Thomas H. Leonard's Publications in Statistics, History, Geophysics and Medicine (1972-2022) with Annotations

 

Thomas H. Leonard's Publications in Statistics, History, Geophysics and Medicine (1972-2022) with ANNOTATIONS

                                             AMENDED AND ANNOTATED,  January 2022

                                                                

                                                            Thomas H. Leonard Wiki

                   Numerous technical reports e.g. published by the American College Testing Program (1971-2) and by the Department of of the Universities of Warwick ( 1972-1980) have been omitted as have my published  comments on papers which have been read to the Royal Statistical Society, I however include some of my  self-published work. I am still trying to update the links.

                                                                                

 

                        Books,Self-Published Novels and Histories 

                        1.SCIENTIFIC INFERENCE, DATA ANALYSIS, AND ROBUSTNESS
                       (Academic Press, 1983. Co-edited with George Box and Chien-Fu Wu)

                        2.BAYESIAN METHODS (Cambridge University Press, 1999, with John Hsu)

                             Well reviewed e.g. Chapter 4 takes apart the Bernoulli- Savage Expected

                         Utility Hypothesis

                        3. A COURSE IN CATEGORICAL DATA ANALYSIS ( Chapman and Hall 2000,
                        with contributions by Orestis Papasouliotis. Taylor and Francis e-book, 2020) 

                                  I retired from University of Edinburgh in 2001.

                        

                        4 GRAND SCHEMES ON QINSATORIX (2012) self-published novel studylib.net 

                        

                        5.THE LIFE OF A BAYESIAN BOY (2012, self-published)

                        6.**.A PERSONAL HISTORY OF BAYESIAN STATISTICS up to

                                 1971 (2014, Wiley)

                        Wiley Hot Article of the Week 28th April 2014

                   Article Level Metrics


                          Score in context

Is one of the highest ever scores in this journal (ranked #7 of 136)

Puts article in the top 25% of all articles ranked by attention

Very good compared to articles of the same age (82nd percentile)

      
                        7. A PERSONAL HISTORY OF BAYESIAN STATISTICS  (2014, StatsLife)

                        8. A PERSONAL HISTORY OF BAYESIAN STATISTICS from 1972  (2014,                                    revised  2021)

                              Self published

                        9.  THE EARLY HISTORY OF BAYESIAN STATISTICS (2014)    Slidetodoc.com

                             As presented to a meeting of the Edinburgh Section of the Royal Statisticsl                                     Society

                              

                        10.(2THE LIFE OF A BAYESIAN BOY: AN INTERVIEW WITH THOMAS                                          HOSKYNS LEONARD 014, Statistics Views)

I believe that most statistical investigations are inherently subjective in nature, and that statisticians should no longer attempt to achieve ‘false objectivity’. Rather than attempting to educate the public in a possibly misleading manner, I think that our leading statistical societies should focus on encouraging their members to invariably insist on fairness, professionalism, and impartial honesty, while acknowledging the subjective nature of their conclusions. It is only then that we can hope to properly educate the public regarding the real benefits that can be gained from statistical investigations.

                  
                        11..REBORN ON SOUTRA (2017, Self-Published Novel)

                        12. INTERVIEW BY DIEGO ANDRES LUIS PEREZ (Bulletin of the International
                        Society for Bayesian Analysis, 2016)


                        13.WRITTEN AND VERBAL SUBMISSIONS TO THE  COMMISSION

                      OF INQUIRY   INTO THE HISTORY OF EUGENICS AT UCL 

                      (with Scott Forster 2019)

                         Our quote

                      has been cited by Professor Ann Alison Phoenix of UCL

             Eugenics was not universally popular in its heydays. Early critics of Eugenics included Lester Frank Ward, GK Chesterton(see his 1917 book Eugenics and Other Evils), Franz Boas, Halliday Sutherland, and Aldous Huxley, Liberal MP Josiah Wedgwood would speak against the 1913 Mental Deficiency Act. This Act, though containing elements of welfare state provision, also made judgements on mental abilities as if they were fixed and biological rather than the result of material social conditions.

       The early eugenicists cannot therefore be exonerated on the grounds that their preachings were unquestioned at that time.

                        14.OUR  ARCHIVES ON GALTONIAN EUGENICS (2019- 2021)   

    

                    15. PROFESSOR DAVID FINNEY, SIR GODFREY THOMPSON AND 

                                  EUGENICS IN EDINBURGH 

           

                        16. LOOKING BACK THROUGH THE FIREBALL  (2022) COMPLETED                                        NOVEL

                                         

                                                  

             

                                                  
                                                                             Dissertations

                       Bayesian Methods for Several Multinomial Distributions (1971)
                      M.Sc, Dissertation,University College London. Supervised by D.V. Lindley.

                       Mark of Distinction on advanced, research level Masters,

                       Bayesian Methods for the Simultaneous Estimation of Several Parameters (1973)
                       Ph.D. Thesis, University of London    Supervised by D.V. Lindley 

                          External Examiner: Patricia Altham, University of Cambridge,

                                                             Patricia Altham, pioneer of

                                                        Bayesian Categorical Data Analysis

Chapter 1                 Introduction

Chapter 2                 The Estimation of Several Parameters

Chapter 3                 The Simultaneous Estimation of Multinomial Cell Probabilities

Chapter 4                 A Bayesian Method for Histograms

Chapter 5                 A Bayesian Analysis for Several Multinomial Distributions

Chapter 6                 Two-Way Contingency Tables and Related Topics

Chapter 7                 The Linear Model with Unequal Variances

Chapter 8                 Regression Models

                                                          ARTICLES     ** 22 best papers (in my opinion!)
                                     

                       DURING 1970s    Papers 1,2,7, and 12 were inspired by D.V. Lindley,

                       and have since been regarded  by Hitchcock and Agresti  (2005)  as initiating 

                       a key 'logistic' approach in the history  of Bayesian Categorical Data                                      Analysis, that followed the methodologies of Jack Good and Patricia Altham.

                                Nan Laird, Matthew Knuiman and Terry Speed have also contributed to                          this logistic approach, and it  was pursued exhaustively by Jon Forster, and                           by John Geweke and other econometricians.

                                     

                       1. BAYESIAN METHODS FOR BINOMIAL DATA (1972) Biometrika

                                         (I published a related paper with John Hsu in 2017 i.e. 45 years later!)

                             


                       2**. A BAYESIAN METHOD FOR HISTOGRAMS (1973) Biometrika


                      3. A MODIFICATION TO THE BAYES ESTIMATE OF THE MEAN OF  A NORMAL
                            DISTRIBUTION (1974) Biometrika

                       4, COMMENT ON THE ESTIMATION OF PROPORTIONS IN
                           M GROUPS (1974) Psychometrika

                      5. Letter on Parapsychology and Coincidences (1974) Sunday Times
                          Later reproduced in INCREDIBLE COINCIDENCE by Alan Vaughan

                      6.**. A BAYESIAN APPROACH TO THE LINEAR MODEL WITH
                          UNEQUAL VARIANCES (1975) Technometrics

                     Later extensively applied by Jean Foulley, Daniel Gianola, and Rob Tempelman

                     to Animal Breeding, and by John Geweke to Econometrics. 

                      7 **BAYESIAN ESTIMATION METHODS FOR TWO-WAY
                          CONTINGENCY TABLES (1975) JRSSB

                      8. SOME ALTERNATIVE APPROACHES TO MULTI-PARAMETER
                           ESTIMATION (1976) Biometrika

                      9. AN INVESTIGATION OF THE F-TEST PROCEDURE AS AN
                           ESTIMATION SHORTCUT (with J.K.Ord, 1976) JRSSB.

                                 Provides an early Bayesian justification of Akaike's criterion AIC,

                     10. BAYES ESTIMATION SUBJECT TO UNCERTAINTY ABOUT PARAMETER
                           CONSTRAINTS (with A O'Hagan, 1976) Biometrika

                     11. A BAYESIAN APPROACH TO SOME MULTINOMIAL ESTIMATION
                           AND PRETESTING PROBLEMS (1977) JASA. Another Bayesian justification

                         of AIC.

                     12.** AN ALTERNATIVE BAYESIAN APPROACH TO THE BRADLEY-TERRY
                           MODEL FOR PAIRED COMPARISONS (1977) Biometrics

                             USCF later considered my methodology for ranking chess players.

                             

                     13. BAYESIAN SIMULTANEOUS ESTIMATION FOR SEVERAL
                           MULTINOMIAL DISTRIBUTIONS (1977) Comm. Statist. A

                   14. AN APPLICATION OF MULTIVARIATE HIERARCHICAL
                            FORECASTING (with P.J. Harrison and T.Gazard, 1977)
                            RSS Annual Conference Proceedings

                     15**.  DENSITY ESTIMATION, STOCHASTIC PROCESSES AND
                            PRIOR  INFORMATION (with Discussion, 1978) JRSSB

               (This paper initiated a very extensive high quality literature, by Peter Lenk, Daniel                 Thorburn, Chong Gu, Finbarr O'Sullivan,  Dennis Cox, Jaako Riihimaki, and Aki                      Vehtari. Approximate solutions can be computed using Havard Rue's computer

                package INLA)

                                                     289 citations including

                                         CITATIONS (semantic scholar)

                        Peter Lenk (2019) has fully implemented his methodology on his BSAM package                            on   R

                               
                          
                          
                     DURING 1980s (Includes long fallow period during time I worked half-time for

                    U.S. Army with MRC, and until I began by my  research with John Hsu)

                                     

                       1**. THE ROLES OF COHERENCE AND INDUCTIVE MODELLING
                           IN BAYESIAN STATISTICS (with Discussion,1980) Valencia 1

                       2.**THE PROBABILITY OF FETAL METALOBIC ACIDOSIS DURING
                           LABOR IN A POPULATION AT RISK AS DETERMINED BY
                           CLINICAL FACTORS (with Discussion, 1981 with Jim Low et al)
                           American Journal of Obstetrics and Gynaecology 

                       3 ** Comment on A SIMPLE PREDICTIVE DENSITY FUNCTION (1982)
                            JASA. Contains a seminal result introducing conditional Laplacian
                            Approximations into the Bayesian literature. Amazing accuracy was                                               demonstrated by John Hsu

                           during his subsequent Ph.D. research. Cited by Tierney and Kadane as source                               reference,

                       4  AN EMPIRICAL BAYES APPROACH TO THE SMOOTH
                           ESTIMATION OF UNKNOWN FUNCTIONS (1982) MRC Report

                          This technical report and my research with Finbarr O'Sullivan initiated a large                                literature on the

                         effectively Bayesian smoothing of logistic regression functions, It was adapted by

                                          O'Sullivan, Yandell, and Raynor (JASA 1986)

                        John Hsu and I were not to publish a fully Bayesian approach to semi-parametric

                     logistic regression until our paper in Biometrika (1997). 

                  

                                  

                       5. AN INFERENTIAL APPROACH TO THE BIOSSAY DESIGN
                           PROBLEM (1982) MRC Report     
                           
                       6. APPLICATIONS OF THE EM ALGORITHM TO THE
                           ESTIMATION OF BAYESIAN HYPERPARAMETERS (1982)
                           MRC Report

                       7.  STATISTICAL INFERENCE FOR THE SKEWED NORMAL
                            AND RELATED DISTRIBUTIONS (1982, with Louis Broekhoven)
                            MRC Report
  
                       8.  A BAYESIAN APPROACH TO MARKOVIAN  MODELS FOR
                            NORMAL AND POISSON DATA (1982) MRC Report

                       9. BAYES ESTIMATION OF A MULTIVARIATE DENSITY
                           (1982) MRC Report

                     10. SOME PHILOSOPHIES OF INFERENCE AND MODELING
                          (1983) In Scientific Inference, Robustness and Data Analysis

                     11 Comment on PARAMETRIC EMPIRICAL BAYES INFERENCE by Carl Morris
                           (1983)JASA    

                     12. SOME DATA-ANALYTIC MODIFICATIONS TO BAYES-STEIN
                            ESTIMATION (1984) Ann Inst Statist Math

                     13 ON BAYES THEOREM, PATERNITY TESTING AND WISCONSIN
                           LAW (1985) UW Report 

                     14  COMMENT ON THE PAPER BY DIACONIS AND EFRON (1985) Annals of                                Statistics                     

                     15. BAYESIAN INFERENCE AND DIAGNOSTICS FOR THE
                           THREE PARAMETER LOGISTIC MODEL (1985, with M.R.Novick)
                           ONR Report, cited in psychometrics literature.           

                     16**. BAYESIAN FULL-RANK MARGINALIZATION FOR TWO-WAY
                           CONTINGENCY TABLES (1986, with M.R. Novick) JES

                            Includes analysis of the Marine Corps Data, and Laplacian Approximations,

                     17 ON THE APPLICATION OF AIC TO BIVARIATE DENSITY
                           ESTIMATION, NON-PARAMETRIC REGRESSION, AND
                           DISCRIMINATION (1985, with T. Atilgan) in Multivariate Statistical Modeling 

                           and Data Analysis (ed by Bozdogan and Gupta)
                       

                     18.** BAYESIAN MARGINAL INFERENCE (1989, with John Hsu
                           ands Kam-Wah Tsui) JASA

                    This paper got conditional Laplacian approximations right

                                                              John and Serene Hsu

            

                

                    DURING 1990s  


                      1. Comment on PREDICTIVE LIKELIHOOD-A REVIEW
                          (1990, with John Hsu and Kam-Wah Tsui) Statistical Science

                      2. Commentary on PARENTING PROBABILITY, AN
                          UNNECESSARY ARTIFACT (1991, by John Wood) 
                          (Reference obscure)

                      3. **STATISTICAL INFERENCE FOR MULTIPLE CHOICE TESTS
                          (1991, with John Hsu and Kam-Wah Tsui) Psychometrika

                      4.** BAYESIAN INFERENCE FOR A COVARIANCE MATRIX
                          (1992, with John Hsu) Annals of Statistics

                        Motivated a large literature  e.g. by John Hsu, Marick Sinay, Chih-Wen Hsu,                                  Xinwei Deng, Kam Wah Tsui, Jim Berger and Ruoyong Yang, Manabu Asai and                                    MIcheal McAleer (stochastic volatility models), and Peter Williams (neural                                        networks)              

                      5. BAYESIAN ANALYSIS, AN OVERVIEW      
                          (1992, first ISBA newsletter)

                      6. THE BAYESIAN ANALYSIS OF CATEGORICAL DATA,
                          A SELECTIVE REVIEW (1994, with John Hsu) In Aspects of Uncertainty: 
                         A Tribute to D.V. Lindley     
                         

                      7. THE LAPLACIAN T-APPROXIMATION IN BAYESIAN INFERENCE
                         (1994, with John Hsu and Christian Ritter) Statistica Sinica

                      8. BAYESIAN AND LIKELIHOOD METHODS FROM
                          EQUALLY WEIGHTED MIXTURES
                          (1994, with John Hsu et al) Ann Inst Statist Math

                      9.ON SMALL SAMPLE BAYESIAN INFERENCE AND DESIGN FOR
                          QUANTAL RESPONSE CURVES (1994,with John Hsu)
                           In Modeling and Prediction honouring Seymour Geisser
                                                                 

                     10. AN INVESTIGATION OF HIERARCHICAL BAYES PROCEDURES
                          IN ITEM RESPONSE THEORY (1994, with S.H. Kim et al)
                           Psychometrika

  

                     11.** ON EXCHANGEABLE SAMPLING DISTRIBUTIONS FOR
                          UNCONTROLLED DATA (1996) Stat and Prob Letters

                     12**. THE MATRIX-LOGARITHMIC COVARIANCE MODEL
                           (1996, with Tom Chiu and Kam-Wah Tsui) JASA

                               Described as seminal in the Econometrics literature by Asai and McAleer

                                Applied to spatial processes by Le Sage and Pace (2012) , Le Sage and                                        Pace implemented their extensions on their computer package MESS,

                             

                     13.**BAYESIAN METHODS FOR VARIANCE COMPONENTS MODELS
                          (1996, with Li Sun, John Hsu and Irwin Guttman) JASA

                                       

                     14. BAYESIAN ESTIMATION FOR SHIFTED EXPONENTIAL
                          DISTRIBUTIONS (1996, with M.T, Madi) J Stat Plan Inf.

                     15 ESTIMATION OF QUANTITIES HANDLED AND BURDEN
                          OF PROOF ( 1996, with Colin Aitken et al) JRSSA

                     16  PRONOUNCED CYTOPLASMIC PH GRADIENTS ARE NOT
                           REQUIRED FOR TIP GROWTH IN PLANT AND FUNGAL CELLS
                          (1997 with R.M.Parton et al) Journal of Cell Science

                     18 ** A TWO-ITEM SCREENING QUESTIONNAIRE FOR ALCOHOL
                            AND OTHER DRUG PROBLEMS (1997, with R.L. Brown et al)
                          Journal of Family Practice  

                     19**.HIERARCHICAL BAYESIAN SEMI-PARAMETRIC PROCEDURES
                           FOR LOGISTIC REGRESSION. (1997, with John Hsu) Biometrika

                                     Cited in history of Bayesian Categorical Data Analysis

                                                 by Hitchcock and Agresti (2005)

                     20 THE PREVALENCE AND DETECTION OF SUBSTANCE ABUSE
                           DISORDERS IN PATIENTS  OF AGES 18 TO 49
                          (1998, with R.L. Brown et al) Preventive Medicine  

                  21, Izenman A. J., Papasouliotis, 0., Leonard, T., and Aitken, C. G. G. (1998). 

                  Bayesian predictive evaluation of measurement error with application to 

                  the assessment of illicit drug quantity. 

                 Technical Report 3, Statistical Laboratory, University of Edinburgh

                     22.**  ONE SLOPE OR TWO? DETECTING STATISTICALLY
                            SIGNIFICANT BREAKS OF SLOPE IN GEOPHYSICAL DATA
                           (1999, with Ian Main et al) Geophysical Research Letters


                       AD 2000 and beyond ( I took time off and then retired early in 2001)

                      Three joint papers, concerning a statistical approach to radial basis
                      networks, with International Chess Master Mark Orr and his colleagues in 
                      A.I. are omitted as I did not substantively contribute. They appeared in
                      the International Journal for Neural Systems (1999, 2000). 

                       The Geophysics patent and two related papers evolved from Chapter 5 of 
                      Orestis Papasouliotis ' Ph.D. thesis The first four chapters of Orestis' thesis

                       describe his as yet unpublished research, supervised by myself ,on the Bayesian 

                       Analysis of Covariance, with an application in Forensic Psychology.

                               

                      1. BAYES ESTIMATION WITH UNCERTAIN ORDER CONSTRAINTS
                          (2000, with M.T.Madi and Kam-Wah Tsui) J Stat Plan Inf

                      2 A TWO-ITEM CONJOINT SCREEN FOR ALCOHOL AND OTHER 
                          DRUG RELATED PROBLEMS (2001, with R.L.Brown et al)
                          Journal of the Board of Family Practice  

                      3 ** A BAYESIAN FIXED EFFECTS ANALYSIS OF THE 
                          MANTEL-HAENSZEL MODEL APPLIED TO META ANALYSIS
                          (2002, with John Duffy) Statistics in Medicine   

                      4. COVARIANCE MATRIX ESTIMATION  (2003, with O. Papasouliotis)
                             Encyclopedia of Environmetrics

                      5.** A POISSON MODEL FOR IDENTIFYING CHARACTERISTIC SIZE
                          EFFECTS IN FREQUENCY DATA (2001, with O. Papasouliotis and
                           Ian Main) Journal of Geophysical Research

                      6 THE SAFARI CAT DATA, PERFORMANCE INDICATORS AND 
                          POSSIBLY MONOTONIC POPULATION PROPORTIONS
                          (2005, with John Hsu) UCSB, Unpublished Manuscript

                      7 BAYESIAN INFERENCE FOR MODEL CHOICE
                          (2006, with John Hsu) UCSB, Unpublished Manuscript, a bit flawed             

                      8** .LONG RANGE CRITICAL POINT DYNAMICS IN OILFIELD
                          FLOW RATE DATA (2006, with Ian Main et al)
                          Geophysical Research Letters

                      9. HYDROCARBON RECOVERY FROM A HYDROCARBON RESERVOIR
                           (2006, with Ian Main et al) International Patent

                     10.** THE STATISTICAL RESERVOIR MODEL: CALIBRATING FAULTS
                           AND FRACTURES AND PREDICTING RESERVOIR RESPONSE TO
                           WATER FLOOD (2007, with Ian Main et al) Geological Society London

                                This and Low et al (1981) are my two best joint applied papers. 

                 They seem to have been seminal in Medicine and in Geophysics. Orestis and I 

                  contributed the key statistical ideas to the Geophysics paper,

                11 Numerous international posts as moderator Mental Health Discussions                                        Edinburgh (2015-date)

                     12. ON ANALYSING THE SCOTTISH CRIME DATA, AND MENTAL 
                           HEALTH (2015)
                           Thomas Hoskyns Leonard Blog

                                

                    13 **INSURANCE MORTALITY RATES., PERFORMANCE INDICATORS AND                              POSSIBLY MONOTONIC POPULATION PROPORTIONS       

                         (with John Hsu) International Journal of Statistics and Probability 2017
                

                     14ALL ABOUT ATTENTION DEFICIT DISORDER (2019)  Self-published, in                                   preparation.

                     15. DISCUSSION (WITH DIEGO PEREZ) OF KIDD AND KATZFUSS'S 

                    DISCUSSION PAPER ON SPATIAL PROCESSES TO ISBA,

                                     BAYESIAN ANALYSIS (2022). 

                      WOW! I HAVE NOW PUBLISHED IN THE INTERNATIONAL JOURNALS FOR 50                        YEARS

                          


                      I have also self-published over 100 poems and published about 10 poems in church publications, the Broughton Spurtle and elsewhere. My short story Joe's Mole (2012) is published in an obscure book. 

                           


                                  

                              
                               Tom, aged 67, reading a poem to the 'Blind Poetics'
                                performance group, in the Blind Poet Bar, Edinburgh
        

THE STATISTICAL RESERVOIR MODEL

 

                                   

OIL AND GAS RESERVOIR

                                                                

                                                                 Ian Main, Geophysics

                                              THE STATISTICAL RESERVOIR MODEL

                           Paper with Ian Main, Kes Heffer, Orestis Papasouliotis et al:

                                                   Please click on:

                                                  GEOLOGICAL SOCIETY (2007)

                          One of the best joint papers on statistical applications that  I've had the honour 

                of being involved in.  Orestis and I contributed some of the key statistical ideas. 

                                         See Chapter 5 of Orestis' Ph.D. Thesis (20000

                                       Lun Li's Ph.d. Thesis (2006) 

‘             

Includes detailed Bayesian inferences for the

             models we applied in geophysics 

           Lungui Li Institute for Nuclear Research 

          Joint Institute for Nuclear Research,. Dubna, Moscow Oblast                                  

                                                         

THE RISING OF ACADEMIC STATISTICS DEPARTMENTS IN THE US

 

                                                                   

                                                     Bob Hogg, University of Iowa, Iowa City

                                                                         ON THE HISTORY

                                                Carnegie-Mellon University

                                                                A Celebration of Statistics

                                           

                                     STRENGTH IN NUMBERS  (Springer Link, 2013)

                                              Edited By Alan Agresti and  Xiao-Li Meng

)

                                                                                                     PDF

                

                                                                 

                                                        Alan Agresti, University of Florida

                            For Department of Statistics, UW Madison please click on

                                                                            GOOGLE BOOKS

                                   and view pp525-537    

                                             

                                               HISTORY OF STATISTICS AT UCSB

                                                                   MILTON SOBEL

                                                                 

DISCUSSION OF THE ISBA DISCUSSION PAPER ON SPATIAL PROCESSES BY KIDD AND KATZFUSS (by Diego Perez and Tom Leonard)

 

                                                               Diego Perez, University of Manchester

                                                 PAPER BY KIDD AND KATZFUSS

                                                           

                                                              Brian Kidd, Texas A&M

The following written contribution to the discussion has been accepted for publication by editor Michele Guindani:

Diego Perez (University of Manchester) and Tom Leonard (retired Wisconsin and Edinburgh)

Maybe the authors should refer to the Bayesian Econometric approach pioneered by Le Sage and Kelley (2002). Le Sage and Kelley proposed the matrix exponential spatial specification (MESS) as a way of simplification of the log-likelihood allowing a closed form solution to the problem of maximum likelihood estimation and simplification of the Bayesian estimation of the model. MESS can produce estimates and inferences similar to those from conventional spatial auto-regressive (AR) models, but has analytical, computational, and interpretive advantages.

Inference and estimation of traditional spatial autoregressive (SAR) models requires non-linear optimization for estimation and inference. The conventional spatial autoregressive approach introduces additional theoretical complexity relative to non-spatial autoregressive models and is difficult to implement in large samples.

MESS replaces the conventional geometric decay of influence over space with an exponential pattern of decay. It results in theoretical simplicity as well as improved numerical performance relative to the conventional spatial autoregression. MESS models the dependence of the covariances on explanatory variables by observing that for any real symmetric matrix A the matrix exponential transformation C is a positive definite matrix.

Le Sage and Kelley utilise an approach proposed  by Chiu, Leonard, and Tsui (1996). Chiu et al develop a generalized linear model for covariance matrices together with a linear model for the means, using the matrix logarithmic transformation A=log C. This  provides a very general paradigm for modeling a multitude of spatial processes, particularly when random effects are included with fixed effects, Why is another approach needed?

Perhaps the authors should also consider the large  literature for Bayesian inference for a covariance matrix C that refers to the matrix transformation A =log C. Key papers include Leonard and Hsu (1996) and Hsu, Sinay, and Hsu (2012), who assume a matrix normal prior distribution for the upper triangular elements of A, In particular, Deng and Tsui (2012) address the estimation of large sparse covariance matrices. Most recently,Magnus, Pils and Sentana (2021) derive an explicit expression for the Jacobian of the matrix exponential transformation, with even further applications in Econometrics.

        References included in : BACKGROUND MATERIAL

Ryan Law, Plymouth Argyle, Hero of St. Andrews

 

                                                          RYAN LAW, WIKI

                                   Age 22 Birthplace Kingsteignton, Devon

     Scored spectacular winning goal against Birmingham City in 4th Round of FA Cup on 8th January 2022 at St. Andrews Stadium Birmingham after only 7 appearances in football league,. His goal will be remembered in perpetuity. Please watch it on BBC video. The highlights are extremely exciting.

                                                       Brum 0 Argies 1   (BBC VIDEO) 

                                                            

                                                           Kingsteignton, Devon

  

Appearances and goals by club, season and competition

Club Season League FA Cup League Cup Other Total

Division Apps Goals Apps Goals Apps Goals Apps Goals Apps Goals

Plymouth Argyle 2017–18[13] League One 0 0 0 0 0 0 0 0 0 0

2018–19[14] League One 0 0 0 0 0 0 1[a] 0 1 0

2019–20[15] League Two 0 0 0 0 0 0 0 0 0 0

2020–21[16] League One 7 1 0 0 2 0 3[a] 0 12 1

Plymouth Argyle Total 7 1 0 0 2 0 4 0 13 1

Gloucester City (loan) 2018–19 National League South 2 0 0 0 — 0 0 2 0

Truro City (loan) 2019–20 Southern League Premier South 27 3 2 1 — 1[b] 0 30 4

Torquay United (loan) 2020–21[16] National League 8 0 0 0 — 0 0 8 0

Career total 44 4 2 1 2 0 5 0 49 4

                      LAW SIGNS NEW DEAL

                     Brum 0 Argies 1   (BBC VIDEO)

THE JACOBIAN OF THE MATRIX EXPONENTIAL TRANSFORMATION: BAYESIAN INFERENCE FOR A COVARIANCE MATRIX

                        

                                                             Senior co-author  Jan Magnus

                                                        Let       C= exp (A)

      where C is a positive definite covariance matrix and A=log C denotes the matrix logarithm of C

             Then

                                Magnus, Pils, and Centana(2021)

           were the first to complete the monumental task of deriving a closed form expression for the Jacobian of this transformation. My congratulations to the authors!!

            For example,

            (1) If C possesses an inverted Wishart distribution, then the density of A may be stated in closed form.

            (2) If the upper triangular elements of A possess a matrix normal distribution, then the density of C cam be stated in closed form.

            This result will find many applications in Bayesian Inference for a Covariance Matrix. The large previous literature includes:

                                     Leonard and Hsu (1992)

                                     Lesage and Pace (2002)

                                    Hsu, Sinay, and Hsu (2012)

                                     Deng and Tsui (2012)

                                     Asai and McAteer (2020)

                  

      

JAMES LE SAGE AND R. KELLEY PACE---A SEMINAL 2002 BAYESIAN PAPER ON MODELING SPATIAL DATA

 

                        

           James Le Sage

                                                 

                                                                    R. Kelley Pace

.                                                              LESAGE AND PACE (2002)

   We introduce the matrix exponential as a way of modelling spatially dependent data. The matrix exponential spatial specification simplifies the loglikelihood allowing a closed form solution to the problem of maximum likelihood estimation, and greatly simplifies Bayesian estimation of the model. The matrix exponential spatial specification can produce estimates and inferences similar to those from conventional spatial autoregressive models, but has analytical, computational, and interpretive advantages. We present maximum likelihood and Bayesian approaches to estimation for this spatial model specification along with model diagnostic and comparison methods

                                          MODELING AN EXPONENTIAL PATTERN OF DECAY

                    Data collected from geographic regions such as countries, states, and counties or individual points in space such as houses often exhibit spatial dependence. Estimation of traditional spatial autoregressive (SAR) models requires non-linear optimization for estimation and inference. The conventional spatial autoregressive approach introduces additional theoretical complexity relative to non-spatial autoregressive models and is difficult to implement in large samples. We advocate use of a matrix exponential spatial specification (MESS) of dependence that replaces the conventional geometric decay of influence over space with an exponential pattern of decay. We show that this results in theoretical simplicity as well as improved numerical performance relative to the conventional spatial autoregression. 

       Chiu, Leonard, and Tsui (1996) proposed the use of the matrix exponential for covariance matrix modelling and discussed several of its advantages. One advantage is that the matrix exponential always leads to positive definite covariance matrices, eliminating the need to restrict the parameter space or test for positive definiteness during optimization. A second advantage is that inversion of the matrix exponential takes a simple mathematical form that is easy to implement in applied practice. Finally, use of the matrix exponential spatial specification leads to a log-likelihood where a troublesome term involving the log-determinant of an nxn covariance matrix vanishes. Collectively, these aspects of the matrix exponential spatial specification greatly simplify maximum likelihood as well as Bayesian estimation and inference. Specifically, we are able to provide a closed-form solution for maximum likelihood estimates, and produce Bayesian estimates using univariate integration over a scalar polynomial expression. In addition, we show how MESS can be used for model diagnostics and comparison of models based on different spatial weight structures or sets of explanatory variables. We demonstrate these procedures using a number of data sets that vary in size and area of application.

 

KIDD AND KATZFUSS OF TEXAS A&M SEEM TO BE UNAWARE OF THIS APPROACH

---SEE THEIR FORTHCOMING DISCUSSION PAPER TO ISBA WHICH IS SCHEDULED TO APPEAR IN "BAYESIAN ANALYSIS".  

       Please click on    https://bit.ly/3ykbLr2. 

     The paper by Chiu et al was published in JASA and proposes a generalised linear model for covariance matrices, together with a linear model for the means. It provides a very general paradigm, in its own right, for modelling a multitude of spatial processes, particularly when random effects are incorporated with fixed effects. Why do we need anything else? SEMANTIC SCHOLAR

.

                                          MATTHIAS KATZFUSS'S PUBLICATIONS

                                                   Brian Kidd, Graduate Student, Texas A&M

                  

                                                                   ****************

Tom,

 

There has been a bit of work on the matrix exponential in econometrics/spatial econometrics following our initial work.

 

LeSage, James P. and R. Kelley Pace,

A matrix exponential spatial specification,

Journal of Econometrics, September, 2007, Volume 140, Issue 1, pp. 190-214.

 

Debarsy, Nicolas, Fei Jin, and Lung-Fei Lee

Large sample properties of the matrix exponential spatial specification with an application to FDI.

Journal of Econometrics 2015, Volume 188 Issue 1, pp. 1–21.

 

The second article discusses non-stationarity issues specifically and produces some results showing that estimates are robust to non-constant variance in the disturbance structure.

 

By the way, I saw you present some work on the matrix exponential at one of the Zellner Seminars on the Interface between Bayesian econometrics and statistics, (or whatever the title of the NSF funded conferences that Arnold ran for quite a few years).

 

Kelley and I also devote a chapter of our book on spatial econometrics to the matrix exponential,

 

LeSage, James P. and R. Kelley Pace, Introduction to Spatial Econometrics, CRC Press, Taylor & Francis Group: Boca Raton, FL, January 2009.

 

James P. LeSage, Professor Emeritus

University of Toledo

Department of Economics

                                                   ***************

      SEE ALSO 

              COVARIANCE MATRIX ESTIMATION AND ITS APPLICATIONS

                  By Xinwei Deng and co-authors, including Kam Wah Tsui

            IN PARTICULAR

                                       Deng and Tsui (2013)

                                                         

                                                         Xinwei Deng, Virginia Tech

                                           Refers to Leonard and Hsu (1992) Annals of Statistics P.D.F

                                                     (Bayesian Inference for a Covariance Matrix)

                       which was extended by Hsu, Sinay, and Hsu (2012) PDF, using more easily computable conditional Laplacian approximations to various marginal posterior distributions. Appeared in Annals of Math Stat

                                                See also  Yang and Berger (1994) Annals of Statistics (who use matrix logarithmic transformation when creating reference prior for a covariance matrix). Good risk properties.

                                                               Sinay, Hsu, and Hsu (2013)

                                                               Sinay and Hsu (2014)

                                                                  John and Serene Hsu

                                                              

                                                      Marick Sinay, Finance One Inc, L.A,

                                                                                 

                                                                         Jim Berger, Duke

      I (Tom) first learnt about the matrix exponential (ME) transformation from Dennis Cox at UW Madison during the early 1980s, at which time I was advised about Richard Bellman's mathematics at the UW Army Math Research Center, by a scholar whose name I don't remember.

 It was not until 1990 that John Hsu and I finished deriving our matrix normal approximation to the likelihood of the log of the covariance matrix. I never realised what a large literature ME would generate, much of it subsequent to my early retirement in 2001, for example some of the multivariate stochastic volatility models developed by Manabu Asai and others, in particular the highly effective MEGARCH model proposed by the eminent co-authors

                                                          Asai, Chang and McAleer(2016)

                                  who regard Chiu et al (1996) as seminal, and

                                                         Asai and McAleer (2000)

                                                        Michael McAleer (1951-2021)

                                                        Asia University, Taiwan

. My Ph.D. supervisor Dennis Lindley advised me in 1973 that the problem with smoothing a covariance matrix would be keeping it positive definite, and the matrix exponential transformation  well handles this.

.

                                                                       

                                                                Kam Wah Tsui

                             

                          The following  recent result was derived by Jan Magnus et al, It will be

      very useful in various Bayesian and Econometric applications, as the authors fully demonstrate:

                       THE JACOBIAN OF THE MATRIX EXPONENTIAL FUNCTION

                                                                             

                                                             Jan Magnus, Vrige University

                                             

       I believe that it's possible to derive a simpler expression for the Jacobian, as a function of  the eigenvalues of the covariance matrix, but I was never quite sure that my algebra was correct, and I didn't preserve my scribblings.