Free online courseStatistics for Applications

Conteúdo do Curso

• 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)?