timebin

A timebin is a fixed interval of time used to aggregate events or measurements into discrete slots along a timeline. By mapping continuous or irregularly spaced data onto a regular time grid, timebinning enables simple computation of rates, counts, and statistics over time.

Bin width selection: The choice of bin width, Δt, balances temporal resolution against statistical noise. A smaller bin width preserves details but increases variance in counts; a larger width reduces noise but can smear rapid changes. For Poisson processes, the expected count in a bin is λΔt, where λ is the event rate. Fixed-width binning uses non-overlapping intervals, while sliding or overlapping bins create a moving window to reduce edge effects. Adaptive binning adjusts Δt to maintain roughly constant counts per bin or to track rate changes.

Applications: In astronomy, photon arrival times are binned to produce light curves for variability studies. In neuroscience, spike trains are binned into time bins to estimate firing rates. In monitoring, analytics, and finance, time bins summarize events or measurements to compute rates, means, or histograms over time.

Considerations: Binning can introduce bias and loss of temporal detail, especially for fast transients or irregular event patterns. Irregular sampling, data gaps, or nonstationary processes may require alternative approaches such as kernel density estimation, unbinned likelihood methods, or adaptive binning strategies. Timebin techniques remain a foundational tool for turning raw time-stamped data into interpretable time series.