🔁 Parameter(s) of Interest

Parameter(s) of Interest#

The unknown quantities an analysis sets out to estimate.

Important

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What it is#

The parameter(s) of interest are the population characteristics you set out to estimate or test — usually unknown population values like a true mean, a true proportion, a difference in means, or regression coefficients. The whole study or experiment is designed to learn about them. In short: the parameter of interest is the thing you actually care about measuring.

Parameter vs statistic#

The crucial distinction: the parameter is the fixed (usually unknown) population value; the statistic is the sample quantity you compute to estimate it.

Population mean \(\mu\) — estimated by the sample mean \(\bar{x}\).
Population proportion \(p\) — estimated by \(\hat{p}\).
Difference in means \(\mu_1 - \mu_2\) — estimated by the difference in sample means.
Regression coefficients \(\beta\) — estimated by \(\hat{\beta}\).

Examples#

A/B test — the true conversion rates \(p_A\) and \(p_B\), or their difference \(p_B - p_A\).
Medical trial — the average treatment effect,

\[\text{ATE} = P(\text{recovery} \mid \text{drug}) - P(\text{recovery} \mid \text{placebo}).\]
Regression — the coefficients \(\beta_1, \beta_2, \dots\) linking predictors to the outcome.

Why it matters#

Naming the parameter of interest is the first step in designing any study: every estimator, hypothesis test (\(H_0\) vs \(H_1\)) and confidence (or credible) interval is built to make inferences about it. Frequentists treat it as a fixed unknown constant; Bayesians put a posterior distribution over it — but in both frameworks it is the target of the analysis.

Theme: Bayesian Inference · All terminology

Hint

Mind map — connected ideas

Frequentist · Posterior · Prior Belief (or Prior Probability) · A/B Testing · True Conversion Rate

Hint

More in Bayesian Inference

Bayes’ Theorem · Bayesian Correction · Bayesian Decision Theory (BDT) · Bayesian Inference. · Bayesian Neural Networks (BNNs) · Binomial Likelihood · Gaussian Processes (GPs) · Marginal Likelihood (also called The Model Evidence or Integrated Likelihood) · MCMC (Markov Chain Monte Carlo) · Posterior · Posterior belief · Posterior Probability · Posterior probability of uplift · Prior Belief (or Prior Probability)