Fast robustness quantification with variational Bayes

Bayesian hierarchical models are increasing popular in economics. When using hierarchical models, it is useful not only to calculate posterior expectations, but also to measure the robustness of these expectations to reasonable alternative prior choices. We use variational Bayes and linear response methods to provide fast, accurate posterior means and robustness measures with an application to measuring the effectiveness of microcredit in the developing world.

[1]  D. Rubin.  Estimation in Parallel Randomized Experiments , 1981 .

[2]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[3]  David Ríos Insua,et al.  Robust Bayesian analysis , 2000 .

[4]  Paul Gustafson,et al.  Local Robustness in Bayesian Analysis , 2000 .

[5]  E. Moreno.  Global Bayesian Robustness for Some Classes of Prior Distributions , 2000 .

[6]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[7]  Bo Wang,et al.  Inadequacy of interval estimates corresponding to variational Bayesian approximations , 2005, AISTATS.

[8]  Radford M. Neal.  Pattern Recognition and Machine Learning , 2007, Technometrics.

[9]  Michael I. Jordan,et al.  Graphical Models, Exponential Families, and Variational Inference , 2008, Found. Trends Mach. Learn..

[10]  Dorota Kurowicka,et al.  Generating random correlation matrices based on vines and extended onion method , 2009, J. Multivar. Anal..

[11]  Richard E. Turner,et al.  Two problems with variational expectation maximisation for time-series models , 2011 .

[12]  David Barber,et al.  Bayesian Time Series Models , 2011 .

[13]  B. Fosdick.  Modeling Heterogeneity within and between Matrices and Arrays , 2013 .

[14]  M. Burke,et al.  Climate and Conflict , 2014 .

[15]  Bob Carpenter,et al.  The Stan Math Library: Reverse-Mode Automatic Differentiation in C++ , 2015, ArXiv.

[16]  Eva Vivalt,et al.  Heterogeneous Treatment Effects in Impact Evaluation , 2015 .

[17]  Rachael Meager,et al.  Understanding the Impact of Microcredit Expansions: A Bayesian Hierarchical Analysis of 7 Randomised Experiments , 2015, 1506.06669.

[18]  Michael I. Jordan,et al.  Linear Response Methods for Accurate Covariance Estimates from Mean Field Variational Bayes , 2015, NIPS.

[19]  Arnaud Doucet,et al.  On Markov chain Monte Carlo methods for tall data , 2015, J. Mach. Learn. Res..