Empiiriset uskottavuudet vaikeasti laskettaville uskottavuusmalleille

Standard Bayesian inference is infeasible when likelihood functions are intractable due to factors such as model stochasticity, chaos, or high dimensionality. Several methods have been suggested for such cases, such as approximate Bayesian computation. The Bayesian Synthetic Likelihood (BSL) approach addresses the problem by constructing the likelihood using summary statistics that are assumed to follow a normal distribution. Traditional summary statistics require tuning parameters, making their efficient application laborious. This thesis studies the performance of a likelihood that requires minimal tuning: the empirical cumulative distribution function (eCDF) and the Chamfer distance. In addition to raw data, the eCDF is constructed using features derived from the original data: the correlation integral likelihood, intrinsic dimension nearest-neighbor ratios, and finite differences. The study examines the impact of these summaries on parameter estimation efficiency and accuracy. These methods are tested on three models of increasing complexity: the Ornstein-Uhlenbeck process, the Lorenz 63 system, and Nicholson's Blowfly model. The results indicate that augmenting the empirical cumulative distribution function and correlation integral likelihood with first-order differences is the most effective strategy, significantly improving estimation accuracy. While intrinsic dimension ratios enhanced parameter identifiability in the chaotic Lorenz 63 system and the Chamfer distance reduced uncertainty for specific parameters in the Lorenz 63 and Blowfly models, their general applicability remains an open question for future research. The study concludes that combining empirical cumulative distribution statistics with finite differences offers a robust, computationally efficient, and almost tuning-free approach for parameter estimation across various intractable likelihood models.