• bringing together leaders in likelihood asymptotics, parametric likelihood methodology, computational issues, and applied areas for which new likelihood methods are needed
• consolidate our accumulated wisdom and knowledge about parametric likelihood inference, much of which is contained only in the minds or file cabinets of the many senior researchers who have led this field for decades, and crucially has not appeared in published works
  
• for a large number of open problems, be they theoretical, methodological, computational, or applied, we will discuss the history, current state of progress, and relative importance for current and future statistical practice, as well as their relative importance to our foundational understanding of statistical theory
• arrive at some sort of consensus about which open problems are relatively more important according to each measure of importance, along with clear reasons for this ordering, and fair acknowledgment of differences of opinion
  
• develop a written document which summarizes each of these problems, together with annotated bibliographies, indications of relative importance, and comments about what would constitute significant progress on each problem; this will serve as a guide for editors and new researchers
• discuss barriers to adoption and implementation of existing parametric likelihood tools which are known to be superior to what is currently being used in practice
  

• There will be online discussion forums and slides posted (and videos if possible).
  
• The organizer(s) will distribute documents with some examples of open problems in advance of the workshop, and expert feedback will be solicited.
  
• We would greatly appreciate anyone pointing out open problems. If you can write a brief description and mention key references (if they exist), that would be wonderful!
  
• Help is also needed with writing the comprehensive summary document. Anyone who contributes substantially will be a co-author. The document will be posted on arXiv and updated by the group as new developments arise in the field.

• Heather Battey
  Imperial College London
  
• David R. Cox
  University of Oxford
  
• ^John Kolassa
  Rutgers University
• Ioannis Kosmidis
  University of Warwick
  
• ^Todd Kuffner **organizer
  Washington University in St. Louis
• ^Nancy Reid
  University of Toronto
• Richard Samworth
  University of Cambridge
  
• ^Pragya Sur
  Harvard University
• Larry Wasserman
  Carnegie Mellon University
  
• ^Alastair Young
  Imperial College London
  

• M. Akahira and K. Takeuchi (1981). Asymptotic Efficiency of Statistical Estimators: Concepts and Higher Order Efficiency. Springer Lecture Notes in Statistics.
  
• David F. Andrews and James E. Stafford (2000). Symbolic Computation for Statistical Inference. Oxford University Press.
• Adelchi Azzalini (1996). Statistical Inference Based on the Likelihood. Chapman & Hall/CRC Press.
• Ole E. Barndorff-Nielsen (2014, re-issued from 1978 original). Information and Exponential Families in Statistical Theory. Wiley.
  
• Ole E. Barndorff-Nielsen (1988). Parametric Statistical Models and Likelihood. Springer Lecture Notes in Statistics.
  
• Ole E. Barndorff-Nielsen and David R. Cox (1989). Asymptotic Techniques for Use in Statistics. Chapman & Hall/CRC Press.
  
• *Ole E. Barndorff-Nielsen and David R. Cox (1994). Inference and Asymptotics. Chapman & Hall/CRC Press.
• D. Basu with J.K. Ghosh, editor (1988). Statistical Information and Likelihood: A Collection of Essays. Springer Lecture Notes in Statistics.
  
• *Alessandra R. Brazzale, Anthony C. Davison and Nancy Reid (2007). Applied Asymptotics: Case Studies in Small-Sample Statistics. Cambridge University Press.
• Ronald W. Butler (2007). Saddlepoint Approximations with Applications. Cambridge University Press.
• G.M. Cordeiro and F. Cribari-Neto (2014). An Introduction to Bartlett Correction and Bias Reduction. Springer Briefs in Statistics.
  
• David R. Cox and D.V. Hinkley (1974). Theoretical Statistics. Chapman & Hall/CRC Press.
  
• Christopher Field and Elvezio Ronchetti (1990). Small Sample Asymptotics. Institute of Mathematical Statistics.
• D.A.S. Fraser (1968). The Structure of Inference. Wiley.
• D.A.S. Fraser (1979). Inference and Linear Models. McGraw-Hill.
  
• J.K. Ghosh (1994). Higher Order Asymptotics. NSF-CBMS Regional Conference Series in Probability and Statistics, IMS and ASA.
• C.C. Heyde (1997). Quasi-Likelihood and Its Application: A General Approach to Optimal Parameter Estimation. Springer Series in Statistics.
  
• J.L. Jensen (1995). Saddlepoint Approximations. Oxford University Press.
  
• R.E. Kass and P.W. Vos (1997). Geometrical Foundations of Asymptotic Inference. Wiley Series in Probability and Statistics.
• John E. Kolassa (2006). Saddlepoint Approximation Methods in Statistics, Third Edition. Springer Lecture Notes in Statistics.
  
• *Peter McCullagh (1987). Tensor Methods in Statistics. Chapman & Hall.
• Peter McCullagh and J.A. Nelder (1989). Generalized Linear Models, Second Edition. Chapman & Hall/CRC Press.
  
• *Luigi Pace and Alessandra Salvan (1997). Principles of Statistical Inference from a Neo-Fisherian Perspective. World Scientific.
  
• Yudi Pawitan (2001). In All Likelihood: Statistical Modeling and Inference Using Likelihood. Oxford University Press.
  
• J. Pfanzagl (1994). Parametric Statistical Theory. Walter de Gruyter.
  
• *Thomas A. Severini (2000). Likelihood Methods in Statistics. Oxford University Press.
• Masanobu Taniguchi (1991). Higher Order Asymptotic Theory for Time Series Analysis. Springer Lecture Notes in Statistics.
  
• Masanobu Taniguchi and Yoshihide Kakizawa (2000). Asymptotic Theory of Statistical Inference for Time Series. Springer Series in Statistics.
  
• G. Alastair Young and Richard L. Smith (2005). Essentials of Statistical Inference. Cambridge University Press.
  

 Topics might include open problems related to, for example:

• higher-order efficiency
• higher-order accuracy
• power improvements and sources of low power
  
• Fisherian conditionality and ancillarity principles
• robustness
• computational issues
• approaches to inference for interest parameters in presence of nuisance parameters
• high-dimensional inference problems
  
• Bartlett correction
• pseudolikelihoods and Bartlett identities
• applied problems for which new or better likelihood inference procedures are needed
• the role of differential geometry in understanding and improving likelihood inference