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ARC Centres of Excellences - Grant ID: CE140100049

Title
ARC Centres of Excellences - Grant ID: CE140100049
Funding
ARC | ARC Centres of Excellences
Contract (GA) number
CE140100049
Start Date
2014/01/01
End Date
2020/12/31
Open Access mandate
no
Organizations
-
More information
http://purl.org/au-research/grants/arc/CE140100049

 

  • Hamiltonian Monte Carlo with Energy Conserving Subsampling

    Dang, Khue-Dung; Quiroz, Matias; Kohn, Robert; Tran, Minh-Ngoc; Villani, Mattias (2017)
    Projects: ARC | ARC Centres of Excellences - Grant ID: CE140100049 (CE140100049)
    Hamiltonian Monte Carlo (HMC) has recently received considerable attention in the literature due to its ability to overcome the slow exploration of the parameter space inherent in random walk proposals. In tandem, data subsampling has been extensively used to overcome the computational bottlenecks in posterior sampling algorithms that require evaluating the likelihood over the whole data set, or its gradient. However, while data subsampling has been successful in traditional MCMC algorithms s...

    Estimating Residual Connectivity for Random Graphs

    Computation of the probability that a random graph is connected is a challenging problem, so it is natural to turn to approximations such as Monte Carlo methods. We describe sequential importance resampling and splitting algorithms for the estimation of these probabilities. The importance sampling steps of these algorithms involve identifying vertices that must be present in order for the random graph to be connected, and conditioning on the corresponding events. We provide numerical results ...

    What causes the increase in aggregation as a parasite moves up a food chain?

    Lester, R. J. G.; McVinish, R. (2016)
    Projects: ARC | ARC Centres of Excellences - Grant ID: CE140100049 (CE140100049)
    General laws in ecological parasitology are scarce. Here we evaluate data published by over 100 authors to determine whether the number of hosts in a life cycle is associated with the degree of aggregation of fish parasites at different stages. Parasite species were grouped taxonomically to produce 20 or more data points per group as far as possible. Most parasites that remained at one trophic level were less aggregated than those that had passed up a food chain. We use a stochastic model to ...

    The block-Poisson estimator for optimally tuned exact subsampling MCMC

    Quiroz, Matias; Tran, Minh-Ngoc; Villani, Mattias; Kohn, Robert; Dang, Khue-Dung (2016)
    Projects: ARC | ARC Centres of Excellences - Grant ID: CE140100049 (CE140100049)
    Speeding up Markov Chain Monte Carlo (MCMC) for datasets with many observations by data subsampling has recently received considerable attention in the literature. The currently available methods are either approximate, highly inefficient or limited to small dimensional models. We propose a pseudo-marginal MCMC method that estimates the likelihood by data subsampling using a block-Poisson estimator. The estimator is a product of Poisson estimators, each based on an independent subset of the o...

    Bayesian Inference for State Space Models using Block and Correlated Pseudo Marginal Methods

    Choppala, P.; Gunawan, D.; Chen, J.; Tran, M. -N.; Kohn, R. (2016)
    Projects: ARC | ARC Centres of Excellences - Grant ID: CE140100049 (CE140100049)
    This article addresses the problem of efficient Bayesian inference in dynamic systems using particle methods and makes a number of contributions. First, we develop a correlated pseudo-marginal (CPM) approach for Bayesian inference in state space (SS) models that is based on filtering the disturbances, rather than the states. This approach is useful when the state transition density is intractable or inefficient to compute, and also when the dimension of the disturbance is lower than the dimen...

    A comparison of random walks in dependent random environments

    Scheinhardt, Willem R.W.; Kroese, Dirk (2016)
    Projects: ARC | ARC Centres of Excellences - Grant ID: CE140100049 (CE140100049)
    Although the theoretical behavior of one-dimensional random walks in random environments is well understood, the actual evaluation of various characteristics of such processes has received relatively little attention. This paper develops new methodology for the exact computation of the drift in such models. Focusing on random walks in dependent random environments, including $k$-dependent and moving average environments, we show how the drift can be characterized and found using Perron-Froben...

    Scalable MCMC for large data problems using data subsampling and the difference estimator

    Quiroz, Matias; Villani, Mattias; Kohn, Robert (2015)
    Projects: ARC | ARC Centres of Excellences - Grant ID: CE140100049 (CE140100049)
    We propose a generic Markov Chain Monte Carlo (MCMC) algorithm to speed up computations for datasets with many observations. A key feature of our approach is the use of the highly efficient difference estimator from the survey sampling literature to estimate the log-likelihood accurately using only a small fraction of the data. Our algorithm improves on the $O(n)$ complexity of regular MCMC by operating over local data clusters instead of the full sample when computing the likelihood. The lik...

    Computing the Drift of Random Walks in Dependent Random Environments

    Scheinhardt, Werner R. W.; Kroese, Dirk P. (2014)
    Projects: ARC | ARC Centres of Excellences - Grant ID: CE140100049 (CE140100049)
    Although the theoretical behavior of one-dimensional random walks in random environments is well understood, the numerical evaluation of various characteristics of such processes has received relatively little attention. This paper develops new theory and methodology for the computation of the drift of the random walk for various dependent random environments, including $k$-dependent and moving average environments.

    Stratified Splitting for Efficient Monte Carlo Integration

    Vaisman, Radislav; Salomone, Robert; Kroese, Dirk P. (2017)
    Projects: ARC | ARC Centres of Excellences - Grant ID: CE140100049 (CE140100049)
    The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as data science, statistical physics, and machine learning. However, exact computation methods suffer from the curse of dimensionality. However, due to the curse of dimensionality, deterministic numerical methods are inefficient in high-dimensional settings. Consequentially, for many practical problems, one must resort to Monte Carlo estimation. In this paper, we i...

    Variational Bayes with Intractable Likelihood

    Tran, Minh-Ngoc; Nott, David J.; Kohn, Robert (2015)
    Projects: ARC | ARC Centres of Excellences - Grant ID: CE140100049 (CE140100049)
    Variational Bayes (VB) is rapidly becoming a popular tool for Bayesian inference in statistical modeling. However, the existing VB algorithms are restricted to cases where the likelihood is tractable, which precludes the use of VB in many interesting situations such as in state space models and in approximate Bayesian computation (ABC), where application of VB methods was previously impossible. This paper extends the scope of application of VB to cases where the likelihood is intractable, but...
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