Astrophysicists design complex models of the evolution of galaxies, biologists develop intricate models of cells, ecologists model the dynamics of ecosystems at a world scale. The work of the statistician is to take such a model, along with relevant data, and turn the pair into decisions and knowledge. Given a model for a cardiac cell and the observation of the electric activity around stem cells in the lab, how do we know whether an anti-arrythmic drug is efficient? Given an epidemiological model for Covid and the data provided by hospitals, should a political decision-maker close schools?
Making such decisions requires first to use data to guess the free parameters in a physical model. One standard way of formalizing this problem in risk-sensitive areas like medicine is called "Bayesian inference". The standard family of algorithms to perform Bayesian inference is in turn Monte Carlo methods. Unfortunately, their application requires millions of evaluations of the model under scrutiny, one after the other. For complex biological systems, such an evaluation can last a few minutes. A million minutes is close to two years. For most problems, it is not realistic to wait for two years for an intermediate task of the overall decision pipeline. In Blackjack, our goal is turn down these two years to a few weeks, or two weeks to a few hours. If successful, our algorithms would thus allow to use more complex models when making important scientific decisions, such as characterizing the dangerosity of drugs, or quantifying a key physical parameter of a model of the universe.
More concretely, Monte Carlo methods are based on evaluating many random values of the parameters of a model. While randomness is useful when the number of parameters is large, there is randomness and randomness. We claim that it is possible to impose regularity on random patterns of points, and that this regularity can be used to achieve faster Monte Carlo algorithms. Because regularity is to be interpreted as "spreading the random values of the parameters as uniformly as possible across physically possible values, we speak of "negative dependence", or "repulsive point processes": two random paramater sets should stay at long distance from each other. In Blackjack, we study the repulsive point processes that accelerate Monte Carlo methods. We study their theoretical properties ("How well does this point process solve my statistical problem?") as well as algorithms to put these point processes to work ("How fast can I solve my problem on a single computer? On a supercomputer?").
