Prepaid parameter estimation without likelihoods

In various fields, statistical models of interest are analytically intractable and inference is usually performed using a simulation-based method. However elegant these methods are, they are often painstakingly slow and convergence is difficult to assess. As a result, statistical inference is greatly hampered by computational constraints. However, for a given statistical model, different users, even with different data, are likely to perform similar computations. Computations done by one user are potentially useful for other users with different data sets. We propose a pooling of resources across researchers to capitalize on this. More specifically, we preemptively chart out the entire space of possible model outcomes in a prepaid database. Using advanced interpolation techniques, any individual estimation problem can now be solved on the spot. The prepaid method can easily accommodate different priors as well as constraints on the parameters. We created prepaid databases for three challenging models and demonstrate how they can be distributed through an online parameter estimation service. Our method outperforms state-of-the-art estimation techniques in both speed (with a 23,000 to 100,000-fold speed up) and accuracy, and is able to handle previously quasi inestimable models.Author summary: Interesting nonlinear models are often analytically intractable. As a result, statistical inference has to rely on massive, time-intensive, simulations. The main idea of our method is to avoid the redundancy of similar computations that typically occur when different researchers independently fit the same model to their particular dataset. Instead, we propose to pool computational resources across the researchers interested in any given model. The prepaid method starts with an extensive simulation of datasets across the parameter space. The simulated data are compressed into summary statistics, and the relation to the parameters is learned using machine learning techniques. This results in a parameter estimation machine that produces accurate estimates very quickly (a 23,000 to 100,000-fold speed up compared to traditional methods).