This course introduces the Bayesian approach to statistics, starting with the concept of probability and moving to the analysis of data. We will learn about the philosophy of the Bayesian approach as well as how to implement it for common types of data. We will compare the Bayesian approach to the more commonly-taught Frequentist approach, and see some of the benefits of the Bayesian approach. In particular, the Bayesian approach allows for better accounting of uncertainty, results that have more intuitive and interpretable meaning, and more explicit statements of assumptions. This course combines lecture videos, computer demonstrations, readings, exercises, and discussion boards to create an active learning experience. For computing, you have the choice of using Microsoft Excel or the open-source, freely available statistical package R, with equivalent content for both options. The lectures provide some of the basic mathematical development as well as explanations of philosophy and interpretation. Completion of this course will give you an understanding of the concepts of the Bayesian approach, understanding the key differences between Bayesian and Frequentist approaches, and the ability to do basic data analyses.

Offered By

## Bayesian Statistics: From Concept to Data Analysis

## About this Course

### Learner Career Outcomes

## 21%

## 15%

### Skills you will gain

### Learner Career Outcomes

## 21%

## 15%

#### 100% online

#### Flexible deadlines

#### Intermediate Level

#### Approx. 22 hours to complete

#### English

## Syllabus - What you will learn from this course

**3 hours to complete**

## Probability and Bayes' Theorem

In this module, we review the basics of probability and Bayes’ theorem. In Lesson 1, we introduce the different paradigms or definitions of probability and discuss why probability provides a coherent framework for dealing with uncertainty. In Lesson 2, we review the rules of conditional probability and introduce Bayes’ theorem. Lesson 3 reviews common probability distributions for discrete and continuous random variables.

**3 hours to complete**

**8 videos**

**4 readings**

**5 practice exercises**

**3 hours to complete**

## Statistical Inference

This module introduces concepts of statistical inference from both frequentist and Bayesian perspectives. Lesson 4 takes the frequentist view, demonstrating maximum likelihood estimation and confidence intervals for binomial data. Lesson 5 introduces the fundamentals of Bayesian inference. Beginning with a binomial likelihood and prior probabilities for simple hypotheses, you will learn how to use Bayes’ theorem to update the prior with data to obtain posterior probabilities. This framework is extended with the continuous version of Bayes theorem to estimate continuous model parameters, and calculate posterior probabilities and credible intervals.

**3 hours to complete**

**11 videos**

**5 readings**

**4 practice exercises**

**2 hours to complete**

## Priors and Models for Discrete Data

In this module, you will learn methods for selecting prior distributions and building models for discrete data. Lesson 6 introduces prior selection and predictive distributions as a means of evaluating priors. Lesson 7 demonstrates Bayesian analysis of Bernoulli data and introduces the computationally convenient concept of conjugate priors. Lesson 8 builds a conjugate model for Poisson data and discusses strategies for selection of prior hyperparameters.

**2 hours to complete**

**9 videos**

**2 readings**

**4 practice exercises**

**3 hours to complete**

## Models for Continuous Data

This module covers conjugate and objective Bayesian analysis for continuous data. Lesson 9 presents the conjugate model for exponentially distributed data. Lesson 10 discusses models for normally distributed data, which play a central role in statistics. In Lesson 11, we return to prior selection and discuss ‘objective’ or ‘non-informative’ priors. Lesson 12 presents Bayesian linear regression with non-informative priors, which yield results comparable to those of classical regression.

**3 hours to complete**

**9 videos**

**5 readings**

**5 practice exercises**

### Reviews

#### 4.6

##### TOP REVIEWS FROM BAYESIAN STATISTICS: FROM CONCEPT TO DATA ANALYSIS

Good intro to Bayesian Statistics. Covers the basic concepts. Workload is reasonable and quizzes/exercises are helpful. Could include more exercises and additional backgroung/future reading materials.

Great course. The content moves at a nice pace and the videos are really good to follow. The Quizzes are also set at a good level. You can't pass this course unless you have understood the material.

the notes for the lectures are missing.\n\nIn my opinion the notes, which includes the video materials could be very useful.\n\nthe course was good. I learnt some new concepts in bayesian thinking.

Very concise and helpful for an intro to Bayesian statistics. Good level of difficulty to encourage learning. This well prepares further study of more advanced topics such as MCMC and more.

This is first time exposure to bayesian statistics and I must say it has given me a different perspective to analyzing data especially when dealing with unpredictable data or unknown data.

It was a good course for me to get familiar with the new perspective on statistics. Thank you!\n\nMaybe, some extended practice exercise at the end of the course would make it even better)

Very clear and informative. Would like a more extensive and combined reference material (PDF, so less need to lookup e.g. definitions of effective sample size for various distributions).

A good course but neither notes nor lectures were not in much details. But still it was worth my time. I strongly recommend it if you want a subtle introduction to Bayesian Statistics.

I like the course and how the questions are designed. I wish it can be accompanied by a booklet of transcripts of some sort. Videos are good, but so are traditional reading materials.

Exceptional course on probabilities and statistics from a Bayesian point of view. I would recommend this course to anyone wishing to learn more about probabilities and statistics.

One of the best courses I took to date. Paralleled only by ML (by Andrew Ng). Non-trivial assignments, focused on practice, well-explained concepts in readings. Truly impressed.

A great intro to Bayesian analysis and probability distributions. Personally I skipped the Excel content and converted the R code to python, which was itself valuable learning.

Very well structured course. Problems and quiz are real life problems, and it's challenging and rewarding to solve them. Thanks to Prof. Lee for delivering an awesome course.

I think the course would benefit by recommending a textbook that would supplement the lecture material. It's nice to have a reference to refer to after viewing the lectures.

simple, clear and enjoyable. will take the second course in the series, then move to heavy literature on the topic.\n\nSpecial thank you to the instructor! you are amazing!

Alot of information, concise and clarity is awesome. Would recommend this course to anyone. And I did too. Great, professor. My only suggestion is to speak a little slower.

Very good overview to the area. Efficient and clear lectures - emphasis on the quizzes that required just a proper amount of focus and time from my personal point of view.

A great introduction to bayesian statistics. I warmly recommend this course to those already familiar with the frequentist approach and willing to expand their knowledge.

This is a good course. The instructor offers additional material that help with the understanding of the material, along with enough quizzes to help with practical use.

Very good and concise course. I would, however, propose to delve more into theoretical mathematics and explain them with more detail as it seemed to advance very fast.

### Offered by

#### University of California, Santa Cruz

UC Santa Cruz is an outstanding public research university with a deep commitment to undergraduate education. It’s a place that connects people and programs in unexpected ways while providing unparalleled opportunities for students to learn through hands-on experience.

## Frequently Asked Questions

When will I have access to the lectures and assignments?

Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

What will I get if I purchase the Certificate?

When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

What is the refund policy?

Is financial aid available?

What are the pre-requisites for this course?

You should have exposure to the concepts from a basic statistics class (for example, probability, the Central Limit Theorem, confidence intervals, linear regression) and calculus (integration and differentiation), but it is not expected that you remember how to do all of these items. The course will provide some overview of the statistical concepts, which should be enough to remind you of the necessary details if you've at least seen the concepts previously. On the calculus side, the lectures will include some use of calculus, so it is important that you understand the concept of an integral as finding the area under a curve, or differentiating to find a maximum, but you will not be required to do any integration or differentiation yourself.

What computing resources are expected for this course?

Data analysis is done using computer software. This course provides the option of Excel or R. Equivalent content is provided for both options. A very brief introduction to R is provided for people who have never used it before, but this is not meant to be a course on R. Learners using Excel are expected to already have basic familiarity of Excel.

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