Poems

Why quatrains in a statistics textbook? It’s explained, tongue in cheek, on p. 2:

the chapters commence with a stanza of elegant and insightful verse composed by a famous poet. The quatrains¹ are formed of dactylic² tetrameter³, or, colloquially speaking, “country waltz” meter. The poems regard conceptual themes of the chapter via allusion from immortal human motifs in waltz timing.

¹ quatrain [noun]: Four lines of verse. Unless it’s written “qua train,” in which case it’s a philosopher comparing something to a locomotive.

² dactylic [adjective]: A metrical foot in poetry comprising one stressed and two unstressed syllables. Not to be confused with a pterodactyl, which was a flying dinosaur, and which probably sounded nothing like a dactyl unless it fell from the sky and bounced twice: THUMP-bump-bump.

³ tetrameter [noun]: A line of verse containing four metrical feet. Not to be confused with a quadraped, which has four feet, but is averse to lines.

Ch 1. What’s in this book (read this first!)

Oh honey I’m searching for love that is true,
But driving through fog is so dang hard to do.
Please paint me a line on the road to your heart,
I’ll rev up my pick up and get a clean start.

Notes

This chapter provides a road map to the book, which hopes to have you fall in love with Bayesian analysis even if you previously had unhappy relationships with statistics. The poem plays with those ideas.

Ch 2. Introduction: Credibility, Models, and Parameters

I just want someone who I can believe in,
Someone at home who will not leave me grievin’.
Show me a sign that you’ll always be true,
and I’ll be your model of faith and virtue.

Notes

This chapter introduces ideas of mathematical models, credibility of parameter values, and the semantics of models. The poem plays with the words, “model,” “believe,” and “true,” in an everyday context, and hints that Bayesian methods (personified) may be someone to believe in. (And yes, grammatically, the first line should be “in whom I can believe,” but the poem is supposed to be colloquial speech. Besides, the grammatically correct version is iambic not dactylic!)

Ch. 3. The R Programming Language

You said, dear Descartes, that “je pense, donc je suis,”
Deriving existence from uncertainty.
Now, you are gone, and we say, “au revoir,”
Doubtless we think, René, therefore we R.

Notes

This chapter introduces the programming language R. The poem provides motivation for using R, primarily in the form of an extended setup for the final pun on the word “are.” Further background: The French philosopher and mathematician, René Descartes (1596-1650), wondered how he could be certain of anything. The only thing he could be certain of was his own thoughts of uncertainty, and therefore he, as thinker, must exist. In English, the idea is captured by the phrase, “I think therefore I am.” Changed to plural, the phrase becomes “we think therefore we are.”

Ch. 4. What Is This Stuff Called Probability?

Oh darlin’ you change from one day to the next,
I’m feelin’ deranged and just plain ol’ perplexed.
I’ve learned to put up with your raves and your rants:
The mean I can handle but not variance.

Notes

This chapter discusses ideas of probability distributions. Among those ideas are the technical definitions of the mean and variance of a distribution. The poem plays with colloquial meanings of those words.

Ch. 5. Bayes’ Rule

I’ll love you forever in every respect
(I’ll marginalize all your glaring defects)
But if you could change some to be more like me
I’d love you today unconditionally.

Notes

This chapter is about Bayes’ rule, which shows how marginal probabilities relate to conditional probabilities when taking data into account. The terms “marginal” and (un-)“conditional” are used in the poem with their colloquial meanings. The poem also plays with the reversal of meaning between conditional and unconditional: The poem says that the conditional love, p(love|change), is greater than the marginal love, p(love), but ironically says that satisfying the condition would bring unconditional love

Ch. 6. Estimating a Binomial Probability

I built up my courage to ask her to dance
By drinking too much before taking the chance.
I fell on my butt when she said see ya later;
Less priors might make my posterior beta.

Notes

This chapter is about using the beta distribution as a prior distribution for the Bernoulli likelihood function, in which case the posterior distribution is also a beta distribution. The poem explains another way to make a posterior beta.

Ch. 7. Markov Chain Monte Carlo

You furtive posterior: coy distribution.
Alluring, curvaceous, evading solution.
Although I can see what you hint at is ample,
I’ll settle for one representative sample.

Notes

This chapter is about methods for approximating a posterior distribution by collecting from it a large representative sample. These methods are important because complex posterior distributions are otherwise very challenging to get a handle on. The poem says merely that complexly shaped posterior distributions are evasive, but instead of demanding a precise solution, we will do practical analysis with a representative sample. Some people have suggested that the poem seems to allude to something else, but I don’t know what they could mean.

Ch. 8. JAGS

I’m hurtin’ from all these rejected proposals;
My feelings, like peelings, down garbage disposals.
S’pose you should go your way and I should go mine,
We’ll both be accepted somewhere down the line.

Notes

This chapter is about the software package “JAGS,” which stands for Just Another Gibbs Sampler. In Gibbs sampling, unlike Metropolis sampling, all proposed jumps are accepted, but all jumps are along a line parallel to a parameter axis. The quatrain personifies two different parameters in Gibbs sampling: they go orthogonal directions but both are accepted somewhere down the line.

Ch. 15: The Generalized Linear Model

Straight and proportionate, deep in your core
All is orthogonal, ceiling to floor.
But on the outside the vines creep and twist
’round all the parapets shrouded in mist.

Notes

The poem is a metaphorical description of the generalized linear model (GLM). The core of the GLM is a linear combination of predictors; the resulting value is proportional to the magnitudes of the predictors, as described in the poem. The GLM can have a nonlinear inverse link function; this is the twisting vine in the poem. The GLM has a random noise distribution that obscures the underlying trend; this is the shrouding mist of the poem.

Ch. 19: Metric Predicted Variable with One Nominal Predictor

Put umpteen people in two groups at random.
Social dynamics make changes in tandem:
Members within groups will quickly conform;
Difference between groups will soon be the norm.

Notes

The models in this chapter are analogous to traditional analysis of variance (ANOVA), which partitions variance into within-group variance and between-group variance. The poem suggests that for groups of people, within-group variance tends to decrease while between-group variance tends to increase.

Ch. 21: Dichotomous Predicted Variable

Fortune and Favor make fickle decrees, it’s
Heads or it’s tails with no middle degrees.
Flippant commandments decreed by law gods, have
Reasons so rare they have minus log odds.

Notes

This chapter is about logistic regression, and one of the concepts is called “log odds,” explained in Section 21.2.1. I was fortunate to rhyme “log odds” with “law gods” and then work backwards to their names, Fortune and Favor.

Ch. 23: Ordinal Predicted Variable

The winner is first, and that’s all that he knows, whether
Won by a mile or won by a nose. But
Second recalls every inch of that distance, in
Vivid detail and with haunting persistence.

Notes

This chapter is about modeling ordinal data. The poem emphasizes the emotional difference between ordinal and metric measurement.

Ch. 25: Tools in the Trunk

She changes her hair, and he changes his style,
She paints on her face, and he wears a fake smile,
She shrink wraps her head, and he stretches the truth,
But they’ll always be stuck with their done wasted youth.

Notes

One of the topics in this chapter is reparameterization, in which parameters of a model are transformed into new parameters. For example, a rectangle can be described in terms of its length and width, or in terms of its area and aspect ratio, where area = length x width and aspect ratio = length/width. Either way, it’s the same rectangle. The poem personifies reparameterization.

Doing Bayesian Data Analysis, 2nd Edition , Academic Press, 2015.

Looking east before sunrise I like to
see the slender crescent moon (sky haiku
so abbreviated it is only
an opening parenthesis, holy
punctuation setting aside last night’s
constellations, planets, and satellites
as mere afterthoughts like the Milky Way,
which justify staying living for today).

The Orchards Poetry Journal , Winter 2024 (7 December 2024), p. 115.
Download PDF file.

Notes

This poem tries to embody the scene it describes. The words “cresent moon” are immediately illustrated by an opening parenthesis, “(”, and all the elements of the night sky are contained by the parenthetical remark. Notice the lines are decasyllabic (10 syllables). Notice also the triple rhyme of “I like to” with “sky haiku”.

SAGE Magazine , 17 February 2025

Notes

The poem is intended to be read first as in standard English, left to right, top to bottom, then to be read again as a geologist would read strata, from bottom to top, and right to left. Feel your eyes as you read upward. The poem is formatted to resemble a rock formation in Monument Valley and The Valley of the Gods.

When you consider
the carbon footprint
of butt sitting,

manufacturing text for hours, flushing
wasted words up the delete-key smokestack
while the glaciers and ice caps melt,

then you realize
this poem has
enormous power for change

because the depth of its impact
is how much
it made the oceans rise.

The Lake , 01 March 2025.

Notes

This poem was provoked, in part, by reading this article: “The carbon emissions of writing and illustrating are lower for AI than for humans.” Tomlinson B, Black RW, Patterson DJ, and Torrance AW. Scientific Reports, 2024, 14(1):3732. DOI: 10.1038/s41598-024-54271-x Of course, the carbon emissions of (humans) writing quick doggerel are less than the carbon emissions of (humans) writing carefully crafted and moving poetry. Is it worth the cost?

Any time spent
Not making babies.
Or not making money.

Any time spent
Not tilling the soil.
Or not dancing the floor.

Any time spent
Not watching the sunset.
Or watching the sunset.

Any time spent
Not being outraged.
Or being outraged.

Any time spent
Being forced to choose.
Or regretting your choice.

Any time spent
Having no choice.
Or lamenting your fate.

Any time spent
Going on living.
Or giving up.

SAGE Magazine , 17 February 2025

Notes

What is wasted time? It’s any time spent doing fruitless or worthless things, or not doing fruitful and worthy things. But what are those? Each tercet contemplates a different angle on what’s worth doing or contemplating. The first suggests what matters is production: babies and money. The second suggests (Protestant) ethics: working hard and dancing (in my mind, but not explicit in the poem, according to the traditional song Simple Gifts: “by turning, turning we come down right”). The third suggests gratitude and appreciation of beauty; but then backtracks, wondering if that’s a waste because it violates the first and second. The fourth suggests moral engagement and outrage is important, but then suggests mere outrage is unproductive. The fifth and sixth go together, pondering categories of choice, because the whole issue of How To Spend One’s Time presumes one has some degree of choice. The last tercet abstracts to the highest level. It was provoked by reading an article in the NYT about a climate activist who committed suicide but his loved ones and colleagues did not give up.

The poet steps up to the mic,
looks at us in the audience,
then reaches deep inside
and pulls out
a seashell,
twisted with finger-thick whorls,
lined with life ridges
and broken heart spires.
Cradling their seashell in their upturned hand,
the poet opens their mouth and exhales:

I can almost hear the ocean.

People lean forward
and cock their heads,
then lift their cupped hands
behind their ears.
I examine my hands
for cuppability,
and notice my palms
with fingerprints whorled,
life-lines ridged
and heart-lines broken.
I cradle these palms behind my ears
to amplify the poet’s keening.
But gradually
I turn my clam-shell hands
to cover my ears completely:

and now I hear the ocean.

The Lake , 01 March 2025.

Notes

When poets read their poems aloud, especially in the context of background noises in a crowd of people at an open-mic night, I find it challenging to hear every word and to fully comprehend the poem. Beyond comprehension, appreciation of a poem also depends on how it resonates with the listener. Perhaps, sometimes, a listener likes a poem best when it lets them hear themselves. Have you had this kind of experience listening to poetry? Is that the ocean you hear?

My shelves lift volumes covered soft and hard,
a thousand books I’ve given brief regard.
Slower gazing reveals the multitude
all clasping slender markers that protrude
like flowers lazing where the reading paused
and then expired when the flow was lost.

Like them my body is a flower clasped
between the fast-read chapters of my past
and all my future pages still untold.
After each day’s loud narration, my soul
retreats to some hidden library room
while body marks where story should resume.

The vast hillside lawn has horizontal
shelves of tightly shouldered bookmarks, some tall
some short, but all denoting interrupt-
ted narratives of people who have upped
and stuck a headstone where life was leading,
and where visitors may resume reading.

Grand Little Things , 05 February 2025.

Notes

The lines are all decasyllabic. There is intentional echoing of sounds beyond the end rhymes; for example, “slower gazing” with “flowers lazing” and with “flow was lost”. I had fun rhyming “interrupt-/ ted” with “upped/ and”. The metaphors – body as bookmark and headstone as bookmark – still affect me even after reflection, and I hope they may work for you too.

Summer’s hot and summer’s humid:
Summer’s trifling, endless, stupid.

Summer’s games waste on all night,
insects swarm under the lights,
mindless phototropic creatures,
like the people in the bleachers,
mesmerized by play-by-play,
eating dogs while they decay.

Dogs bark man at crack of dawn,
roaring mowers bite the lawn,
deaf’ning blowers blast the dust,
wound with gas exhaust disgust.

August: Annexed 8 B.C., when
Ceasar named a month “for Me!”
because his uncle Julius
already seized July from us.

July the Fourth: The flag’s still there!
The fireworks, bursting in air,
remind us all of war’s delights:
Our children’s fate is firefights.

But wait… retreat.
                                       The firefly —
in quiet night, in starlit sky,
with summer’s Milky Way aglow —
still winks of wonders yet to know.

The Tipton Poetry Journal , Issue #61, 01 Septempber 2024, p. 10.

Notes

Ever wonder why the months – September, October, November, and December – are the 9th to 12th months of the year, instead of the 7th to 10th as their names imply? Now you know: Julius Caesar and Caesar Augustus.

[Withheld until publication.]

Pine Hills Review , perhaps July 2025.

Notes

Just a love poem.

I pray to the Invisible:

Please protect us
from blizzard and hail, from blaze and swelter,
from flying insects that sting and swarm,
from pestilence and sulfurous miasma,
and from the crowded bluster and welter.

But let us see the light,
through your architectured frame,
of sun, of stars, of moon, of clouds,
of dappled leaves, of shimmering creek,
and all your gentle creatures without names.

And give us wisdom –
when through your fearsome grace,
you slay a bird mid-flight
and leave an ashen smudge
suspended mid-air in its place.

AND when non-believers
doubt your clear perfection,
then at dusk reveal the veil
of dust and spots and filth
co-mingled in their own reflection,

So then, in them,
it will grow known
that they reside within
the mercy of your windowed house
and they should not throw stones.

SAGE Magazine , 17 February 2025

Notes

Windows are miraculous. They are nearly invisible. We rely on them. Yet they depend on our treating them reverently. Do you believe in windows, even when you cannot see them? Perhaps other things too? Form: In every stanza of five lines, the second and fifth lines rhyme, with double rhymes (e.g., “architectured frame” with “creatures without names”, and “fearsome grace” with “air in its place”). Content: In the third stanza, the image of the bird slain by crashing into a window uses the words “ashen smudge”, which are an allusion to Vladimir Nabokov’s poem, Pale Fire, which begins: “I was the shadow of the waxwing slain / by the false azure in the windowpane; / I was the smudge of ashen fluff – and I / lived on, flew on, in the reflected sky.”

The sun shines fluidly on every house,
spilling over the sheep and cattle
in view of the cowboy brothers (twins
– by different fathers – it’s a long story),
while at the water’s edge a crab
scuttles unnoticed by a cat
dozing beside an adolescent girl
weighing her options, curious
of the scorpion poised
at the hooves of a centaur (yes,
a half-horse man roams this landscape)
with bow and arrow slung open-carry,
galloping to meet his chimeric brethren
the sea-goat at the seaside where
a gorgeous boy pours them wine
and two fish swim together
connected by a luminous thread,
which, star by star, connects to every
creature in this scene because
the sun shone fluidly in every house
the day each one was born,
and would keep shining even if
the cat appraised its options,
and the scorpion claimed to be crab
and the bull converted to ram
and the brothers came out as fishes
and the centaur dressed as a sea-goat
and the boy became a girl.

Flying Island Journal , 29 November 2024.

Notes

This poem suggests that a person’s sun sign at birth should not define their identity. The poem goes through all twelve signs of the zodiac, also called houses, in order: sheep = aries; cattle = taurus; brothers = gemini; crab = cancer; cat = leo; girl = virgo; weighing options = libra; scorpion = scorpio; centaur = sagittarius; sea-goat = capricorn; boy = aquarius; fish = pisces.

                              In response to a poem by X. J. Kennedy

Pushed from your mother’s womb plop into your
nursing home, or having sex while the re-
sulting teenager leaves home forever,
your skin youth smooth .blink. old-age leathery;
if all life’s moments collapsed impromptu,
the sensory flash would be too intense.
So, they quip, “the purpose of time is to
keep everything from happening at once,”
even though, in retrospect, all of life
implodes into a box we call the past.
Ironic, sure. But off. Time is a knife
that stabs into the dark of our half-assed
moral self, cleaving act from consequence,
daring us to buy now and pay later,
premeditate vengeance after grievance,
ignore the crap we flush downstream. Water
under the bridge – is always stepped in twice,
once by us and again by our descend-
ents. Time the tempter, a con-man’s device
that lures us to ignore and to pretend,
so we desire more and more of now
before the wheel of karma spins around
and slaps the future’s hand-palm on our brow
and time’s true purpose suddenly is found.

Smoky Blue Literary and Arts Magazine , Issue #22 Spring/Summer 2025, p. 29; 20 February 2025.

Notes

Notice the lines are decasyllabic, and every four lines follow an ABAB rhyme scheme. The first ten lines of this poem paraphrase the 1997 poem by X. J. Kennedy, “The Purpose of Time is to Prevent Everything From Happening at Once”.

I can’t put my finger on it, when did it
change? I would ride my bike miles from
home, even at night and in rain. No one
worried, I would just roam. It ended, maybe,
with a spoonful of cereal and a half gallon of
fear, the milk carton asking, feral and wild:
“Have you, have you, seen this child?”

When did having children become an
imposition? Mine were a gift and a reason to
keep trying, a joy and a purpose to postpone
dying. When did people reach the grim
decision that making babies would only reap
regret? Maybe it happened on the internet?
Doom-scrolling starving polar bears and
forests burning down, all trampled to death
by carbon footprints of our own. Therefore,
breeding carbon copies would only be
complicit. Ergo, we will have no
grandchildren to visit.

How did folks forget that we are children of
the universe? That we’re allowed here too.
My toddler daughter knew. At twilight
beaming pure delight, using her own voice:
“Daddy, there’s a ’tar up in the ’ky!”
Maybe, I could also give my voice a try?
Look up and hear the bluebird sing his
ancient Navajo song, “Get up, my
grandchild, it is dawn!” Reminding me that
I belong.

SAGE Magazine , 17 February 2025

Notes

This poem was provoked by thoughts of climate change. In our cultural climate, there has been a change in attitudes about children. This poem is about attitudes toward children (give them freedom, protect them from every conceivable danger), attitudes about children (they are a gift, they are an imposition), attitudes from children (joy and delight), and attitudes of our own affected by children (let’s keep trying to make things better).

[Withheld until publication.]

Blue Unicorn

Notes

Even the smallest decision is fraught with moral weight. To choose one as better is to judge the other as worse, even if no such demerit is intended. Meritocracy feels arbitrary and mendacious. Can a person remain honorable even choosing which sleeve to put on first? By the way, notice every line is decasyllabic, and every four lines follow an ABAB rhyme scheme.

                              With appreciation and apologies to Taylor Swift
                              and her wonderful song, Cruel Summer.

“No rules in breakable heaven.” Looking in your eyes,
no fools could break even. Feeling this high
there’s no falling. I’m floating light out the window,
no angel calling and time lingering slow.
No candles, no street lamps, sighing into the night.
No handles, no guard rails, resigned to the dice.

The hourglass frozen, stuck sand ice,
refracting the icicles into my eyes.
Maybe some summer we can reignite
the airborne embers once bonfire high.
If you don’t see me you’ve set your eyes low,
I’m the spark floating out the window.

I’ve paid the blizzard, what does the wind owe?
Skate on the surface, slip-and-slide ice,
even the glaciers can see we’re too slow,
just waiting and watching our love melt in sighs.
The heat from my mind in this fever-dream high
during the chill of this dark, this insomniac night.

Gravity’s lost and this space stays finite
’round the hovering door and the floating window
that sometime fall low and sometime rise high
like the spots in my eyes or the dots on the dice
that roll over the table and face up realize
that the falling is fast but the waiting is slow.

Shot by that arrow, aim high but miss low,
breaking a vase in the bouquet of night,
marking a flower right between the eyes
while the petals, aroma float out the window,
and the rose thorns and arrow heads chopped into dice
are swept under the carpet we flew magic high.

Angels are watching and advocate shy
while devils pretend to take everything slow
and keep in their pockets the gambling dice
’til everything fades in the shadow of night
and they serenade yearning outside your window
until fever compels that you look in their eyes.

“Fever dream high in the quiet of the night,”
“Killing me slow out the window.”
“Devils roll the dice, angels roll their eyes.”

Discretionary Love , 01 October 2024.

Notes

A sestina is a complex form dating back to twelfth century France. It has six stanzas of six lines each, followed by a seventh stanza, called the envoi, that has three lines. The final words of each line must be repeated in every stanza with a specific permutation from one stanza to the next. If we label the end words in one stanza as 1 2 3 4 5 6, then the end-words must be in the order 6 1 5 2 4 3 in the next stanza. The envoi must contain the same six words, two words per line. To create this poem, I first built the envoi with three phrases from Taylor Swift’s song. I also avoided repeating a word explicitly from the last line of one stanza to the first line of the next; e.g., “dice” becomes “sand ice”, “window” becomes “wind owe”, etc. In the first stanza, I tried to engage the reader by making each pair of lines have parallel sounds throughout the lines.

Dazzling synthetic threads of tangerine orange itched
me happy when I was eight years old, my favorite plaid
shirt, weft with runs of vibrant red and yellow.
Rough florescent fabric beaming brilliant orange as

marigold flowers in front of my sister’s elementary school,
named: Marigold Elementary, next to Pleasant Valley High.
Marigolds by any other name would smell as ochre,
yet they flaunted pollen-heavy petticoats under

orange bosomed trees my father grew backyard.
Thorny green-leafed branches flashing orbs of orange
skins we peeled away to tongue the sweet segmented
fruits as orange the fields of California golden

poppies on Sierra foothills at the edge of
town if springtime rains would grace the ground transform the
dirt-dry taupe-straw grass to dappled orange gauze:
draping waves of paint daubes on the hills.

At university, long afternoons I’d gaze
from Panoramic Way across the burgeoning bay
to the Golden Gate Bridge spanning sunglint waves
beneath a saffron sunset – which felt very romantic.

There I gave a girl a golden band, slid
despite her eternally seeing red. She insisted
her infernos cleared unhealthy underbrush
but in truth they only burned the greenwood black.

On a honeymoon trip to a coastal forest we puzzled at trees with
bizarrely crenulated ashen bark, solved when slanting
sunlight erupted a rapture of myriad Monarch butterflies,
tornado-thousand poppy petals sublimating sky.

I’d seen orange in trees before: father doubtful
driving our sedan through raging forest fire,
fulminating furies flaying flesh from off the trees on
both sides of the highway with no end in sight.

Long further down that road, though I nearly perished
in the flames, I repossessed the gold ring from
the arsonist girl in the home she set ablaze. The golden
bridge is sunken far below the western waves,

the orange-thread shirt is shed like an abandoned chrysalis.
Yet here the winging monarch flies unbidden into
mind, every orange flutter a flashbulb memory
migrating away, suspending me in a golden state.

Stickman Review , V23N2, 19 December 2024.

Notes

The alacritous alliterations are intended to propel the poem and give it a rhythm and musicality along with the succession of orange imagery. I’m especially fond of the phrase, “tornado-thousand poppy petals sublimating sky,” because it exactly captures the image in my mind. Notice every line is hexameter in its strongest syllables, or at least can be read that way, again intended to propel the poem rhythmically. Every stanza supports another; e.g., the shirt mentioned in the first stanza is recalled in the last, the grade schools in the second stanza are not merely to established idyllic imagery but also to set up the transition to university in the fifth stanza, the orange trees in the third stanza set up the contrast with orange in trees in the eighth stanza, the poppies in the fourth stanza set up the metaphor of Monarchs as poppy petals in the seventh stanza, and so on. The arson is metaphorical but emotionally real.