resample

Resampling is the process of changing the sampling of a signal or dataset. This can involve selecting a new set of samples from an existing collection, estimating samples at new points, or altering the sampling rate of a signal.

In statistics and data analysis, resampling techniques draw new samples from observed data to assess variability. Bootstrap sampling selects observations at random with replacement to form a new dataset, enabling estimation of confidence intervals and standard errors. The jackknife systematically leaves out one or more observations to evaluate estimator bias and variance. Resampling avoids strong parametric assumptions and is widely used for model validation and inference.

In signal processing and time series, resampling refers to changing the sampling rate or resampling grid. Up-sampling inserts new samples, typically using interpolation, while down-sampling reduces the rate, often after applying a low-pass anti-aliasing filter to prevent distortion.

Time series resampling, also called frequency conversion, aggregates or interpolates data to a different frequency, such as converting daily data to monthly or hourly data to daily. Aggregation methods include taking the sum, mean, or last observation, while interpolation estimates values between existing points.

In machine learning and statistics, resampling underpins cross-validation, bootstrapping, and bagging, where multiple training sets are generated from a single dataset to assess model performance and stability.

Common pitfalls include aliasing in downsampling, leakage in time-dependent data, and over- or under-smoothing when interpolating. The appropriate resampling method depends on data properties, the analysis goal, and computational considerations.