The physical properties of nanostructures are controlled by their exact chemical and structural composition. In order to fully understand the structure-property relationship of materials it is important to reliably quantify structure parameters, such as the positions of the atoms, the type of the atoms, and the number of atoms. In this thesis, atomic scale aberration-corrected (scanning) transmission electron microscopy ((S)TEM) is pushed toward precise measurements of unknown structure parameters using advanced statistical techniques in a model-based framework.

For this purpose, quantitative structure determination can be reduced to a statistical parameter estimation problem. The pixel values in the recorded images are then the observations from which the structure parameters can be estimated by fitting a model, which depends on the unknown parameters, to the experimental images. An efficient estimation algorithm for application to larger nanostructures has been proposed.

Ultimately, the precision with which the parameters can be estimated is limited by noise. Statistical parameter estimation theory and statistical detection theory provide a theoretical lower bound on the variance of the parameters, i.e. the attainable precision. This concept has been used to determine the limits to the precision with which structure parameters can be estimated.

In the second part of the thesis, a statistics-based method in order to count the number of atoms of single-element crystalline nanostructures from annular dark field (ADF) STEM images has been discussed in detail together with a thorough study on the possibilities and inherent limitations. In order to count the number of atoms, it is assumed that the total intensity of scattered electrons, i.e. the scattering cross-section, scales with the number of atoms per atomic column. This method has been used to quantify the number of atoms for different nanostructures from experimental ADF STEM images.

In this manner, it has experimentally been shown that single atom sensitivity can be attained. From the experimental analyses, it could be concluded that the statistics-based method should be complemented with another method in order to confirm the validity of the atom-counting results. In this thesis, a simulation-based approach has mainly been used for this purpose. The experimental scattering cross-sections are then compared with simulated scattering cross-sections obtained using detailed STEM simulations.