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Simulation models are often used to study a system or phenomenon. However, before a simulation model can be used, its parameter needs to be fit to mimic observed data. This is called the parameter inference problem. This thesis approaches this problem for stochastic simulations using sequential Monte Carlo approximate Bayesian computation in conjunction with summary statistics trained by a convolutional neural network as the main method. Other approaches to solving this problem were also explored using traditional summary statistics with the aforementioned method and a completely different approach called simulation-based inference where a density estimator is trained. The approach using convolutional neural network-trained statistics showed promising results for two of the five explored data sets given by collaborators from the University of Edinburgh (Prof. Ramon Grima) and the Netherlands Cancer Institute (Prof. Tineke Lenstra). Further investigation is needed in order to enable accurate parameter inference for the other three datasets.