stats

• What is the main focus of the Statistics 2 course?

  Mathematics underpinning scientific investigation
• What is the aim of the Statistics 2 course?

  To understand phenomena and make decisions under uncertainty
• What are the sources of uncertainty mentioned in the course?

  Imperfect measurements, modeling, and random aspects
• How does the statistical approach quantify uncertainty?

  By using probability to describe observed data
• What does probability allow in scientific investigations?

  To account for uncertainty in conclusions
• What was introduced in Statistics 1 that this unit develops further?

  The statistical approach to analyzing data
• What experiment is used as a motivating example in the course?

  Flipping a coin n times
• What is the unknown probability of observing heads in the coin flip?

  θ ∈ [0, 1]
• How is θ estimated in the coin flip experiment?

  Using the observed frequency of heads
• What does the estimate ˆθn represent?

  The observed frequency of heads
• Why is drawing conclusions based on ˆθn unsatisfactory?

  It does not indicate confidence in the value
• What is one goal of the course regarding uncertainty?

  To formalize and quantify confidence in estimates
• What will be supplemented with point estimates in the course?

  Ranges of possible values for θ
• What is the purpose of confidence intervals?

  To ensure the true value of θ falls within a range
• What can be inferred from repeating the coin flip experiment m times?

  Typical values for n coin flips can be obtained
• How does the distribution of ˆθi n behave for small and large n?

  Spread for small n, concentrated for large n
• What is a challenge when m = 1 in real-world scenarios?

  Cannot repeat the experiment to gather data
• What will the course develop to address the challenge of m = 1?

  Tools to infer spread of estimates
• What is a natural question regarding the estimator ˆθn?

  Whether it is the best estimator
• What does the course cover regarding Fisher information?

  It discusses the Fisher information
• What does the course discuss about efficiency?

  It covers the Cramer–Rao bound
• What is covered regarding the asymptotic distribution of the MLE?

  It discusses the asymptotic distribution of the MLE
• What does the course cover about confidence sets?

  Confidence sets around the ML estimator
• What does the course discuss about asymptotic approximations?

  Asymptotic approximations of confidence intervals
• What is included in estimating the information for ML estimators?

  Estimating the information for ML estimators
• What does the course cover regarding transformations?

  Transformations and confidence intervals
• What does the course discuss about likelihood ratio confidence sets?

  Wilks’ approach to likelihood ratio confidence sets
• What does the course cover about transformation invariant confidence sets?

  Transformation invariant confidence sets
• What does the course introduce regarding hypothesis tests?

  Introduction to hypothesis tests
• What does the course cover about hypothesis testing significance?

  Significance and power in hypothesis testing
• What approach does the course discuss for designing tests?

  The Neyman-Pearson approach
• What does the course cover about p-values?

  p-values and equivalent test statistics
• What does the course discuss regarding uniformly most powerful tests?

  Uniformly most powerful tests
• What does the course cover about generalized likelihood ratio tests?

  Generalized likelihood ratio tests
• What does the course cover regarding categorical distributions?

  Categorical distributions and Pearson’s chi-squared test
• What examples are provided for goodness-of-fit?

  Examples from genetics, like Mendel’s peas
• What does the course cover about Bayesian inference?

  Bayesian inference and its applications
• What does the course discuss regarding posterior distributions?

  Bayes estimates and credible intervals
• What does the course cover about Bayesian hypothesis testing?

  Bayesian hypothesis testing
• Where can online resources for the unit be found?

  Via Blackboard