Likelihood for censored data

[rccreswell]

A censored data point is known to fall in a certain interval, but its actual location within that interval is unknown.

In time series analysis partially left-censored data often arises when instrumentation is affected by a limit of detection. The instrument records values above the limit of detection as continuous values, while values below the limit of detection are recorded as LOD or "0" (but this 0 is does not imply that the value at that data point is actually equal to zero).

This type of censoring occurs, for example, in viral abundance data which we want to fit to ODE models using pints.

Assuming that there is a noise process (e.g., Gaussian) before the censoring process and this is independent, the likelihood for the censored time series data looks calculable. We would add Censored Gaussian and Censored Truncated Gaussian Log Likelihood classes to pints.