, use a t, use a t
    Student knows the answer: Use a t.

    And when the broken hearted students
    in a stats class can't agree
    You can show the answer: Use a t.

    Some want to use a Z test,
    and a chi-square is a mystery
    The truth is very simple: Use a t

    Use a t, use a t, use a t, use a t
    Student knows the answer: Use a t.

    And when your thoughts are cloudy,
    RA Fisher may not hear your plea
    But Gosset will deliver, with a t.

    He knows you are trying
    and he wants to set your mind at ease
    Don't think twice about it, use a t.

    Use a t, use a t, use a t, use a t
    Student knows the answer: Use a t.

  • MLE

    Lyric ©2007 Lawrence Mark Lesser
    may sing to tune of "Let it Be" (Paul McCartney/Beatles)

    When I'm in need of estimation,
    Ronald Fisher comes to me,
    Speaking words of wisdom: MLE.
    And though there may be bias,
    this will vanish asymptotically,
    Speaking words of wisdom: MLE
    MLE, MLE, MLE, MLE,
    whisper words of wisdom, MLE.

    And when the statisticians
    put a focus on efficiency,
    There will be an answer: MLE.
    For samples really large, tell me:
    where's the lowest M.S.E.?
    There will be an answer: MLE.
    MLE, MLE, MLE, MLE,
    there will be an answer, MLE.

    And when a theta hat is found
    to be theta's MLE,
    Then g of theta has what MLE?
    Well, if g is 1-to-1,
    an invariance property
    Says g of theta hat is the MLE.
    MLE, MLE, MLE, MLE -
    the most likely answer is MLE.
    MLE, MLE, asymptotic normality --
    whisper its precision, MLE.

  • Sung by Gurdeep Stephens. Lyrics copyright and music performed by Michael Greenacre.
    See also their "The Millenium Song" project.
    May sing to tune of "It Don't Mean a Thing (If It Ain't Got That Swing)" (Duke Ellington and Irving Mills)

    It don't mean a thing if you don't do modelling,
    Doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-waah
    It don't mean a thing if you don't do modelling,
    Doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-waah

    It don't matter if you're frequentist or Bayesian,
    You just need a model with some alphas and betas, and x's and y's, and i's and j's and k's in

    So it don't mean a thing if you don't do modelling
    Doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-waah
    It don't mean a thing if you don't do modelling,
    Doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-waah
    Doo-wah-doo-wah-doo-wah-doo-wah - doo-wah-doo-wah - wah!

  • Sung by Gurdeep Stephens. Lyrics copyright and music performed by Michael Greenacre.
    See also their "The Millenium Song" project.
    May sing to tune of "The Man I Love" (George Gershwin)

    Some day it'll come along
    The model I love,
    It'll be robust and strong
    The model I love,
    And when it comes my way
    I'll put it on my resume!

    Of all the models out there,
    Is there one for me?
    I'll give it all my love and care,
    Mathematically,
    And then - finally,
    I'll get my PhD

    Maybe I'll do estimation
    Using likelihood, or least-squares,
    Or with some approximation,
    Or just eyeballin',
    That's the job we're all in.

    To get some publications,
    I'll write papers, at least two,
    For my job applications,
    I think that'll do, don't you?
    So hear me, Lord above, I'm waiting for that model I love,
    I'm waiting for the model I love.

  • Sung by Gurdeep Stephens. Lyrics copyright and music performed by Michael Greenacre.
    See also their "The Millenium Song" project.
    May sing to tune of "It Ain't Necessarily So" (George Gershwin)

    It ain't necessarily so
    It ain't necessarily so
    That for models to be formal
    Data have to be normal
    But it ain't necessarily so

    My data had values real skew,
    Relationships nonlinear too,
    But with spline-approximation
    Or Box-Cox-transformation
    My data are more normal than you.

    Now it ain't necessarily so
    That your deviance has to be low,
    Use less parameters, (pronounce: paramee-ters)
    Less alphas and betas,
    Then apply Akaike,
    Although it sounds freaky,
    And less will be more as you know...

    It ain't necessarily so
    It ain't necessarily so
    That for models to be formal
    Data have to be normal
    But it ain't necessarily so.
    It ain't necessarily - It ain't necessarily
    It ain't necessarily - It ain't necessarily
    It ain't necessarily - It ain't necessarily
    It ain't necessarily SO!

  • Sung by Gurdeep Stephens. Lyrics copyright and music performed by Michael Greenacre.
    See also their "The Millenium Song" project.
    May sing to tune of "Summertime" (George Gershwin)

    It's summertime,
    Statistical modelling is easy,
    Data are fitting,
    Explained variance is high.

    Your data are rich,
    And your model's good-looking,
    So hush, statisticians, don't you cry

  • Lyrics ©2013 by Lawrence Mark Lesser
    May be sung to the tune of "Call Me Maybe" (Carly Rae Jepsen, Tavish Crowe, and Josh Ramsay)

    I went to find people's heights, I measured each person thrice:
    The numbers didn't match nice - and I said "Oy vey!"
    When I was asked for the mean, I knew I had to come clean:
    I said it's something between - and I gave a range.

    Climb: That's variation: There is correlation
    with stat education, knowin' what's exact or maybe.

    CHORUS: Hey, I don't know mu - and that's not crazy,
    But here's my window: call it maybe.
    I can't say I'm right; I'm not laaaaazy:
    There's always error, so call it maybe.
    Hey, life's uncertain, and that's not crazy,
    But here's my window: call it maybe.
    No way to know mu - quite exaaaaactly,
    But here's my window: call it maybe.

    I give my best argument - so I can feel confident
    At ninety-five percent - for what I portray.
    I need a sense of how far - from my sample's x-bar
    My true parameters are: that's just the way.

    (Repeat Climb, Repeat Chorus)

    Bridge: Before I took a class in stats, I reasoned so bad,
    I reasoned so bad, I reasoned so, so bad!
    Before I took a class in stats, I reasoned so bad,
    And you should know that - I reasoned so, so bad!

    (Repeat Chorus, omitting vocals over first quarter;
    Repeat Bridge, except last 6 words)

    So call it maybe!

  • Lyrics copyright by Kyle White and Bradley Turnbull
    May be sung to the tune of "Jerk It Out" (Caesars)

    Theta one, theta two, which estimator do I choose?
    Both of them unbiased, what now? I'm still so confused.
    I need a better measure than just looking at means. Calculating variance is smart, it seems.
    So here we go!

    'Cause it's easy when you know how it's done.
    Invert the information when the bias is none.
    Can't beat it, bounded from below!
    C-R lower bound!

    Too bad my stat is lacking some efficiency.
    Why can't someone out there tell how to fix this please?
    Sufficient estimators will do the trick --
    condition on them, that will be my fix!
    So thank you Rao!

    'Cause it's easy when you know how it's done.
    Improve an estimator with a sufficient one.
    Just try it, you've got nothing to lose!
    Rao-Blackwell improves!

    'Cause it's easy when you know how it's done.
    Invert the information when the bias is none.
    Can't beat it, bounded from below!
    C-R lower bound

    Watch the video

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