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IS-18: Invited session | Likelihood-free methods of inference (organized by Laura Ventura)
8:30am - 10:30am
Session Chair: Laura Ventura
8:30am - 9:00am
A Robust Bayesian Exponentially Tilted Empirical Likelihood Method
Zhichao Liu, Catherine Forbes, Heather Anderson
Monash University, Australia
This paper proposes a new Bayesian approach for analysing moment condition models using data that may be contaminated by ‘outliers’. Building on the Bayesian exponentially tilted empirical likelihood (BETEL) approach of Schennach (2005), auxiliary variables are used in conjunction with relevant moment conditions to stochastically trim potential outliers from the desired posterior distribution. We also demonstrate that both the BETEL and the new robust BETEL (RBETEL) posteriors may be linked to the recent work of Bissiri, Holmes and Walker (2016) who propose a general framework for updating prior belief via a specified loss function. In addition to an empirical illustration, the results of simulation experiments will be reviewed.
9:00am - 9:30am
Mean and median bias-reducing estimating equations for meta analysis
Ioannis Kosmidis1, Annamaria Guolo2, Sophia Kyriakou3, Nicola Sartori2, Cristiano Varin4
1University of Warwick, United Kingdom; 2University of Padova; 3University College London; 4Ca' Foscari University
This talk focuses on recent work on bias-reducing estimating equations for the heterogeneity parameter in meta-analysis and meta-regression settings. These estimating equations result in estimators that have mean or median bias of lower order than the maximum likelihood one. We will discuss how estimation can be performed via a convenient two-step coordinate descent process, and how the estimating equations give rise to new pivots with enhanced inference performance for meta-analytic hypotheses. The new pivots are also found to be robust under model misspecification. The exposition of the methodology will be accompanied by illustrations with real-data case studies.
9:30am - 10:00am
Saddlepoint approximations for short and long memory time series: a frequency domain approach
Davide La Vecchia, Elvezio M. Ronchetti
University of Geneva, Switzerland
Saddlepoint techniques provide numerically accurate, small sample approximations to the distribution of estimators and test statistics. Except for a few simple models, these approximations are not available in the framework of stationary time series. We contribute to fill this gap. Under short or long range serial dependence, for Gaussian and non Gaussian processes, we show how to derive and implement saddlepoint approximations for two relevant classes of frequency domain statistics: ratio statistics and Whittle’s estimator. We compare our new approximations to the ones obtained by the standard asymptotic theory and by two widely-applied bootstrap methods. The numerical exercises for Whittle’s estimator show that our approximations yield accuracy’s improvements, while preserving analytical tractability. A real data example concludes the paper.
10:00am - 10:30am
Approximate Bayesian analysis with adjusted composite likelihoods with an application to meta-analysis with binary outcomes
Nicola Sartori, Michele Lambardi di San Miniato
University of Padova, Italy
We explore the use of composite likelihoods for Bayesian inference in under-specified models, in which, for instance, some marginal distributions are assumed, but higher-order dependences in the data are ignored. Calibration and adjustment methods have been proposed in the literature to allow the use of composite likelihoods in Bayesian analysis. We propose a new simple adjustment method that can be used in studies in which the focus is on specific parameters of interest. The comparison of different adjustments, under a given prior, is performed using a simulation-based procedure that allows to validate the use of the composite likelihood in the Bayesian framework. Results are illustrated in a model for meta-analysis with binary outcomes.