#### Overview of this book

Machine learning applications are highly automated and self-modifying, and continue to improve over time with minimal human intervention, as they learn from the trained data. To address the complex nature of various real-world data problems, specialized machine learning algorithms have been developed. Through algorithmic and statistical analysis, these models can be leveraged to gain new knowledge from existing data as well. Data Science Algorithms in a Week addresses all problems related to accurate and efficient data classification and prediction. Over the course of seven days, you will be introduced to seven algorithms, along with exercises that will help you understand different aspects of machine learning. You will see how to pre-cluster your data to optimize and classify it for large datasets. This book also guides you in predicting data based on existing trends in your dataset. This book covers algorithms such as k-nearest neighbors, Naive Bayes, decision trees, random forest, k-means, regression, and time-series analysis. By the end of this book, you will understand how to choose machine learning algorithms for clustering, classification, and regression and know which is best suited for your problem
Title Page
Packt Upsell
Contributors
Preface
Free Chapter
Classification Using K-Nearest Neighbors
Time Series Analysis
Python Reference
Statistics
Glossary of Algorithms and Methods in Data Science
Other Books You May Enjoy
Index

## Medical tests – basic application of Bayes' theorem

A patient takes a special cancer test that has an accuracy of `test_accuracy=99.9%`—if the result is positive, then 99.9% of the patients tested will suffer from that particular type of cancer. Conversely, 99.9% of the patients with a negative result will not suffer from that particular cancer.

Suppose that a patient is tested and the result is positive. What is the probability of that patient suffering from that particular type of cancer?

### Analysis

We will use Bayes' theorem to ascertain the probability of the patient having cancer:

To ascertain the prior probability that a patient has cancer, we have to find out how frequently cancer occurs among people. Say that we find out that 1 person in 100,000 suffers from this kind of cancer. Therefore, P(cancer)=1/100,000. So, P(test_positive|cancer) = test_accuracy=99.9%=0.999 given by the accuracy of the test.

P(test_positive) has to be computed as follows:

Therefore, we can calculate the following:

So...