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Subsampling sequential Monte Carlo for static Bayesian models
- Source :
- Statistics and Computing. 30:1741-1758
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- We show how to speed up sequential Monte Carlo (SMC) for Bayesian inference in large data problems by data subsampling. SMC sequentially updates a cloud of particles through a sequence of distributions, beginning with a distribution that is easy to sample from such as the prior and ending with the posterior distribution. Each update of the particle cloud consists of three steps: reweighting, resampling, and moving. In the move step, each particle is moved using a Markov kernel; this is typically the most computationally expensive part, particularly when the dataset is large. It is crucial to have an efficient move step to ensure particle diversity. Our article makes two important contributions. First, in order to speed up the SMC computation, we use an approximately unbiased and efficient annealed likelihood estimator based on data subsampling. The subsampling approach is more memory efficient than the corresponding full data SMC, which is an advantage for parallel computation. Second, we use a Metropolis within Gibbs kernel with two conditional updates. A Hamiltonian Monte Carlo update makes distant moves for the model parameters, and a block pseudo-marginal proposal is used for the particles corresponding to the auxiliary variables for the data subsampling. We demonstrate both the usefulness and limitations of the methodology for estimating four generalized linear models and a generalized additive model with large datasets.
- Subjects :
- Statistics and Probability
Markov kernel
Computer science
Bayesian probability
Posterior probability
010103 numerical & computational mathematics
Bayesian inference
01 natural sciences
Statistics::Computation
Theoretical Computer Science
Hybrid Monte Carlo
010104 statistics & probability
Computational Theory and Mathematics
Resampling
Kernel (statistics)
0101 mathematics
Statistics, Probability and Uncertainty
Particle filter
Algorithm
Subjects
Details
- ISSN :
- 15731375 and 09603174
- Volume :
- 30
- Database :
- OpenAIRE
- Journal :
- Statistics and Computing
- Accession number :
- edsair.doi...........1cd47354aa47bad0c8acd17dafacf874