Deepen your knowledge of probability theory and application using R! These courses will provide you with a fun structure to learn a key skill for statisticians, data scientists, and quantitative analysts.  

These courses will provide you with a fun structure to learn a key skill for statisticians, data scientists, and quantitative analysts.  

with R

Probability and Distributions

One of the simplest and most common examples of a random phenomenon is a coin flip: an event that is either "yes" or "no" with some probability. Here you'll learn about the binomial distribution, which describes the behavior of a combination of yes/no trials and how to predict and simulate its behavior.

The binomial distribution

In this chapter you'll learn to combine multiple probabilities, such as the probability two events both happen or that at least one happens, and confirm each with random simulations. You'll also learn some of the properties of adding and multiplying random variables.

Laws of probability

Bayesian statistics is a mathematically rigorous method for updating your beliefs based on evidence. In this chapter, you'll learn to apply Bayes' theorem to draw conclusions about whether a coin is fair or biased, and back it up with simulations.

Bayesian statistics

So far we've been talking about the binomial distribution, but this is one of many probability distributions a random variable can take. In this chapter we'll introduce three more that are related to the binomial: the normal, the Poisson, and the geometric.

Related distributions

Probability is the study of making predictions about random phenomena. In this course, you'll learn about the concepts of random variables, distributions, and conditioning, using the example of coin flips. You'll also gain intuition for how to solve probability problems through random simulation. These principles will help you understand statistical inference and can be applied to draw conclusions from data.

Introduction to R

In this course, you'll learn about the concepts of random variables, distributions, and conditioning.

Foundations of Probability in R

Probability & Statistics

In this introduction to multivariate data, you will learn how to read and summarize it. You will learn how to summarize multivariate data using descriptive statistics, such as the mean vector, variance-covariance, and correlation matrices. You'll then explore plotting techniques to provide insights into multivariate data.

Reading and plotting multivariate data

This chapter will introduce you to the most important and widely used multivariate probability distribution, the multivariate normal. You will learn how to generate random samples from a multivariate normal distribution and how to calculate and plot the densities and probabilities under this distribution. You will also learn how to test if a dataset follows multivariate normality.

Multivariate Normal Distribution

This chapter introduces a host of probability distributions to model non-normal data. In particular, you will be introduced to multivariate t-distributions, which can model heavier tails and are a generalization of the univariate Student's t-distribution. You will be introduced to various skew distributions, which are specifically designed to model data that are right or left skewed.

Other Multivariate Distributions

In the final chapter, you will be introduced to techniques for analyzing high dimensional data, including principal component analysis (PCA) and multidimensional scaling (MDS). You will also learn to implement these techniques by analyzing data.

Principal Component Analysis and Multidimensional Scaling

Iris

Wine

Birthweight

When working with data that contains many variables, we are often interested in studying the relationship between these variables using multivariate statistics. In this course, you'll learn ways to analyze these datasets. You will also learn about common multivariate probability distributions, including the multivariate normal, the multivariate-t, and some multivariate skew distributions. You will then be introduced to techniques for representing high dimensional data in fewer dimensions, including principal component analysis (PCA) and multidimensional scaling (MDS).

Learn to analyze and plot multivariate data. 

Multivariate Probability Distributions in R

Learn to analyze, plot, and model multivariate data.

This chapter will introduce some basic principles that will be used throughout the course, such as writing loops and functions. Then, we dive into a couple of classic problems: the Birthday Problem, and Monty Hall.

Introduction and Classic Puzzles

In this chapter, we explore games in which dice are rolled, including Yahtzee, Settlers of Catan, and Craps. You will learn tools such as using built-in R functions to calculate combinatorics, and using functions such as replicate and the %in% operator.

Games with Dice

The puzzles in this chapter were inspired by ideas encountered on the internet. In order to solve them, you will learn to combine tools such as nested for loops, and the functions round, identical, and sapply.

Inspired from the Web

This chapter explores questions in poker, including the most often televised version of Texas Hold'em. We will learn to code for win probabilities with any given number of outs, and also explore a more theoretical model of poker known as the von Neumann model. We will learn to use functions such as Reduce, runif, and ifelse.

Poker

Do you want to take your probability skills to the next level? This course will help get you there, using problem-based learning with probability puzzles as the framework. As you are guided through their solutions, you will gain coding tools and general strategies for solving probability problems that you might encounter in many other situations. Organized by theme, the course begins with classic problems like the Birthday Problem and Monty Hall, and ends with puzzles that involve poker like Texas Hold'em and the World Series of Poker!

Intermediate R

Learn how to solve a variety of probability puzzles in R. 

Probability Puzzles in R

Learn strategies for answering probability questions in R by solving a variety of probability puzzles.

In this chapter, you will be introduced to fundamental concepts in model-based clustering and how this approach differs from other clustering techniques. You will learn the generating process of Gaussian Mixture Models as well as how to visualize the clusters.

Introduction to Mixture Models

In this chapter, you will be introduced to the main structure of Mixture Models, how to address different data with this approach and how to estimate the parameters involved. To accomplish the estimation, you will learn an iterative method called Expectation-Maximization algorithm.

Structure of Mixture Models and Parameters Estimation

This chapter shows how to fit Gaussian Mixture Models in 1 and 2 dimensions with `flexmix` package. The data used is formed by 10.000 observations of people with their weight, height, body mass index and informed gender.

Mixture of Gaussians with `flexmix`

In this module, you will learn how Mixture Models extends to consider probability distributions different from the Gaussian and how these models are fitted with `flexmix`. The datasets used are handwritten digits images and the number of crimes in Chicago city. For the first dataset you will find clusters that summarize the handwritten digits and for the second dataset, you will find clusters of communities where is more or less dangerous to live in.

Mixture Models Beyond Gaussians

Chicago Crimes dataset

Digits dataset

Gender dataset

Mixture modeling is a way of representing populations when we are interested in their heterogeneity. Mixture models use familiar probability distributions (e.g. Gaussian, Poisson, Binomial) to provide a convenient yet formal statistical framework for clustering and classification. Unlike standard clustering approaches, we can estimate the probability of belonging to a cluster and make inference about the sub-populations. For example, in the context of marketing, you may want to cluster different customer groups and find their respective probabilities of purchasing specific products to better target them with custom promotions. When applying natural language processing to a large set of documents, you may want to cluster documents into different topics and understand how important each topic is across each document. In this course, you will learn what Mixture Models are, how they are estimated, and when it is appropriate to apply them!

Introduction to the Tidyverse

Learn mixture models: a convenient and formal statistical framework for probabilistic clustering and classification.

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