Statistical Inference in Complex Situations

Due to the *digital transformation**, the amount of data collected is rapidly increasing in many fields of application. With „Big Data“ available, deviations from simple standard models can usually be detected, and it becomes tempting to consider more complex models instead. Despite the increase in computational power, classical statistical methods such as maximum likelihood and Bayesian inference, as well as modern simulation based methods (e.g. approximate maximum likelihood, approximate Bayesian computation, indirect inference), often reach limits when applied in the context of such complex statistical models. Often a trade-off has to be found between exploiting most of the relevant information in the data, and the computational feasibility. Both a clever algorithmic implementation, and speed improving concepts (such as importance sampling) can also help to obtain results with reasonable computational effort.