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Learning Bayesian Models with R

Learning Bayesian Models with R

By : Hari Manassery Koduvely
3.4 (7)
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Learning Bayesian Models with R

Learning Bayesian Models with R

3.4 (7)
By: Hari Manassery Koduvely

Overview of this book

Bayesian Inference provides a unified framework to deal with all sorts of uncertainties when learning patterns form data using machine learning models and use it for predicting future observations. However, learning and implementing Bayesian models is not easy for data science practitioners due to the level of mathematical treatment involved. Also, applying Bayesian methods to real-world problems requires high computational resources. With the recent advances in computation and several open sources packages available in R, Bayesian modeling has become more feasible to use for practical applications today. Therefore, it would be advantageous for all data scientists and engineers to understand Bayesian methods and apply them in their projects to achieve better results. Learning Bayesian Models with R starts by giving you a comprehensive coverage of the Bayesian Machine Learning models and the R packages that implement them. It begins with an introduction to the fundamentals of probability theory and R programming for those who are new to the subject. Then the book covers some of the important machine learning methods, both supervised and unsupervised learning, implemented using Bayesian Inference and R. Every chapter begins with a theoretical description of the method explained in a very simple manner. Then, relevant R packages are discussed and some illustrations using data sets from the UCI Machine Learning repository are given. Each chapter ends with some simple exercises for you to get hands-on experience of the concepts and R packages discussed in the chapter. The last chapters are devoted to the latest development in the field, specifically Deep Learning, which uses a class of Neural Network models that are currently at the frontier of Artificial Intelligence. The book concludes with the application of Bayesian methods on Big Data using the Hadoop and Spark frameworks.
Table of Contents (11 chapters)
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10
Index

Conditional probability

Often, one would be interested in finding the probability of the occurrence of a set of random variables when other random variables in the problem are held fixed. As an example of population health study, one would be interested in finding what is the probability of a person, in the age range 40-50, developing heart disease with high blood pressure and diabetes. Questions such as these can be modeled using conditional probability, which is defined as the probability of an event, given that another event has happened. More formally, if we take the variables A and B, this definition can be rewritten as follows:

Conditional probability

Similarly:

Conditional probability

The following Venn diagram explains the concept more clearly:

Conditional probability

In Bayesian inference, we are interested in conditional probabilities corresponding to multivariate distributions. If Conditional probability denotes the entire random variable set, then the conditional probability of Conditional probability, given that Conditional probability is fixed at some value, is given by the ratio of joint probability of Conditional probability and joint probability of Conditional probability:

Conditional probability

In the case of two-dimensional normal distribution, the conditional probability of interest is as follows:

Conditional probability

It can be shown that (exercise 2 in the Exercises section of this chapter) the RHS can be simplified, resulting in an expression for Conditional probability in the form of a normal distribution again with the mean Conditional probability and variance Conditional probability.

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