I will discuss two applications where probabilistic and statistical techniques can aid decision making processes.
The first is a problem in operations research, where some quantity is to be maximised subject to certain, random, constraints. In order to quantify the randomness, scenarios are formed. However, optimizing with respect to all scenarios is computationally costly and it is often not easy to see how a change in the scenario set changes the optimal solution obtained. I will discuss how applying unsupervised clustering methods to the scenarios can enable upper and lower bounding strategies to be obtained as well as a better insight into the problem itself.
The second application concerns personalised medicine, particularly the problem of quantifying a tumour's response to a therapy, based on a growth curve. I will discuss a probabilistic approach to model tumour growth and quantify response to therapy. By explicitly including randomness in the model we obtain a more accurate and flexible measurement of the responses. Since data is scarce due to the cost of experiments, this is vital in order to lower development costs and increase the efficiency of new drugs.
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