The Modern Bootstrap

Wednesday 18th April 2018

This meeting is intended as an introduction to modern uses of bootstrap technology, from three speakers working in different application areas. The meeting starts with an introductory talk to make the rest of the afternoon more accessible to non-experts.

Venue:  the Hardy Room, De Morgan House, 57-58 Russell Square, London WC1B 4HS

Date: 2-5pm, Wednesday 18th April 2018

Registration fees: BIR full or retired member £25; BIR student member £10; non-member £70.

 

Programme

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1400 - 1420Introduction to the Modern Bootstrap - Daniel Farewell (University of Cardiff)

An introductory talk to provide background to the rest of the afternoon.

 
1420 - 1505Bootstrapped synthetic likelihood - Dr Richard Everitt (University of Reading)

Approximate Bayesian computation (ABC) is now an established technique for statistical inference in the form of a simulator, and approximates the likelihood at a parameter θ by simulating auxiliary data sets x and evaluating the distance of x from the true data y. Synthetic likelihood is a related approach that uses simulated auxiliary data sets to contract a Gaussian approximation to the likelihood. However, these approaches are not computationally feasible in cases where using the simulator for each θ is very expensive. This talk investigates using the bootstrap to cheaply estimate the synthetic likelihood from a single sample from the likelihood. We also examine a synthetic likelihood approximation that is constructed, using the bag of little bootstraps, from subsampled data sets. Applications to stochastic differential equation models and doubly intractable distributions will be presented. The work in this talk is described further in the paper “Bootstrapped synthetic likelihood”, arxiv.org/abs/1711.05825

 
1505 - 1530Tea/coffee break
 
1530 - 1615Bootstrapping dynamic count models - Dr Adriana Cornea-Madeira (University of York)

Estimation and testing on the boundary of the parameter space is nontrivial, particularly if the variable of interest is discrete. We derive the asymptotic distribution of the quasi-maximum likelihood estimator for dynamic count models with exogenous covariates. We then develop asymptotic and bootstrap Wald tests for the significance of the model’s parameters on the boundary of the parameter space. We apply these results to first test for temporal clustering in extra-tropical cyclones and investigate whether or not storm occurrence is driven not only by large-scale atmospheric conditions but also by means of secondary cyclogenesis (a parent cyclone that generates offsprings). Finally we use our results to investigate whether or not corporate defaults in US are driven by economic fundamentals and/or contagion effects (when one firm’s default triggers other firms defaulting).

 
1615 - 1700Hybrid Block Bootstrap Under Weak Dependence - Prof Alastair Young (Imperial College)

The subsampling bootstrap and the moving blocks bootstrap provide effective methods for nonparametric inference with weakly dependent data. Both are based on the notion of resampling (overlapping) blocks of successive observations from a data sample: in the former single blocks are sampled, while the latter splices together random blocks to yield bootstrap series of the same length as the original data sample. Here we discuss a general theory for block bootstrap distribution estimation for sample quantiles, under mild strong mixing assumptions. A hybrid between subsampling and the moving blocks bootstrap is shown to give theoretical benefits, and startling improvements in accuracy in distribution estimation in important practical settings. An intuitive procedure for empirical selection of the optimal number of blocks and their length is proposed. The conclusion that bootstrap samples should be of smaller size than the original data sample has significant implications for scalability of bootstrap methodologies in dependent data settings.

 

This is joint work with Todd Kuffner and Stephen Lee and is described at https://arxiv.org/abs/1710.02537.

 

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