Course overview:

1
Course overview
Data Mining (Exploratory Data Analysis)
Probabiliy Theory Stochastic Theory
Estimation Inferences
Statistics
Modeling Prediction

• ATM 315 Environmental Statistics Course

2014-01-28
2
Suggested READING

• R-Programming
• The Art of R Programming Norman Matloff
• (free e-book PDF http//it-ebooks.info/book/1734/)
  
• R in a Nutshell Joseph Adler (OReilly)
• ONLINE Tutorials
• http//cran.r-project.org/doc/contrib/Verzani-Simp
  leR.pdf (Verzani-SimpleR.pdf)
• http//www.nceas.ucsb.edu/files/scicomp/Dloads/RPr
  ogramming/BestFirstRTutorial.pdf
• More links http//math.ucdenver.edu/RTutorial/RBo
  okResources.html

The Art of R Programming.pdf
Veranzi-SimpleR.pdf
BestFirstRTutorial.pdf
3
Suggested READING

• Statistics
• Statistical Methods in the Atmospheric Sciences
  (Daniel S. Wilks, 2nd ed., AP)
• Introduction to Probability and Statistics Using
  R G. Jay Kernshttp//cran.r-project.org/web/pac
  kages/IPSUR/vignettes/IPSUR.pdf
• Statistical Concepts in Environmental Sciences
  Dr. David. B. Stephenson (A Course Book no
  updated link found) (http//www.spatial.maine.edu/
  beard/Documents/basicstats.pdf)
• Collaborative Statistics - Barbara Illowsky,
  Susan Dean
• http//cnx.org/content/col10522/latest/

introductory_course_statistics.pdf
basicstats.pdf
IPSUR.pdf
4
Course overview

• Probability Theory
• Laws of Probability
• The Frequentists Interpretation of Probability
• Independence and Conditional Dependence
• Causal Reasoning
• Exploratory Data Analysis
• Description of the data sample
• Mean,Median,Standard Deviation, Histograms,
  Boxplots, Quantiles
• Empirical Distributions (Probability Density
  Function)

5
Course overview

• Data samples
• Sample size
• Independent, Identically Distributed Data
• Linear Transformation Shifting and Rescaling
• Non-linear transformation
• Paired Observations
• Scatter Plot
• Covariance Correlation
• Linear Regression
• Principal Component Analysis Part I
• Logistic Regression

Mid-Term Exam 03/11/2014
6
Course overview

• Probability Density Distributions
• From Discrete to Continuous Distributions
• Cumulative Density Function (CDF)
• Probability Density Function (PDF)
• Uniform Distribution
• Gaussian Distribution
• Gamma Distribution
• (General Extreme Value Distribution)

7
Course overview

• Statistical Inferences
• Testing against the evidence
• The Null-Hypothesis
• Significance vs Confidence
• Two Types of Errors

8
Course overview

• Time series analysis
• Trends
• Seasonal Cycles and Harmonic Analysis
• Filtering Low-Pass High-Pass and Band-Pass
• White, Red and Blue Noise
• Spectral analysis The basics

9
Course overview

• Multivariate Data Analysis
• Multiple Linear Regression
• Principal Component Analysis Part II
• Introduction to Geospatial Data analysis
• Irregularly-spaced Data samples
• Interpolation methods
• Block-averaging
• Distance-weighted
• Bilinear Interpolation
• (Advanced methods Kriging)

10
Course overview
Data Mining (Exploratory Data Analysis)
Probabiliy Theory Stochastic Theory
Estimation Inferences
Statistics
Modeling Prediction

• ATM 315 Environmental Statistics Course

2014-01-28
11
Course overview
Data Mining (Exploratory Data Analysis)
Probabiliy Theory Stochastic Theory
?
Estimation Inferences
Statistics
?
?
Modeling Prediction
?
Give a fitting verb to each connecting arrow that
describes their relationships.

• ATM 315 Environmental Statistics Course

2014-01-28
12
A first session with R-Studio (Windows 7)
Memory window list of objects Currently in the
memory for use
Multi-function Window (for file browsing,
plotting, Software package management
Command-line window

• ATM 315 Environmental Statistics Course

2014-01-23
13
Our first R-session data types and objects

• example001.R

14
Our first R-session data types and objects

• example001.R

example001.R
15
Our first R-session data types and objects

• example001.R

16
Our first R-session data types and objects

• example001.R

17
R Installing Packages

• Packages are collections of extra functions (and
  data) for specific purposes
• Packages make R a universal toolbox
• We will install the package prob
• Menu Tools -gt Install Packages Type packge
  name prob

18
R basic probability with R

19
R basic probability with R

Note! This is not a valid command in R
Descriptive text into comment lines starting with

library(prob) does the same, it loads the package
into the R session
rolldie() is a function from the package prob
20
Notes

• The winning streak of Oakland Athletics in 2002
  was 20 consecutive games in a row. Assume it was
  a fair game , all teams at even level.
• What are the odds to witness such a winning
  streak?
• What makes it even more unreal?

21
Axioms and Laws Of Probability

• The Axioms of Probability set the mathematical
  foundation for the calculus!
• We can measure probability of events and compare
  them.
• Probability of any event is nonnegative
• Probability of the compound event is 1
• The probability of two mutually exclusive events
  is the sum of the two individual probabilities
• Or
• P(e) gt 0
• P(S) 1 (S is the compound event, i.e. coin
  S(head OR tail)
• 3) P(e1 OR e2) P(e1)P(e2) (e.g. throwing
  the die shows 1 OR 2)

• NOTE In Axiom (3) it is important to refer to
  mutually exclusive events! Test yourself What
  are mutually exclusive events ?
• Tomorrow weather forecast It will rain (e1) or
  it wont rain (e2)
• Tomorrow weather forecast It will rain (e1) or
  it will snow (e2)

22
The Sample Space
The 6-sided die game
The coin flipping game
Tail
Head
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2
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5
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