Mean Vectors and Covariance Matrices

More documents

Recommendations

Info

MULTIVARIATE DISTRIBUTIONS (VARIABLES ≥ 2) PSYC 943: Lecture 11 34
Multivariate Normal Distribution • The multivariate normal distribution is the generalization of the univariate normal distribution to multiple variables ‣ The bivariate normal distribution just shown is part of the MVN • The MVN provides the relative likelihood of observing all V variables for a subject p simultaneously: x p = x p1 x p2 … x pp • The multivariate normal density function is: f x p = 1 2π V 2 Σ 1 2 exp − x p T − μ T Σ −1 x p T − μ 2 PSYC 943: Lecture 11 35
Page 1 and 2: More Matrix Algebra; Mean Vectors a
Page 3 and 4: DATA EXAMPLE AND SAS PSYC 943: Lect
Page 5 and 6: The Data… In Excel: In SAS: PSYC
Page 7 and 8: MATRIX ALGEBRA PSYC 943: Lecture 11
Page 9 and 10: Matrix Addition and Subtraction •
Page 11 and 12: Matrix Multiplication • Matrix mu
Page 13 and 14: Multiplication in Statistics • Ma
Page 15 and 16: Zero Vector • The zero vector is
Page 17 and 18: Matrix “Division”: The Inverse
Page 19 and 20: Matrix Determinants • A square ma
Page 21 and 22: Matrix Algebra Operations (for help
Page 23 and 24: Multivariate Statistics • Up to t
Page 25 and 26: Mean Vector: Graphically • The me
Page 27 and 28: Correlation of a Pair of Varibles
Page 29 and 30: From Covariance to Correlation •
Page 31 and 32: In SAS: PSYC 943: Lecture 11 31
Page 33: Total Sample Variance • The total
Page 37 and 38: Comparing Univariate and Multivaria
Page 39 and 40: Multivariate Normal Notation • St
Page 41 and 42: Bivariate Normal Plot #2 (Multivari
Page 43 and 44: Multivariate Normal Distribution in
Page 45: Wrapping Up • The last two classe

Mean Vectors and Covariance Matrices

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?