Probability theory is a fundamental aspect of mathematics and data science, essential for understanding uncertainty and making informed decisions. In Python, a versatile and widely used programming language, various types of probability methods and distributions are employed for statistical analysis, machine learning, and simulations.
Basic Probability Concepts in Python:
Understanding probability as a measure of uncertainty.
Probability basics: sample space, events, and outcomes.
Using Python libraries such as NumPy and SciPy for basic probability calculations.
Calculating probabilities of simple and compound events.
Discrete Probability Distributions:
Overview of discrete probability distributions (e.g., Bernoulli, Binomial, Poisson).
Implementation of discrete probability distributions in Python.
Generating random variates and calculating probabilities using built-in functions.
Applications of discrete distributions in modeling random processes.
Continuous Probability Distributions:
Introduction to continuous probability distributions (e.g., Normal, Exponential, Uniform).
Probability density functions (PDFs) and cumulative distribution functions (CDFs).
Utilizing Python libraries like SciPy and NumPy for working with continuous distributions.
Generating random numbers from continuous distributions and performing statistical analysis.
Joint Probability Distributions:
Definition of joint probability distributions for multiple variables.
- Understanding joint probability mass functions (PMFs) and probability density functions (PDFs).
Visualizing joint distributions using scatter plots and contour plots in Python.
- Computing marginal and conditional probabilities from joint distributions.
Bayesian Probability:
Introduction to Bayesian probability theory and Bayes' theorem.
Bayesian inference using Python libraries like PyMC3 and Stan.
Performing Bayesian parameter estimation and hypothesis testing.
Applications of Bayesian probability in machine learning, data analysis, and decision-making.
Markov Chains and Monte Carlo Simulation:
Basics of Markov chains and their applications in modeling sequential processes.
- Implementing Markov chains using Python libraries such as NumPy.
Monte Carlo simulation techniques for estimating probabilities and solving complex problems.
Examples of Monte Carlo simulations for risk assessment, option pricing, and optimization.
Probabilistic Graphical Models:
Overview of probabilistic graphical models (PGMs) such as Bayesian networks and Markov networks.
Using libraries like pgmpy and PyMC3 for building and analyzing PGMs in Python.
- Inference algorithms for probabilistic graphical models: exact and approximate methods.
Real-world applications of PGMs in healthcare, finance, and natural language processing.