Abstract
A system to update estimates from a sequence of probability distributions is presented. The aim of the system is to quickly produce estimates with a user-specified bound on the Monte Carlo error. The estimates are based upon weighted samples stored in a database. The stored samples are maintained such that the accuracy of the estimates and quality of the samples are satisfactory. This maintenance involves varying the number of samples in the database and updating their weights. New samples are generated, when required, by a Markov chain Monte Carlo algorithm. The system is demonstrated using a football league model that is used to predict the end of season table. The correctness of the estimates and their accuracy are shown in a simulation using a linear Gaussian model.
Highlights
We are interested in producing estimates from a sequence of probability distributions
Our system involves saving the samples produced from the MCMC sampler in a database
Another feature of our system is that the MCMC sampler is paused whenever the estimate is accurate enough
Summary
We are interested in producing estimates from a sequence of probability distributions. The sequence can be the posterior distributions of parameters from a Bayesian model as additional data becomes available, with the aim of reporting the posterior means with the variance of the Monte Carlo error being less than 0.01. Our system involves saving the samples produced from the MCMC sampler in a database. In order to control the accuracy of the estimates, the samples in the database are maintained. This maintenance involves increasing or decreasing the number of samples in the database. Another feature of our system is that the MCMC sampler is paused whenever the estimate is accurate enough. The system is efficient, as it reuses samples and only generates new samples when necessary
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