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Bayesian Statistics: Techniques and Models, 1.01 (V) Course Introduction

[MUSIC] Hello, I'm Matt Heiner, a Doctoral Student of Statistics and Applied Mathematics at the University of California, Santa Cruz. After assisting Professor Herbie Lee in bringing you the first course in this series, I'm excited to present to you the second course on Bayesian Statistics. Welcome to the class. The next step in your development as a Bayesian statistician is a crucial one. Real world data involving multiple variables often require more complex models to reach realistic conclusions. As we encounter more widely applicable models. We will need advanced computational techniques to fit them. This course will introduce Markov Chain Monte Carlo. Often referred to as MCMC methods, which allow sampling from posterior distribution that have no analytical solution. These methods have revolutionized Bayesian statistics because they vastly expand the possibilities of models that are available to us. In this course, we will build on the fundamentals that were introduced in Professor Lee's course. We will assume that you have completed that course using r for your calculations. Or that you have a basic familiarity with Bayesian concepts and can do some basic programming in r. If you're out of practice in these or in calculus-based probability, don't worry. We'll review important skills as they do come necessary in our work. The courses organized into five modules. In the first module, we will discuss statistical modelling and review how to approach your problem from a Bayesian perspective. We will also introduce the concept of using probabilistic stimulation to approximate quantities that are difficult to compute directly. The second module is dedicated to introducing MCMC. We will describe and demonstrate two algorithms that have brought Bayesian statistics into the mainstream. We will also introduce Jags, an open source software which implements MCMC for you. So that you can focus on modelling rather than coding intricate algorithms. In the third module, we'll begin modelling real data. Will demonstrate some of the most common statical models including linear and logistic regression. In the fourth module we'll look at regression for account data. And we'll introduce hierarchical modeling as a way to account for correlated data. Throughout this demonstrations will explore different techniques to adjust challenges that often arise in data analysis. The last module contains only in assignments. This assignment puts you in the driver seat. It's your opportunity to bring together all the pieces we've built throughout these two courses and conduct your own data analysis on a project that you select. This peer reviewed assignment is also your chance to practice communicating the methods you use to solve a problem. It's also an important opportunity to get feedback on your work and help others to improve their work. Each module has about 90 minutes to two hours of video instruction. We recommend that you watch instructional videos at the highest screen resolution. You can set this up option by clicking on the gear icon in the lower right portion of the screen. We encouraged you to watch the videos multiple times. The programming demonstration videos come with code so that you can follow along. Many lessons come with required background reading. Or optional supplementary reading which may make the material more accessible. Each module comes with an honors quiz if you're looking for a challenge or for extra practice. Also the honors sections of modules three and four address additional topics you might find interesting. In order to synthesize and solidify what you learn it is necessary to get plenty of practice in an ordinary course we would give you regular home work assignment. In the Coursera framework we provide the homework problem as quizes. We encourage you to approach the quizes as homework sets. Which may require reviewing the relevant material, attempting to find a solution, returning again to the material and correcting errors. If it takes a half hour or more to complete a quiz You're probably approaching how we intended and you'll get more out of this course. The problems may require several attempts, but don't be discouraged we allow multiple quiz attempts. Also we provide a lot of feedback in the quizzes themselves, even if you get a problem correct. You may learn something by reading the feedback. Again, welcome to the course. We hope this will be a rewarding experience as you dive into applied Bayesian modeling and broaden your analytical skill set. [MUSIC]



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[MUSIC] Hello, I'm Matt Heiner, a Doctoral Student of Statistics and Applied Mathematics at the University of California, Santa Cruz. After assisting Professor Herbie Lee in bringing you the first course in this series, I'm excited to present to you the second course on Bayesian Statistics. Welcome to the class. The next step in your development as a Bayesian statistician is a crucial one. Real world data involving multiple variables often require more complex models to reach realistic conclusions. As we encounter more widely applicable models. We will need advanced computational techniques to fit them. This course will introduce Markov Chain Monte Carlo. Often referred to as MCMC methods, which allow sampling from posterior distribution that have no analytical solution. These methods have revolutionized Bayesian statistics because they vastly expand the possibilities of models that are available to us. In this course, we will build on the fundamentals that were introduced in Professor Lee's course. We will assume that you have completed that course using r for your calculations. Or that you have a basic familiarity with Bayesian concepts and can do some basic programming in r. If you're out of practice in these or in calculus-based probability, don't worry. We'll review important skills as they do come necessary in our work. The courses organized into five modules. In the first module, we will discuss statistical modelling and review how to approach your problem from a Bayesian perspective. We will also introduce the concept of using probabilistic stimulation to approximate quantities that are difficult to compute directly. The second module is dedicated to introducing MCMC. We will describe and demonstrate two algorithms that have brought Bayesian statistics into the mainstream. We will also introduce Jags, an open source software which implements MCMC for you. So that you can focus on modelling rather than coding intricate algorithms. In the third module, we'll begin modelling real data. Will demonstrate some of the most common statical models including linear and logistic regression. In the fourth module we'll look at regression for account data. And we'll introduce hierarchical modeling as a way to account for correlated data. Throughout this demonstrations will explore different techniques to adjust challenges that often arise in data analysis. The last module contains only in assignments. This assignment puts you in the driver seat. It's your opportunity to bring together all the pieces we've built throughout these two courses and conduct your own data analysis on a project that you select. This peer reviewed assignment is also your chance to practice communicating the methods you use to solve a problem. It's also an important opportunity to get feedback on your work and help others to improve their work. Each module has about 90 minutes to two hours of video instruction. We recommend that you watch instructional videos at the highest screen resolution. You can set this up option by clicking on the gear icon in the lower right portion of the screen. We encouraged you to watch the videos multiple times. The programming demonstration videos come with code so that you can follow along. Many lessons come with required background reading. Or optional supplementary reading which may make the material more accessible. Each module comes with an honors quiz if you're looking for a challenge or for extra practice. Also the honors sections of modules three and four address additional topics you might find interesting. In order to synthesize and solidify what you learn it is necessary to get plenty of practice in an ordinary course we would give you regular home work assignment. In the Coursera framework we provide the homework problem as quizes. We encourage you to approach the quizes as homework sets. Which may require reviewing the relevant material, attempting to find a solution, returning again to the material and correcting errors. If it takes a half hour or more to complete a quiz You're probably approaching how we intended and you'll get more out of this course. The problems may require several attempts, but don't be discouraged we allow multiple quiz attempts. Also we provide a lot of feedback in the quizzes themselves, even if you get a problem correct. You may learn something by reading the feedback. Again, welcome to the course. We hope this will be a rewarding experience as you dive into applied Bayesian modeling and broaden your analytical skill set. [MUSIC]


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