Statistical Inference and Prediction

These flashcards cover important concepts pertaining to statistical inference, prediction, and their methodologies as discussed in the lecture.

Inference vs Prediction

Inference focuses on understanding relationships and estimating parameters, while prediction focuses on forecasting unseen outcomes with accuracy.

Parameter

A fixed but unknown quantity that describes the population, which we aim to estimate through inference.

Likelihood Function

A function that measures how plausible different values of a parameter are given the observed data.

Maximum Likelihood Estimation (MLE)

A statistical method that chooses the parameter value that makes the observed data most plausible.

Bayesian Framework

A statistical framework that treats parameters as random variables and updates beliefs about them after observing data.

Credible Interval

A range of values within which a parameter is believed to lie with a certain probability, analogous to confidence intervals in frequentist statistics.

Bootstrap

A resampling technique that allows estimation of sampling distribution and uncertainty when theoretical formulas are difficult to obtain.

Bias

Systematic error in estimation; an unbiased estimator has an expected value equal to the true parameter value.

Variance

A measure of the instability of an estimator across different samples.

Mean Squared Error (MSE)

A single number that combines bias and variance, calculated as the sum of the variance and the square of the bias.

Overfitting

A modeling error that occurs when a model captures noise in the training data, leading to poor performance on new data.

James-Stein Estimator

An estimator that shows that shrinking estimates towards a common mean can improve overall accuracy.

ROC Curves

Graphs that display the performance of a binary classification model by illustrating the trade-off between true positive rate and false positive rate.

Area Under the Curve (AUC)

A metric that measures the overall ability of a model to distinguish between two classes, where higher values indicate better performance.

Training Error

The error measured on the data used to fit the model; it often underestimates true prediction error due to overfitting.

A/B Testing

An experimental method where two versions are compared to determine which one performs better, often involving random assignments to control and treatment groups.