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Lecture 5: Estimation

Lecture 5: Estimation Goals Basic concepts of Estimation Statistical approaches for estimating parameters Parametric interval Estimation Nonparametric interval Estimation (bootstrap). Central Dogma of Statistics probability Population Descriptive Statistics Sample Inferential Statistics Estimation Estimator: Statistic whose calculated value is used to estimate a population parameter, ". Estimate: A particular realization of an estimator, " . ! Types of Estimators: - point estimate: single number that can be regarded ! as the most plausible value of ". - interval estimate: a range of numbers, called a confidence interval indicating, can be regarded as likely containing the true value of ". ! Properties of Good Estimators In the Frequentist world view parameters are fixed, statistics are rv and vary from sample to sample ( , have an associated sampling distribution).

The likelihood is the probability of the data given the parameter and represents the data now available. The prior is the probability of the parameter and represents what was

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