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    Course Introduction
    Course Syllabus
    Unit 1: What is Data Science?
    1.1: Introduction to Data Science
    A History of Data Science
    Understanding Data Science
    1.2: How Data Science Works
    How Data Science Works
    The Data Science Pipeline
    The Data Science Lifecycle
    1.3: Important Facets of Data Science
    Data Scientist Archetypes
    What is the Field of Data Science?
    Thinking about the World
    Unit 1 Assessment
    Unit 1 Assessment
    Unit 2: Python for Data Science
    2.1: Google Colaboratory
    Introduction to Google Colab
    2.2: Datatypes, Operators, and the math Module
    Data Types in Python
    Operators and the math Module
    2.3: Control Statements, Loops, and Functions
    Functions, Loops, and Logic
    Functions and Control Structures
    2.4: Lists, Tuples, Sets, and Dictionaries
    Data Structures in Python
    Sets, Tuples, and Dictionaries
    Examples of Sets, Tuples, and Dictionaries
    2.5: The random Module
    Python's random Module
    2.6: The matplotlib Module
    Visualization and matplotlib
    Precision Data Plotting with matplotlib
    Unit 2 Assessment
    Unit 2 Assessment
    Unit 3: The numpy Module
    3.1: Constructing Arrays
    Using Matrices
    Creating numpy Arrays
    numpy Fundamentals
    numpy for Numerical and Scientific Computing
    3.2: Indexing
    numpy Arrays and Vectorized Programming
    Advanced Indexing with numpy
    3.3: Array Operations
    A Visual Intro to numpy and Data Representation
    Mathematical Operations with numpy
    numpy with matplotlib
    3.4: Saving and Loading Data
    Storing Data in Files
    Load Compressed Data using numpy.load
    Saving a Compressed File with numpy
    ".npy" versus ".npz" Files
    Unit 3 Assessment
    Unit 3 Assessment
    Unit 4: Applied Statistics in Python
    4.1: Basic Statistical Measures and Distributions
    Applying Statistics
    Key Statistical Terms
    Descriptive Statistics
    Basic Probability
    Distribution and Standard Deviation
    Continuous Probability Functions and the Uniform Distribution
    The Normal Distribution
    Confidence Intervals
    Hypothesis Testing
    Linear Regression
    4.2: Random Numbers in numpy
    Using numpy
    Random Number Generation
    Using np.random.normal
    A Data Science Example
    4.3: The scipy.stats Module
    Descriptive Statistics in Python
    Statistical Modeling with scipy
    Probability Distributions and their Stories
    4.4: Data Science Applications
    Statistics and Random Numbers
    Statistics in Python
    Probabilistic and Statistical Risk Modeling
    Unit 4 Assessment
    Unit 4 Assessment
    Unit 5: The pandas Module
    5.1: Dataframes
    pandas Dataframes
    How pandas Dataframes Work
    5.2: Data Cleaning
    Data Cleaning
    More on Data Cleaning
    5.3: pandas Operations: Merge, Join, and Concatenate
    pandas Data Structures
    Pandas Dataframe Operations
    5.4: Data Input and Output
    Importing and Exporting
    Loading Data into pandas Dataframes
    5.5: Visualization Using the pandas Module
    Using pandas to Plot Data
    Plotting with pandas
    Unit 5 Assessment
    Unit 5 Assessment
    Unit 6: Visualization
    6.1: The seaborn Module
    Visualization with seaborn
    matplotlib and seaborn
    Easy Data Visualization
    6.2: Advanced Data Visualization Techniques
    Data Visualization in Python
    How to Create a seaborn Boxplot
    Practicing Data Visualization
    6.3: Data Science Applications
    Visualization Examples
    Using Jupyter
    Visualizing with seaborn
    Unit 6 Assessment
    Unit 6 Assessment
    Unit 7: Data Mining I – Supervised Learning
    7.1: Data Mining Overview
    Introduction to Data Mining
    Introduction to Machine Learning
    Bayes' Theorem
    Bayes' Theorem and Conditional Probability
    Methods for Pattern Classification
    7.2: Supervised Learning
    Supervised learning
    Feature Selection
    Model Inspection and Feature Selection
    scikit-learn
    7.3: Principal Component Analysis
    Dimensionality Reduction
    Principal Component Analysis
    PCA in Python
    7.4: k-Nearest Neighbors
    The k-Nearest Neighbors Algorithm
    Using the k-NN Algorithm
    Nearest Neighbors
    7.5: Decision Trees
    Dealing with Uncertainty
    Classification, Decision Trees, and k-Nearest-Neighbors
    Decision Trees
    7.6: Logistic Regression
    Logistic Regression
    More on Logistic Regression
    Implementing Logistic Regression
    7.7: Training and Testing
    Supervised Learning and Model Validation
    Training and Tuning a Model
    Unit 7 Assessment
    Unit 7 Assessment
    Unit 8: Data Mining II – Clustering Techniques
    8.1: Unsupervised Learning
    Unsupervised Learning
    More on Unsupervised Learning
    8.2: K-means Clustering
    K-means Clustering
    More on K-means Clustering
    Implementing K-means Clustering
    Interpreting the Results of Clustering
    PCA and Clustering
    8.3: Hierarchical Clustering
    Hierarchical Clustering
    Hierarchical Clustering Using Trees
    Agglomerative Clustering
    Applying Clustering
    Comparing Aggomerative and K-means Clustering
    8.4: Training and Testing
    Clustering with scikit-learn
    Putting It All Together
    Unit 8 Assessment
    Unit 8 Assessment
    Unit 9: Data Mining III – Statistical Modeling
    9.1: Linear Regression
    Simple Linear Regression
    Implementing Simple Linear Regression with scikit-learn
    Practicing Linear Regression
    Multiple Linear Regression
    Multiple Regression in scikit-learn
    9.2: Residuals
    The Assumptions of Simple Linear Regression
    Residual Plots and Regression
    Simple Linear Regression Project
    9.3: Overfitting
    Overfitting
    Overfitting in a Learning Model
    9.4: Cross-Validation
    What is Cross-Validation?
    More on Cross-Validation
    Cross-Validation in Machine Learning
    Statistical Modeling Project
    Unit 9 Assessment
    Unit 9 Assessment
    Unit 10: Time Series Analysis
    10.1: The statsmodels Module
    Introduction to statsmodels
    Regression Using statsmodels
    Using scikit-learn with statsmodels
    10.2: Autoregressive (AR) Models
    Time Series Basics
    Autoregressive Models
    Time Series and Forecasting
    10.3: Moving Average (MA) Models
    Moving-Average Models
    MA Model Examples
    AR and MA Models
    10.4: Autoregressive Integrated Moving Average (ARIMA) Models
    ARIMA Models
    ARIMA in Python
    ARIMA and Seasonal ARIMA Models
    ARIMA(p,d,q)
    Time Series Forecasting with ARIMA
    Unit 10 Assessment
    Unit 10 Assessment
    Study Guide
    CS250 Study Guide
    Course Feedback Survey
    Course Feedback Survey
    Certificate Final Exam
    CS250: Certificate Final Exam
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  1. CS250: Python for Data Science
  2. Unit 4: Applied Statistics in Python
  3. 4.4: Data Science Applications
  4. Probabilistic and Statistical Risk Modeling

Probabilistic and Statistical Risk Modeling

Completion requirements

Study these slides. In this project, you will apply techniques from this unit to analyze data sets using descriptive statistics and graphical tools. You will also write code to fit (that is, estimate distribution parameters) a probability distribution to the data. Finally, you will learn to code various risk measures based on statistical tests. Upon completing this project, you should have a clearer picture of how you can use Python to perform statistical analyses within the field of data science.

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Saylor Academy © 2010-2025 except as otherwise noted. Excluding course final exams, content authored by Saylor Academy is available under a Creative Commons Attribution 3.0 Unported license. Third-party materials are the copyright of their respective owners and shared under various licenses. See detailed licensing information. Saylor Academy®, Saylor.org®, and Harnessing Technology to Make Education Free® are trade names of the Constitution Foundation, a 501(c)(3) organization through which our educational activities are conducted.