A study of correct statistical inference after model selection took place

Classical methods for inference in statistics assume that a model is given before looking at the data and that this model perfectly describes how the data were generated. Statistical practice proceeds in another fashion: the data are used, either visually via plots, and/or by fitting several models, performing variables selection, model selection or regularization to arrive at one or more plausible models. Those selected models are then used for statistical inference. In this thesis, a study will be made of how to obtain valid inference with honest p-values for hypothesis testing and with confidence intervals that have a correct coverage when models are used that have been selected in some form.