•  #### Learning Bayesian Models with R #### Overview of this book

Learning Bayesian Models with R Credits   www.PacktPub.com Preface  Free Chapter
Introducing the Probability Theory The R Environment Introducing Bayesian Inference Machine Learning Using Bayesian Inference Bayesian Regression Models Bayesian Classification Models Bayesian Models for Unsupervised Learning Bayesian Neural Networks Bayesian Modeling at Big Data Scale Index ## Exercises

1. By using the definition of conditional probability, show that any multivariate joint distribution of N random variables has the following trivial factorization: 2. The bivariate normal distribution is given by: Here: By using the definition of conditional probability, show that the conditional distribution can be written as a normal distribution of the form where and .

3. By using explicit integration of the expression in exercise 2, show that the marginalization of bivariate normal distribution will result in univariate normal distribution.

4. In the following table, a dataset containing the measurements of petal and sepal sizes of 15 different Iris flowers are shown (taken from the Iris dataset, UCI machine learning dataset repository). All units are in cms:

Sepal Length

Sepal Width

Petal Length

Petal Width

Class of Flower

5.1

3.5

1.4

0.2

Iris-setosa

4.9

3

1.4

0.2

Iris-setosa

4.7

3.2

1.3

0.2

Iris-setosa

4.6

3.1

1.5

0.2

Iris-setosa

5

3.6

1.4

0.2

Iris-setosa

7

3.2

4.7

1.4

Iris-versicolor

6.4

3.2

4.5

1.5

Iris-versicolor

6.9

3.1

4.9

1.5

Iris-versicolor

5.5

2.3

4

1.3

Iris-versicolor

6.5

2.8

4.6

1.5

Iris-versicolor

6.3

3.3

6

2.5

Iris-virginica

5.8

2.7

5.1

1.9

Iris-virginica

7.1

3

5.9

2.1

Iris-virginica

6.3

2.9

5.6

1.8

Iris-virginica

6.5

3

5.8

2.2

Iris-virginica