Course Content

Data Science Interview Challenge

1. Python

Introduction Challenge 1: List Comprehension Challenge 2: String Manipulation Challenge 3: Dictionary Manipulation Challenge 4: Nested Loops Challenge 5: Classes Theoretical Questions

2. NumPy

Challenge 1: Array Creation Challenge 2: Array Manipulation Challenge 3: Statistical Insights Challenge 4: Handling Missing Values Challenge 5: Subarray Sorting Theoretical Questions

3. Pandas

Challenge 1: DataFrame Creation Challenge 2: Data Grouping Challenge 3: Indexing and MultiIndexing Challenge 4: Altering DataFrame Challenge 5: Iterating Over Data Theoretical Questions

4. Matplotlib

Challenge 1: Fundamentals of Plotting Challenge 2: Other Graph Types Challenge 3: Subplots Challenge 4: Customizing Plots Challenge 5: Adding Text to Plots Theoretical Questions

5. Seaborn

Challenge 1: Visualizing Distributions Challenge 2: Exploring Categorical Data Challenge 3: Relational Plots Challenge 4: Regression Plots Challenge 5: Matrix Plots Theoretical Questions

6. Statistics

Challenge 1: Probabilities and Distributions Challenge 2: Bayes' Theorem Challenge 3: Hypothesis Testing Challenge 4: Confidence Intervals Challenge 5: Correlation Theoretical Questions

7. Scikit-learn

Challenge 1: Data Scaling Challenge 2: Basic Model Creation Challenge 3: Pipelines Challenge 4: Cross-validation Challenge 5: Hyperparameter Tuning Theoretical Questions

Data Science Interview Challenge

Challenge 2: Bayes' Theorem

In the world of probability and statistics, Bayesian thinking offers a framework for understanding the probability of an event based on prior knowledge. It contrasts with the frequentist approach, which determines probabilities based on the long-run frequencies of events. Bayes' theorem is a fundamental tool within this Bayesian framework, connecting prior probabilities and observed data.

Task

Imagine you are a data scientist working for a medical diagnostics company. Your company has developed a new test for a rare disease. The prevalence of this disease in the general population is 1%. The test has a 99% true positive rate (sensitivity) and a 98% true negative rate (specificity).

Your task is to compute the probability that a person who tests positive actually has the disease.

Given:

P(Disease) = Probability of having the disease = 0.01
P(Positive|Disease) = Probability of testing positive given that you have the disease = 0.99
P(Negative|No\ Disease) = Probability of testing negative given that you don't have the disease = 0.98

Using Bayes' theorem:

P(Disease|Positive) = P(Positive|Disease) * P(Disease) / P(Positive)

Where P(Positive) can be found using the law of total probability:

P(Positive) = P(Positive|Disease) * P(Disease) + P(Positive|No Disease) * P(No Disease)

Compute P(Disease|Positive), the probability that a person who tests positive actually has the disease.

Code Description

p_positive_given_no_disease = 1 - p_negative_given_no_disease

Calculates the probability of testing positive given no disease, which is the complement of testing negative given no disease.

p_positive = p_positive_given_disease * p_disease + p_positive_given_no_disease * (1 - p_disease)

Computes the total probability of testing positive using the law of total probability, considering both the probability of testing positive with the disease and without the disease.

p_disease_given_positive = (p_positive_given_disease * p_disease) / p_positive

Applies Bayes' theorem to determine the probability that a person who tests positive actually has the disease.

Everything was clear?

Section 6. Chapter 2