  In this paper, we first discuss the main types of noise in a typical
pump-probe system, and then focus specifically on terahertz time domain
spectroscopy (THz-TDS) setups. We then introduce four statistical models for
the noisy pulses obtained in such systems, and detail rigorous mathematical
algorithms to de-noise such traces, find the proper averages and characterise
various types of experimental noise. Finally, we perform a comparative analysis
of the performance, advantages and limitations of the algorithms by testing
them on the experimental data collected using a particular THz-TDS system
available in our laboratories. We conclude that using advanced statistical
models for trace averaging results in the fitting errors that are significantly
smaller than those obtained when only a simple statistical average is used.
