Probability

  • Lyrics copyright by Bent Natvig and Morris DeGroot
    May sing to the tune of "Strangers in the Night" (Kaenpfert, Singleton, and Snyder)

    Bayesians in the night
    With exchangeable glances
    Assessing in the night
    The prior chances
    We'd be sharing risk
    Before the night was through.

    Something in your prior
    Was so inviting
    Something in your data
    Was so exciting
    Something in my model
    Told me I must have you.

    Bayesians in the night
    Two statisticians
    We were Bayesians in the night
    Then came the moment when we
    walked down to the sea
    Under a fault tree
    Our likelihoods were close together
    And Sir Ronald lost his final feather

    Ever since that night
    We've been adherents
    Leaders of the fight
    To have coherence
    It turned out all right
    For Bayesians in the night.

  • Lyrics copyright by Dennis Pearl and Peter Sprangers
    may sing to the tune of "I Will Follow You" (Ricky Nelson)

    Means will follow you
    Follow you as de Moivre would show
    There isn't a skewness too steep
    An "n" so high it can't keep it away

    Means must follow you
    And since the central limit shows
    That near you I always must be
    And nothing can keep you from me
    You are my density

    If n big, if n big, if n big
    Then Normal you will follow, will follow, will follow
    You'll always be symmetric, symmetric, symmetric
    With smaller deviation, deviation, deviation

    Means will follow you
    Follow you as de Moivre would show
    There isn't a skewness too steep
    An "n" so high it can't keep it away
    Keep it away, away from your curve

    If n big, if n big, if n big
    Then Normal you will follow, will follow, will follow
    You'll always be symmetric, symmetric, symmetric
    With smaller deviation, deviation, deviation

    Means will follow you
    Follow you as de Moivre would show
    There isn't a skewness too steep
    An "n" so high it can't keep it away
    Keep it away, away from your curve

    And Normal then will follow

  • Lyric copyright by Dennis Pearl
    may sing to tune of "Strawberry Fields" (John Lennon, Paul McCartney)

    Let me take you down, 'cause I'm going to the sigma-fields
    Lebesgue things are real, and nothing to get hung about
    Sigma Fields forever

    Living is easy with sets closed, and understanding all you see
    Probabilities map to zero-one and it all works out, that's what matters most to me
    Let me take you down, 'cause I'm going to the sigma-fields
    When things are Borel, there's nothing to get hung about
    Sigma Fields forever

    Sets of sets are events, I mean it must be probability
    That is you know it can't go negative or over one, that is I think it's not too bad
    Let me take you down, 'cause I'm going to the sigma-fields
    When things are Borel, there's nothing to get hung about
    Sigma Fields forever

    Always, no sometimes, probability, but you know I know a gambler's scheme
    I think I know the mean, but the measure is all wrong, that is I think I disagree
    Let me take you down, 'cause I'm going to the sigma-fields
    Lebesgue things are real, and nothing to get hung about
    Sigma Fields forever
    Sigma Fields forever
    Sigma Fields forever

  • Lyric by Mark Glickman
    may sing to the tune of "Venus" (The Shocking Blue)

    I had some extra information,
    don't know where it should go.
    A method to express this knowledge
    is what I don't know!

    I've got it, yeah, baby, I've got it!
    Well, I'm the thesis, I'm the prior that you require!
    Well, I'm the thesis, I'm the prior that you require!

    I had myself a complex model
    I didn't know how to constrain.
    I tried to estimate the unknowns.
    My attempts were in vain!

    I've got it, yeah, baby, I've got it!
    Well, I'm the thesis, I'm the prior that you require!
    Well, I'm the thesis, I'm the prior that you require!

  • Lyric by Mark Glickman
    may sing to the tune of "Time of the Season" (The Zombies)

    It's the time to be Bayesian --
    Don't get me wrong.
    I'll explain all of the reasons
    to pitch your long-run frequency.

    You formulate a prior
    density
    to represent beliefs.
    It's the time to be Bayesian in thinking!

    Who is Bayes? (Who is Bayes?)
    What's the difference? (What's the difference? Is this...)
    Is this MLE?
    Why've you taken (Why've you taken)
    all my time (all my time, to show)
    to show you probability?

    You run a Monte Carlo
    Markov chain
    for model summaries.
    It's the time to be Bayesian in thinking!

  • Lyric by Mark Glickman
    may sing to the tune of "December, 1963 Oh What a Night" (Bob Gaudio and Judy Parker)

    Oh what a prior
    A unimodal proper density
    She captured all my subjectivity
    What a function, what a prior

    Oh what a prior
    Tall and thin, right then I understood
    She towered over every likelihood
    Oh I believed her, what a prior

    Oh I, I fit a Bayesian model after all
    and assumed
    that my results would verify the truth

    Oh what a prior
    Elicited from deep inside my head
    Expert thought I would not use instead
    Oh I committed to the prior

    I saw the others dressed in uniform attire
    But when she came to me, I knew my data would not defy her!

    Oh what a prior
    I was so sure but I could make no sense
    Of this false posterior inference
    Oh I got bitten by a prior

  • Lyric copyright Mary Pat Campbell
    may sing to the tune of "Take a Chance on Me" (ABBA)


    If you roll your dice, and you want the price
    calculate for me
    probability
    If you want to break even, gotta know the chance
    (If you're not too careful then you can lose your pants.)
    When you play a game, matching coins the name,
    calculate for me
    probability
    If the chance for heads is p and for tails it's q
    When we count the flipped coins up, we know what to do

    Take a chance with me
    (What's the distribution, honey?)
    Take a chance with me

    Look at geometric
    Look at binomial
    Get expected value
    1 over p's the first one
    np gives the second
    sum up to find it's true
    'Cos you know the Law!
    Large Numbers says it's sure
    Average X_i's to secure
    the limit --
    EX is where it goes (just as you would suppose)
    Random stuff dies out
    (infinity's got clout)


    It sure can be tough, knowing when to bluff
    calculate for me
    probability
    poker, bridge and backgammon's where you need the odds
    & quantum mech will tell us that we're the dice of God
    Markov models tell brokers when to sell
    calculate for me
    probability
    DNA analysis and learning systems too
    If you get some good priors, Bayes will work for you.

    Take a chance with me
    (Come on, conditional is cool)
    Take a chance with me

    Walk on the lattice
    each edge is weighted equal
    will you return to zero?
    In dimension higher than two -
    if you keep on goin' --
    the answer's gonna be no
    'Cos it's transient!
    But some paths will recur
    of this you can be sure
    It's magic!
    1 and 2D gets you there
    as long as the walk is fair
    though the variance strays, the paths don't get away
    (straying paths don't quit, though there's no last visit)

    If you roll your dice, and you want the price
    calculate for me
    probability
    If you want to break even, gotta know the chance
    (If you're not too careful then you can lose your pants.)
    When you play a game, matching coins the name,
    calculate for me
    probability
    If the chance for heads is p and for tails it's q
    When we count the flipped coins up, we know what to do
    (take a chance, take a chance, take a chance with me)

    ba ba ba ba baa, ba ba ba ba baa
    Calculate for me
    Probability
    poker, bridge, and backgammon, baby can't you see
    it's the way the real world works - probability
    (Take a chance, take a chance, take a chance with me)

    ba ba ba ba baa, ba ba ba ba baa
    it's reality--
    probability

    (fade)

  • Lyric copyright by Dennis Pearl
    May sing to the tune of "I'd like to teach the world to sing" (The New Seekers)

    I'd like to build the world a school
    for students who just love
    to know frequencies and m.l.e.'s
    and stuff statistics solves

    I'd like to teach the world to think
    with probability
    and know to hold the null as fixed
    in calculating p

    I'd like to see the world for once
    all basing things on facts
    and hear them try to gather more
    and find what data lacks
    (that'll make it clear)

    I'd like to teach the world to think
    of reliability

    I'd like to teach the world to think
    with probability

    I'd like to build the world a school
    for students who just love
    to know frequencies and m.l.e.'s
    and stuff statistics solves

    I'd like to teach the world to think
    with probability
    and know to hold the null as fixed
    in calculating p

  • Lyrics and music ©2012-2013 by Lawrence Mark Lesser

    I heard of chance in math class while glancing at Sue from afar;
    Ev'ry outcome equally likely, rolling a die or drawing cards.
    And that gave me hope: she'll either love me or she won't,
    So chances must be 1 in 2 that I'll win Sue!

    Now I got me a ticket for the lottery: either I hit jackpot or I don't.
    So easy to win: I'm ready to spend, and I'll try hard not to gloat
    From my mansion, financed by this 50-50 chance
    To make my dream come true - - me and Sue!

    But odds were "odd" 'cause who would guess
    Having 1 in 2 chances, twice with no success?!

    It's just as well we never jelled: I know divorce hits 1 in 2.
    And lottery's no draw for me: my ping pong ball days are through (they were numbered)!
    Yeah, I'm movin' on - - what I knew was wrong:
    There's more to chance I must pursue, like 1 in 2. Will skies be blue? 1 in 2.

  • Lyric © 2007 by Lawrence Mark Lesser
    May sing to the tune of "One" (Harry Nilsson)

    One is the likeliest number that you'll ever view.
    Two's the next most likely one --
    It's the likeliest number since the number 1
    Benford's the oddest law you'll ever know
    Frequency falls as the digits grow
    'Cause one is the likeliest number that you'll ever view
    One is the likeliest number, more than two

    BRIDGE: They came and took our head accountant away
    They caught his fraud using Benford's law yesterday

    One is the likeliest number, one is the likeliest number
    One is the likeliest number that you'll ever view
    One is the likeliest, one is the likeliest
    One is the likeliest from a power rule

    They came and took our head accountant away

    (Number) one is the likeliest (Number) one is the likeliest
    (Number) one is the likeliest number that you'll ever view
    (Number) one is the likeliest (Number) one is the likeliest
    (Number) one is the likeliest number that you'll ever view

Pages

register