The goal of Non-Intrusive Appliance Load Monitoring (NIALM), or energy disaggregation, is to deduce which devices are active and how much energy they consume from observation of the time evolution of the total voltage or current in the electrical network. In this thesis, energy disaggregation is performed from the time series of power meter readings, by making use of the fact that different types of appliance can be distinguished by the statistical properties of their signatures, i.e., power consumption behaviour over time. Optimal detectors, using the Viterbi algorithm, are derived for three types of signature: 1) only power levels, no time information, 2) power levels with exponentially distributed lifetimes and 3) power levels with Gaussian lifetimes with given means and variances. The detectors have been implemented in MATLAB, and their performance is compared for various inputs.