D.A.S. Fraser

Department of Statistical Sciences
University of Toronto
100 St George Street, Toronto
Canada M5S 3G3

of: Sidney Smith Hall, 100 St George Street,
Dept of Statistical Sciences, 6th floor
ph: 416.482.2911
fx: 416.978.5133.
em: dfraser at utstat.toronto.edu.

Current Statistical Inference Theory

A seminar at the Mathematics Department of Imperial College London gave the
opportunity to present an overview of modern statistical inference theory
The Statistical Tool Box: What can we get from likelihood?
Imperial College, University of London. March 22 2019.
The Statistical Tool Box: What can we get from likelihood?

Eight challenging examples

The methodology discussed in the seminar just described has been applied to eight challenging examples offered by David Cox; see
Some simple but challenging examples

At the fifth Bayesian, fiducial, and frquentist conference

BFF5 Conference-Foundations of data science,
University of Michigan May 6-9, 2018 .
A A What can we get from likelihood? A new prior for Bayes

Distributions for parameters

At the Fourth Bayesian, Fiduucial, and Frequentist Conference (BFF4)
Harvard University May 1-3, 2017
Distributions for theta: Validity and Riks

Bayes Reproducibility and the Quest for Truth

In the current issue of ... Statistical Science: November 2016
Bayes Reproducibility and the Quest for Truth
A mathematical prior and the conditional probability formula
Math in and Math out
And didn't convince Laplace
but maybe could be useful
Check reproducibility....which means confidence
See also
Is Bayes posterior just quick and dirty confidence

Can you integrate confidence distributions and get reproducibility?

BFF Conference, Rutgers University
April 12, 2016
What can we expect from Distributions for parameters?

Combining likelihoods and combining p-values
From many small dependent likelihoods to valid global inference

Dept of Mathematics, Univ of California, San Diego
November 30, 2015.
Combining likelihood functions or p-value functions in the presence of statistical dependence

Definitive combining of log-likelihood or p-value functions

60th World Statistics Congress 2015, Rio de Janeiro, Brazil
IPS036, July 29, 2015.
Combining likelihood functions or p-value functions: Higher accuracy and composite likelihood

On direction in statistics theory

Department of Statistical Sciences, University of Toronto
XC seminar, April 29, 2015.
On direction in statistics theory.

On combining likelihoods or significance functions: What accuracy?

Most familiar methods are not first-order accurate: full first-order accuracy however
is availble with the simple use of widely available information functions.
Combining log-likelihood or significance fuunctions, with or without statistical independence.

Combining likelihood or p-value functions, with or without statistical dependence.

Scheduled seminar: Department of Statistics and Actarial Science, Western University,
London Ontario: Thursday, April 9, 2015; postponed.
Combining likelihood or p-value functions.

Can Bayes give second order reproducibility?

Well maybe! But the choice of prior better be targetted on the parameter of interest
and the change of variable to the interest parameter be inspired!
Can Bayes give second order reproducibility?

On resolving the Bayes enigma: How Jeffreys gives 2nd order Accuracy

Invited talk: Second Conference of the International Society of Nonparametric Statistics
Cadiz, Spain: Friday, June 13, 2014
Distributional inference: Reproducibility and limitations

How saddlepoint and continuity determine statistical inference

Invited talk: Conference in honor of Malay Ghosh, College Park, Maryland
Saturday, May 31, 2014
How SP determines statistical Inference

Priors from a differential viewpoint: How Bayes can attain 2nd order Accuracy

Seminar speaker: Department of Actuarial and Statistical Sciences, Western University, London, Ontario
Thursday, April 10, 2014
Priors from a differentail viewpoint: How Bayes can attain 2nd order Accuracy

Deciphering Bayes: Reproducibility? What accuracy?

Invited talk: Department of Statistics, Univesity of Southern California
Friday, April 4, 2014
Deciphering Bayes: Reproducibility? What accuracy?

"How science goes wrong"

The Economist, October 19th-25th 2013, Vol 409

This is the cover-page editorial in the major jounal The Economist, October 19th-25th 2013, Vol 409, but read on:
Pages 26-30 record the story: and the problems are all Statistics..... like "Reject at the 5% level" .....or minor variants
and they have been well known for more than 40 years.


But statistics does have the answer!

The answer is contained in the p-value function from likelihood theory: p(delta)
Here delta is the relevant parameter with delta_0 as the null value and delta_1 as the alternative needing detection. Then p(delta_0) is the observed p-value, p(delta_1) is the detection probability, and the rest is judgement: the route to the Higgs boson.

Inference distributions for a parameter: Are they calibrated?

Do they mean what they say?

Invited Paper Session 028: World Statistics Congress 2013,
Hong Kong, August 27, 2013.
Inference distributions for a parameter.

Why does statistics have two theories?

Invited talk: World Statistics Congress 2013, ISI Young Statisticians' Meeting
The University of Hong Kong, August 24, 2013.
Why does statistics have two theories.

Contemporary Statistics: Glamour risk and aftermath.

Saw Swee Hock Visiting Professorship in Statistics: Public Lecture,
Department of Statistics & Actuarial Science, August 22, 2013.
Glamour risk and aftermath.

Another view of composite likelihood.

Invited seminar at University of Western Ontario,
Department of Statistics, January 31, 2013.
Another view of composite likelihood.

Combining dependent likelihood functions.

Invited seminar at University College London,
Department of Statistics, November 29, 2012.
Combining dependent likelihood functions.

Priors and Inference: A differential view.

Invited seminar at the University of Oxford,
Department of Statistics, November 8, 2012.
Priors and Inference: A differential view.

Combining dependent likelihoods: some thoughts on composite likelihood.

Invited seminar at University of Padova,
Department of Statistics, September 24, 2012.
Combining dependent likelihoods: some thoughts on composite likelihood.

The role of Bias in Statistics.

Invited seminar at the University of Western Ontario, Dept of Statistical and Actuarial Sciences on April 12, 2012.

Science sees Data but no role for Statistics
Drugs deemed safe so freely prescribe and collect massive data
Drug deemed safe yet thousands dead but billions in profit
And just a mild call for "Data Replication:" ..... The deaths or the dollars?
And a discipline with two logics? Physics wouldn't tolerate that!
And Statistics mildly says it is just "exploring"!
That "exploring" wouldn't wash when they acknowledge they have two logics!
Physicists find billions to test the edges of their theories and avoid contradiction
Perhaps complacency isn't the route for Statistics or they might taste the five billion penalty for contradiction
The role of Bias in Statistics.

The Bias in Bayes: A second-order determination.

Invited address at the Workshop on High-Dimensional Data Ananlysis
held at The Fields Institute, June 9, 2011.
High-Dimensional: The Barrier and Bayes and Bias.

2nd Princeton Day of Statistics.

• Opening Plenary Address at the 2nd Princeton Day of Statistics
  held at Princeton University, October 22, 2010.
  
• Continuity and Statistical Methodology.
  

Higher order likelihood and the curse of curvature.

• An address at the Joint Statistical Meetings 2010
  held at Vancouver, Canada on August 5.
  
  
• Parameter curvature and Bayesian Analysis.
  

Do statistical tools need calibration?

• An address at the conference "Data Analysis and Statistical Foundations"
  held at the Fields Institute in Toronto, April 30 and May 1, 2010.
  
  
• Calibration in Statistics.
  

The Bane of Bayes: Parameter curvature!

• Bayesian analysis or evidence based statistics.

Is r* linear in r? Sort of Yes but mostly No!

• Higher order accuracy for inference arguably began with Daniels (1954) and Lugannani and Rice (1980)
  but was restricted to exponential models and the cumulant generating function context.
  Barndorff-Nielsen (1986) gave extensions to general models with regularity leading to wide
  applicability with general data size n and with nuisance parameters alongside interest parameters.
  Much of the core mechanisms however can be seen with Taylor expansions in the scalar model case.
  
  Is r* linear in r?
  
  Four types of expansions with their interconnections are presented on a poster display initiated by
  Jean-Francois Plante and available with Google search (Temporarily unavailable):
  
  r vs r* - Magic from Taylor Expansions
  

Likelihood, p-values, ancillaries and the vector quantile function

• Statistical Laboratory, U of Cambridge: 5 May, 2009. Is r* linear in r?

Is Bayes really real probability?

• Colloque du CRM: 6 novembre 2009.

Is Bayes posterior just quick and dirty confidence?

• Current manuscript.

Higher accuracy for Bayesian and frequentist inference

• Statistical Science, Vol 22, May 2007.

Studentization and developing p-values

• Biometrika, Vol 95 (2008), 1-16.

Can Bayesians compete with frequentists?

• Bayesian or frequentist: Three enigmatic examples

Controversy or did Lindley get it wrong?

• Did Lindley get the argument the wrong way around?
  

Other Recent Talks and Papers

• University of Cambridge, Statistical Laboratory, Cambridge, U.K. May 8, 2009.
  
  • Likelihood, p-values, ancillaries and the vector quantile function.
    Click here for audio presentation.
    

• University of Wales; Gregynog, Wales, April 18, 19, 2008.
  
  • Parameter curvature and the Bayesian frequentist divergence.
    

• McMaster University, April 1, 2008.
  
  • Bayesian posterior probability is just confidence and inconveniently needs linearity.
    

• University of Western Ontario, February 7, 2008.
  
  • The Bayes myth - Probabilities. Or just approximate confidence.
    

• Princeton University, ORFE, February 13, 2007.
  
  • Data-based probability for parameter values
    

• Univ of Western Ontario, Dept of Actuarial Science and Statistics, December 8, 2005.
  
  • Should Bayesians and frequentists calibrate their parameters?
    

• Univ of Waterloo, Dept of Actuarial Science and Statistics, November 17, 2005.
  
  • Some thoughts on model-based priors
    

• Statistical Society of Canada, Annual meeting, Saskatoon, June13, 2005.
  
  • Bayes or Likelihood: Convergence or Divergence
    

• OBayes5, Branson, Missouri, June 8, 2005
  
  • Objective and other priors
    

• Munk Centre: Department of Statistics seminar, April 28, 2005
  
  • Why a prior?
    

• Recent likelihood theory: Anything new?
  
  • What a model with data says about theta
    

• Statistical Society of Canada, Annual meeting, Saskatoon, Saskatchewan, June 12-15, 2005.
  
  • Session: Bayes or Likelihood: Convergence or Divergence
    Speakers: T. Severini, Northwestern University, J. Rousseau, University of Paris 5, and organizer.
  • Session program: Bayes or Likelihood: Convergence or Divergence
    

• Case Western Reserve University, Department of Statistics
  
  • Is there statistical inference? The Bayesian-frequentist divergence!
    October 1, 2004

• Fields Institute Lectures: Is the future Bayesian or frequentist?
  
  • Lecture 1: April 16, 2002
    History and overview
    
  • Lecture 2: April 18, 2002
    Examples, conflicts, resolutions

Papers by index number

• In pdf format

Current CV

• In pdf format

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