Simulation-based estimation: a case study in oncology (SIMEST) and a case study in portfolio selection (SIMUGRAM)

Abstract

Since the time of Poisson, stochastic processes have been axiomatized in the temporally forward direction. Yet for nearly a century, estimation of parameters and even forecasts have been based on likelihood approaches that start with temporally indexed data and then look backward in time. I shall be using the philosophy of Karl Pearson [Scott DW, Tapia RA, Thompson JR. Karl Pearson was right. Computer Science and Statistics: Tenth Annual Symposium on the Interface; 1978, 179?183] in this article where I create, using a forward model, a large virtual universe of happenings based on the assumption of four parameters characterizing an oncological process based on four Poissonian processes. Bins will be formed in the real time space based on the actual data of real world system of times of discovery of primary and secondary tumors and use bin boundaries that enclose roughly 5% of the actual tumor discover data and compare the bin proportions of virtual data with the proportions of actual data in each of the bins. This will enable us to use Karl Pearson's goodness-of-fit criterion as the objective function for a Nelder-Mead optimization. We present here an oncological example where the objective is to estimate four parameters relevant to the progression of breast cancer. This procedure is termed the SIMEST paradigm.Then we briefly describe the patented SIMUGRAM for estimating the distribution of portfolio values using daily resampling strategies. This procedure makes minimal model assumptions and is completely based on data.