| The costs of sampling are often quite high in biomedical engineering and medicine, where collecting data is often invasive, destructive, or time consuming. This results in experiments that are either sparse or very expensive. Optimal design strategies can help a researcher to make the most of a given number of experimental observations, but neglect the actual problem of sample size determination. For a grey-box experiment with continuous parameter and observation spaces, one must determine how many observations are required in order to ensure precise parameter estimates that resist experimental error and prior uncertainty in the parameter values. This work proposes a novel approach to sample size determination that bridges experimental science with principles of quality engineering and control. Parallel Markov chains are simulated from the prior and preposterior distributions to generate posterior predictive distributions for a proposed experiment. This represents the population of possible posterior distributions for the experiment over the entire observation space. One can compute the expected estimator precision and determine the optimal sample size as a measure of the "consumer's risk", i.e., the probability that the experiment, on the average, will fail to yield a necessary degree of estimator precision. This work evaluates the proposed method by applying it to a combination of simulated and practical experiments, which validate the utility of the algorithm and examine its properties under various prior distributions and degrees of experimental error. This work also created a specialized software package to carry out the computations necessary for sample size determination. |
