-

Posterior using a flat prior

sigma squared

gamma

0.0

0.1

0.2

0.3

0.4

0.5

0.7

0.8

0.9

1.0

1.1

1.2

1.3

Posterior Mode

> x <- seq(0,.5,.005)

> y <- seq(0.7,1.3,.005)

> output <- matrix(nrow=length(x),ncol=length(y))

> for(i in 1:length(x)) {

+

for(j in 1:length(y)) {

+

output[i,j] <- posterior(c(x[i],y[j]))

+

}

+ }

> contour(output,x=x,y=y,xlab="sigma squared",ylab="gamma",main="Posterior using a flat prior")

> points( 0.04647009 , 0.993137,pch=8)

> arrows(.1,.75,0.04647009,0.993137)

> text(.09,.73,"Posterior Mode",pos=4)

50

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Document Outline

• Introductory Comments
  • What is R?
  • How is R Better Than Other Packages?
  • Obtaining R
  • Using R Interactively and Writing Scripts
  • Getting Help
• Working with Data
  • Basic Data Manipulation
  • Caveat: Math Operations and the Recycling Rule
  • Important Data Types
    • Vectors
    • Arrays, Matrices
    • Dataframes
    • Lists
    • S3 Classes
    • S4 Classes
  • Working with Dates
  • Merging Dataframes
  • Opening a Data File
  • Working With Very Large Data Files
    • Reading fields of data using scan()
    • Utilizing Unix Tools
    • Using Disk instead of RAM
    • Using RSQLite
  • Issuing System Commands---Directory Listing
  • Reading Data From the Clipboard
  • Editing Data Directly
• Cross Sectional Regression
  • Ordinary Least Squares
  • Extracting Statistics from the Regression
  • Heteroskedasticity and Friends
    • Breusch-Pagan Test for Heteroskedasticity
    • Heteroskedasticity (Autocorrelation) Robust Covariance Matrix
  • Linear Hypothesis Testing (Wald and F)
  • Weighted and Generalized Least Squares
  • Models With Factors/Groups
• Special Regressions
  • Fixed/Random Effects Models
    • Fixed Effects
    • Random Effects
  • Qualitative Response
    • Logit/Probit
    • Multinomial Logit
    • Ordered Logit/Probit
  • Tobit and Censored Regression
  • Quantile Regression
  • Robust Regression - M Estimators
  • Nonlinear Least Squares
  • Two Stage Least Squares on a Single Structural Equation
  • Systems of Equations
    • Seemingly Unrelated Regression
    • Two Stage Least Squares on a System
• Time Series Regression
  • Differences and Lags
  • Filters
    • Canned AR and MA filters
    • Manual Filtration
    • Hodrick Prescott Filter
    • Kalman Filter
  • ARIMA/ARFIMA
  • ARCH/GARCH
    • Basic GARCH--garch()
    • Advanced GARCH--garchFit()
    • Miscellaneous GARCH--Ox G@RCH
  • Correlograms
  • Predicted Values
  • Time Series Tests
    • Durbin-Watson Test for Autocorrelation
    • Box-Pierce and Breusch-Godfrey Tests for Autocorrelation
    • Dickey-Fuller Test for Unit Root
  • Vector Autoregressions (VAR)
• Plotting
  • Plotting Empirical Distributions
  • Contour Plots
  • Adding Legends and Stuff
  • Adding Arrows, Text, and Markers
  • Multiple Plots
  • Saving Plots---png, jpg, eps, pdf, xfig
  • Adding Greek Letters and Math Symbols to Plots
  • Other Graphics Packages
• Statistics
  • Working with Common Statistical Distributions
  • P-Values
  • Sampling from Data
• Math in R
  • Matrix Operations
    • Matrix Algebra and Inversion
    • Factorizations
  • Numerical Optimization
    • Unconstrained Minimization
    • Minimization with Linear Constraints
  • Numerical Integration
• Programming
  • Writing Functions
  • Looping
  • Avoiding Loops
    • Applying a Function to an Array (or a Cross Section of it)
    • Replicating
  • Conditionals
    • Binary Operators
    • WARNING: Conditionals and NA
  • The Ternary Operator
  • Outputting Text
  • Pausing/Getting Input
  • Timing Blocks of Code
  • Calling C functions from R
    • How to Write the C Code
    • How to Use the Compiled Functions
  • Calling R Functions from C
• Changing Configurations
  • Default Options
    • Significant Digits
    • What to do with NAs
    • How to Handle Errors
    • Suppressing Warnings
• Saving Your Work
  • Saving the Data
  • Saving the Session Output
  • Saving as LaTeX
• Final Comments
• Appendix: Code Examples
  • Monte Carlo Simulation
  • The Haar Wavelet
  • Maximum Likelihood Estimation
  • Extracting Info From a Large File
  • Contour Plot