Data over Space and Time

• Statistical study for processes that unfold over time, or space, or both
• History, science, and lots of practical policy & technology
• Not everything:
  • Good experiments
  • Good surveys
  • Wishful thinking

Special Statistical Issues

• The goal: learn how here and now depends on there and then
• The two problems:
  • Everything depends on everything else \(\Rightarrow\) basic theory doesn’t apply
  • We don’t get multiple samples of time or of space
  • \(\Rightarrow\) \(n=1\), always

Course Mechanics

• Syllabus: http://www.stat.cmu.edu/~cshalizi/dst/18
  • All assignments will be posted there
  • Information about readings and other course resources ditto
• Canvas as a gradebook and to distribute some electronic readings
• Piazza for question-answering

Office hours:

• Me, Wednesdays 1:00–3:00 in Baker Hall 229C
• TAs, TBD

Textbooks

Gidon Eshel, Spatiotemporal Data Analysis

Required, but full text PDF through JSTOR

Expect to read some of this nearly every week

Textbooks

Peter Guttorp, Stochastic Modeling of Scientific Data

• Recommended; required excerpts will be distributed through Canvas

Textbooks

Paul Teetor, The R Cookbook

Recommended; consult as needed

Lectures

• Clarification, amplification, examples, alternatives
• Complements to the readings
  • \(\therefore\) Do the readings ahead of time
• No electronics, except for documented need
• Graded in-class exercises most lectures

R Markdown

• R Markdown is a straightforward way to combine text, math, code, and code output in one document
• Enforces reproducibility: your numbers, figures, etc., are generated by the code, so results always match
• Use is required for this class
  • Your homework and exams will lose points if you don’t use it
  • You will lose more points as the semester goes on
  • Resources for learning R Markdown on the syllabus page

Collaboration, Cheating & Plagiarism

• Except for the in-class group assignments, you need to work on your own
• Full policy for this class is part of the syllabus
• Read that policy and the CMU policy on academic integrity
• Turn in Homework 0 on these policies by Thursday
  • Not graded, but you won’t get credit for any work until you complete it successfully

Any questions?

What are the big issues?

• We see \(X\) at time \(t\) and point \(r\), \(X(r,t)\), and what to know how it relates to \(Y\) at time \(s\) and point \(q\), \(Y(q,s)\)

Problems:

0. Basic statistical theory is about independent, identically distributed (IID) data.
1. But we (usually) only see one realization of a whole process.
2. Every observation is dependent on every other observation.
3. Basic statistical theory then says that \(n=1\) and can’t draw any inferences.

How are we going to deal with these issues?

• Methods for describing relationships and finding patterns in the data
• Especially methods for predicting \(X(r,t)\) from \(Y(q,s)\)
• Incorporate dependence into statistical theory, so we can say when methods will work
• Quantifying uncertain is best done through modeling and simulation

Why is this worth knowing?

• Italo Calvino, “All at One Point” (1963) imagines the world un-extended in time or space¹

• Otherwise, every branch of science deals with data spread over space and time
• Our examples will come from
  • Geology
  • Climatology
  • Meteorology
  • Ecology
  • Epidemiology
  • Demography
  • Economics
  • Neuroscience
  • Physics
• Could (and might) add examples from technology, policy, business, etc.

Cherry blossoms in Kyoto

Cherries at the Hirano shrine in Kyoto (David Montasco on flickr)

Flowering of cherry trees has been a central part of Japanese art & culture for well over a millennium

Hanami

Kitao Shigemasa, Sangatsu, Asukayam Hanami = Third Lunar Month, Blossom Viewing at Asuka Hill, c. 1776, via Library of Congress

Notice the date in the title!

This is data!

• Ancient diaries², poetry, etc., and modern newspapers, record when cherry trees in Kyoto came into bloom
  • Kyoto because it’s the ancient capital and has been a continuous seat of art & culture

Cherry blossoms track climate

• Japan gets cold

Snow at the Hirano shrine (yopparainokobito on flickr)

• Cherries only blossom when it gets warm enough

• \(\therefore\) The date when cherry trees are in full flower tells us about how warm the year was
  • Date of first flowering is also informative, but less often recorded

A data set

• Assembled by Prof. Yasuyuki Aono
  • Data points going back to the early 800s
  • Almost continuous for modern times
  • Re-formatted version at [http://www.stat.cmu.edu/~cshalizi/dst/18/data/kyoto.csv]
• For each year, the day of the year (1–366) of full bloom
  • April 1 = 91 or 92
  • Aono had to search out the ancient records, poems, histories, etc.
  • and convert dates before 1873 to our (Gregorian) calendar and (common) era (Meiji revolution)

A data set

kyoto <- read.csv("http://www.stat.cmu.edu/~cshalizi/dst/18/data/kyoto.csv")
plot(Flowering.DOY ~ Year.AD, data=kyoto, type="l",
     ylab="Day in year of full flowering", xlab="Year (AD)",
     main="Cherry blossoms in Kyoto")

Problems

• How to fill in the data between the observations? (interpolation)
  • When did the cherries bloom in 1015?
• How to extend beyond the observations? (extrapolation)
  • Make a guess for 2020, or for 800
• How to remove measure noise in the observations? (filtering)
  • Poets can be sloppy about dates
• How to separate year-to-year fluctuations from longer-term trends?
  • How do we model fluctuations?
  • How do we model trends?
• How seriously should we treat the warming since about 1800? (inference)
  • Could it be an artifact of denser observations?
  • Does the climate just do stuff like this occasionally?
  • How long do we need to wait to be confident?

Smoothed cherry blossoms

Both curves come from averaging nearby values

More concrete problems

• How do we fit either the blue or the green line to the data?
• How can we tell which one is a better fit?
• There ought to be margins of error — are the two curves even incompatible?
• What do we mean by a “trend” anyway?

Break for small-group exercise

Which of the two curves do you think is better? Or are they both bad? Or, if you can’t tell, what more information would you need?

We’re going to need to build some concepts

• Stochastic process = collection of random variables over time or space or both, typically dependent, say \(X(t)\)

• Trend = central tendency of the process, say \(\mu(t) = \mathbb{E}[X(t)]\)

• Fluctuations = difference from the trend

• How can we figure out the trend if we just see \(X\) once?

By Thursday:

• Make sure you’re on Canvas & Piazza for the course
  • Let me know if not
• Homework 0
  • Read the course policy on collaboration, cheating and plagiarism
  • Read the university policy on academic integrity
  • Read the excerpt from Taurabian’s Manual for Writers (Canvas)
  • Complete Homework 0
• Readings: Eshel, ch. 7; Guttorp, introduction and ch. 1

Take-aways

• Everything is statistically dependent on everything else
• Dependence means what happens here and now gives us information about there and then, so we can predict (interpolate, extrapolate, filter, forecast)
• Dependence means the statistical theory we’ve learned needs to be fixed
• For now, we will focus on describing dependence
• Next time: trends and smoothing