ESM 206

1
ESM 206

• The year is 1979. Concern is growing in Norway
  about acidification of its lakes, and the
  Norwegian government asks Britain and Germany to
  reduce emissions of sulphur dioxide from their
  power plants. In response, Britain demands proof
  that their emissions are acidifying Norwegian
  lakes.

• As science advisor to the Norwegian government,
  you are asked to design a study to produce this
  proof.
• What questions do you need to answer?
• What information should you request be collected?
• How should you analyze that information?

2
COURSE OBJECTIVES

• To formulate qualitative questions about and
  decision criteria for ESM as testable
  quantitative models.
• To select and use analytical tools to estimate
  parameters of these models from data.

• To use the fitted models to answer the
  qualitative questions.
• To explain the results of the analysis in a way
  that does justice to both unpredictability
  (natural variability) and uncertainty (the limits
  of the data).

3
COURSE FORMAT

• Lectures
• 2 per week
• Expected to attend all lectures
• Lecture material applied and motivated with real
  environmental problems

• Labs
• 1 per week. T.A.s Chris Gleason and Antonia
  Lloret.
• In GIS lab.
• Bring questions dont expect to complete
  homework in Lab sessions.

4
RESOURCES

• Fox, Applied Regression Analysis, Linear Models,
  and Related Models (AR)
• Fox, An R and S-plus Companion to Applied
  Regression (CAR)
• Gonick Smith, The Cartoon Guide to Statistics
  (CG)
• Costello Kendall, Data Analysis for
  Environmental Science Management (CK on the
  class web page)

• Class web page www.bren.ucsb.edu/academics/
  course.asp?number206
• Class email list esm206_at_bren.ucsb.edu
• Software R
• Installed on Bren computers
• Can be downloaded from www.r-project.org

5
EXPECTATIONS

• Of You
• Participate in class/lab
• Do readings
• Submit assignments on time
• Do your own work

• Of Ourselves
• Keep it interesting
• Introduce techniques with real-world examples
• Make ourselves accessible
• Make lecture notes available
• Provide homework keys when work is turned in

6
WHAT IS STATISTICS GOOD FOR?

• Transforms data into information
• Describe patterns in data
• What is the trend in CO2 emissions over time?
• What is the covariation between temperature and
  rainfall?
• Enhance scientific understanding
• Is there a relationship between gasoline taxes
  and gasoline consumption?
• What is the nature of the relationship between
  fish stocks and fish recruits?

• Make predictions
• Given the observed relationship between
  investment in green technologies and share price,
  what will be the effect on a firms share price
  of a one-unit increase in its green technology
  investment?
• Need to distinguish between interpolation and
  extrapolation
• Make decisions
• Are we sufficiently confident that arsenic levels
  exceed a regulatory threshold that we should take
  action?

7
WHAT YOU SHOULD ALREADY KNOW

• Simple data summaries (CG 2)
• Basic probability theory (CG 3)
• Properties of random variables (CG 4)
• The normal probability distribution (CG 5)
• Confidence intervals what they are, and how to
  calculate them for means (CG 7)
• Hypothesis testing (CG 8)
• T-tests (CG 9)

• If you dont know these well, then
• Read the Cartoon Guide
• Go to Lisa Berrys workshop

8
A SYSTEMATIC APPROACH TO STATISTICAL ANALYSIS

• Clearly formulate the problem, question, or
  decision that you are facing
• What are the quantities that you need to
  estimate?
• Write down a statistical model that relates the
  quantities of interest to the data you will
  collect (or have collected)
• This model will include a random component that
  represents natural variability or sampling error

• Estimate the parameters of the statistical model
• In addition to the estimate of the most likely
  value, quantify your uncertainty in that estimate
• Use the results to address your problem,
  question, or decision
• Your report should include a quantification of
  the probability that your answer is incorrect

9

gt merc lt- read.csv("MercuryCWS.csv") gt
mean(merc) mercury 0.1569231 gt var(merc)
mercury mercury 0.007123077 gt sd(merc)
mercury 0.08439832 gt n lt- dim(merc)1 gt n 1
13 gt sd(merc)/sqrt(n) mercury 0.02340788
gt t.test(merc, alternative"greater", mu0.1)
One Sample t-test data merc t 2.4318,
df 12, p-value 0.01581 alternative
hypothesis true mean is greater than 0.1 95
percent confidence interval 0.1152035 Inf
sample estimates mean of x 0.1569231
10
HOMEWORK 1 due Thurs. Apr. 8

• Work through chapters 1 and 2 of CAR, entering
  all the commands in R and ensuring that you
  understand the output. You can ignore all the
  parts that are applicable only to S-plus or to
  S4.
• Copy and paste the text in the command window
  (which includes both your input and the resulting
  output) into a word file. Also copy any figures
  that you generate into that file.
• Email the file to your TA by 930 AM on Thurs.
  Apr. 9.