unbinned

Unbinned refers to data or analyses that retain the original, continuous measurements without grouping them into discrete bins. In statistics, data are often summarized with histograms that count observations in predefined intervals; unbinned analysis uses the raw values directly and avoids binning-related artifacts. The term is used in contrast to binned data and analyses that rely on counts per bin.

Common unbinned methods include unbinned maximum likelihood estimation, where the likelihood is built from a probability density function evaluated at each observation. In practice, this means modeling the distribution of the data with a parametric or nonparametric density f(x; θ) and maximizing the product of f(x_i; θ) over all observations. Unbinned likelihood analyses can incorporate measurement resolution, acceptance, and other experimental effects through the density function.

Advantages of unbinned analyses include the preservation of full data information and resolution, avoidance of biases from arbitrary bin edges, and typically more precise parameter estimates, particularly for small datasets or when sharp features are present in the distribution. They are often preferred when exact event-level information matters.

Disadvantages include higher computational cost and the need for an accurate model of the underlying continuous distribution; unbinned methods can be more sensitive to model misspecification and outliers. In multiple dimensions, the complexity and data requirements grow, making density estimation more challenging.

Applications range from particle physics and astronomy to time-series and event-based studies, where data are naturally continuous or collected as individual events. Unbinned approaches are commonly contrasted with binned analyses, which are simpler and faster but may incur information loss.