Statistical Inference

模块目标

Construct point estimators, interval procedures and tests from a stated sampling model, and report them without converting a p-value into a posterior probability.

课程大纲

1. 01 Sampling and estimation 25h

   学习结果 Name the sample, the estimand, and the estimator as distinct objects.

   形成性检查 四选一检查

2. 02 Sample mean and standard error 25h

   学习结果 Derive the standard error of a sample mean under i.i.d. finite-variance sampling.

   形成性检查 书面推导

3. 03 Likelihood 25h

   学习结果 Write a likelihood for an i.i.d. sample and distinguish it from a posterior.

   形成性检查 书面推导

4. 04 Coverage and confidence intervals 35h

   学习结果 State a coverage claim as a property of the procedure, not of one realised interval.

   形成性检查 四选一检查

5. 05 Hypothesis testing 30h

   学习结果 Specify H₀, H₁, the test statistic, and the rejection region before looking at the sample.

   形成性检查 书面推导

6. 06 Errors and power 30h

   学习结果 Distinguish Type I error, Type II error, and power, and give a case where a small p-value is not a large effect.

   形成性检查 反例

7. 07 Examination synthesis 30h

   学习结果 Choose estimation, interval, or test for a short applied stem and justify the choice from the sampling model.

   形成性检查 书面推导

学习结果

For a named sampling model, derive or select an estimator, an interval with a coverage claim, and a test with explicit hypotheses, then state a limitation of each.

学科技能

Sampling models, likelihood, standard errors, coverage, Type I/II errors, power.

可迁移技能

Write the claim a procedure actually warrants; refuse language that treats one sample as a population proof.

相关入门主题

01Sampling and estimation4 个主题

1. Sampling distributions
2. Bias, variance and mean squared error
3. Standard errors and normal approximation
4. Maximum-likelihood estimation

章节链接

02Intervals and tests3 个主题

1. Confidence intervals and coverage
2. Hypothesis tests and p-values
3. Type I error, power and multiplicity

章节链接

03Examination synthesis1 个主题

1. Statistical-inference examination synthesis

章节链接