Free Course Image Statistics for Applications

Free online courseStatistics for Applications

Duration of the online course: 28 hours and 0 minutes

New course

Learn the essentials of statistics with MIT OpenCourseWare's free online course. Covering topics from parametric inference to Bayesian statistics and regression analysis.

In this free course, learn about

  • Foundations of Statistical Inference
  • Maximum Likelihood and Method of Moments
  • Parametric Hypothesis Testing and Goodness of Fit
  • Regression Analysis
  • Bayesian Inference
  • Dimensionality Reduction with PCA
  • Generalized Linear Models

Course Description

Statistics for Applications is a comprehensive course designed to provide a solid foundation in statistical methods and concepts. Spanning 28 hours, this course is part of the Basic studies category, under the subcategory of Statistics. This curriculum is structured to guide learners from introductory concepts to more advanced statistical techniques, ensuring a robust understanding of both theoretical and practical aspects.

The course kicks off with an Introduction to Statistics, laying down the fundamental principles that will be built upon in subsequent lessons. This initial phase ensures that all learners, regardless of prior exposure, are grounded in the basic concepts and terminology of statistics.

As the course progresses, the focus shifts to Parametric Inference and Maximum Likelihood Estimation, key methodologies in the field of statistics. These lessons delve deep into the theoretical underpinnings and practical applications, ensuring that learners gain a robust understanding of these essential techniques. The course also introduces the Method of Moments, offering alternative approaches to parameter estimation.

Parametric Hypothesis Testing is comprehensively covered through several lessons, emphasizing the methodological approaches and practical significance of hypothesis tests. This segment also explores Testing for Goodness of Fit, a crucial aspect for determining how well a model corresponds to observed data.

Regression techniques are extensively discussed, providing insights into modeling relationships between variables. This part of the course ensures that learners can apply regression analysis to real-world data, enhancing their predictive and analytical capabilities.

The course then transitions into Bayesian Statistics, offering a different perspective on inference and decision-making under uncertainty. This innovative approach complements the traditional frequentist methods, providing learners with a well-rounded statistical toolkit.

Principal Component Analysis is another critical topic covered, aimed at data dimensionality reduction while retaining essential information. This technique is particularly valuable in dealing with large, complex datasets.

Finally, the course delves into Generalized Linear Models (GLMs), broadening the scope of regression analysis to include various types of data and response variables. These models are versatile and widely used in numerous fields, making them an essential part of any statistician's skill set.

Throughout the course, learners will engage in substantive evaluations to consolidate their understanding and application of the concepts. Although no reviews are available yet, the detailed and methodical approach of the curriculum ensures that participants will gain significant expertise in the field of statistics.

Statistics for Applications is an invaluable resource for anyone looking to gain a thorough understanding of statistical methods and their applications. Whether you are a beginner or looking to expand your knowledge, this course provides the foundation and advanced skills necessary for statistical analysis in various domains.

Course content

  • Video class: 1. Introduction to Statistics 1h18m
  • Exercise: Is the provided estimator for the mean extbf{ extit{mu}} a biased or unbiased estimator?
  • Video class: 2. Introduction to Statistics (cont.) 1h17m
  • Exercise: When estimating the rate of inter-arrival times of a subway at Kendall station (assuming exponential distribution), what theorem justifies the replacement of the true parameter with its estimator in the variance of the central limit theorem?
  • Video class: 3. Parametric Inference 1h22m
  • Exercise: Which statistical concept explains that the average of sampled estimates will converge to the true population parameter as the sample size increases?
  • Video class: 4. Parametric Inference (cont.) and Maximum Likelihood Estimation 1h17m
  • Exercise: What is the Kullback-Leibler (KL) divergence and how does it differ from the total variation distance in the context of probability distributions?
  • Video class: 5. Maximum Likelihood Estimation (cont.) 1h16m
  • Exercise: For the Bernoulli trials in a maximum likelihood estimation framework, what would be the estimator if we observe the sample (x1, x2, x3) = (1, 0, 1)?
  • Video class: 6. Maximum Likelihood Estimation (cont.) and the Method of Moments 1h19m
  • Exercise: In the method of moments, if the parameter space is d-dimensional, how many moments are typically needed to estimate the parameters adequately?
  • Video class: 7. Parametric Hypothesis Testing 1h18m
  • Exercise: In statistical hypothesis testing, what does a Type I error represent?
  • Video class: 8. Parametric Hypothesis Testing (cont.) 1h18m
  • Exercise: What is the expected value of a chi-squared distribution with d degrees of freedom?
  • Video class: 9. Parametric Hypothesis Testing (cont.) 1h21m
  • Exercise: When performing a hypothesis test for a univariate function g of the parameter vector theta, which method can be used to ensure that the test statistic has an asymptotic standard normal distribution?
  • Video class: 11. Parametric Hypothesis Testing (cont.) and Testing Goodness of Fit 1h22m
  • Exercise: Which of the following significance tests is appropriate to use if a dataset's distribution parameters are unknown and need to be estimated from the data itself for hypothesis testing?
  • Video class: 12. Testing Goodness of Fit (cont.) 1h21m
  • Exercise: What is the primary purpose of binning when applying a chi-square goodness-of-fit test?
  • Video class: 13. Regression 1h16m
  • Exercise: Which statistical method is used to predict one variable based on another variable, and involves finding a line that best fits the data in a least squares sense?
  • Video class: 14. Regression (cont.) 1h13m
  • Exercise: What is the coefficient of determination in a linear regression model?
  • Video class: 15. Regression (cont.) 1h15m
  • Exercise: In the context of linear regression, testing whether an entire vector of coefficients is significantly different from zero simultaneously is an example of what type of test?
  • Video class: 17. Bayesian Statistics 1h18m
  • Exercise: What is a Jeffrey's prior and how is it defined in the context of Bayesian statistics?
  • Video class: 18. Bayesian Statistics (cont.) 1h03m
  • Exercise: What does the Jeffrey's prior represent in Bayesian inference?
  • Video class: 19. Principal Component Analysis 1h17m
  • Exercise: Principal Component Analysis (PCA) aims to maximize the spread or variance when projecting data onto lower-dimensional space. In the context of PCA, what is the significance of eigenvalues and eigenvectors of the data covariance matrix?
  • Video class: 20. Principal Component Analysis (cont.) 1h16m
  • Exercise: Principal component analysis (PCA) is primarily used for which of the following purposes?
  • Video class: 21. Generalized Linear Models 1h15m
  • Exercise: In the context of Generalized Linear Models (GLMs), what is the main role of the canonical link function?
  • Video class: 22. Generalized Linear Models (cont.) 1h17m
  • Exercise: What is the canonical link function in the context of Generalized Linear Models (GLM)?
  • Video class: 23. Generalized Linear Models (cont.) 1h18m
  • Exercise: Explain the concept of Iteratively Re-weighted Least Squares (IRLS) in the context of generalized linear models (GLMs).
  • Video class: 24. Generalized Linear Models (cont.) 54m
  • Exercise: In the context of generalized linear models and optimization algorithms, what is the purpose of the iteratively reweighted least squares (IRLS) method?

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