Journal of Mathematical Psychology Tutorial Tutorial on maximum likelihood estimation In Jae Myung Department of Psychology Ohio State University Neil Avenue Mall Columbus OH USA Received Novem - Description

Theintendedaudienceofthistutorialare researchers who practice mathematical modeling of cognition but are unfamiliar with the estimation method 1nlike least2squares estimation which is primarily a descriptive tool M is a preferred method of parameter ID: 25325 Download Pdf

Similar presentations

Method Section Describing participants
Method Section Describing participants

Created by Alice Frye, Ph.D, Department of Psychology, University of Massachusetts, Lowell. 1. Steps in this tutorial. 1) State the goals of this tutorial. 2) What is a method section. 3) What is in a method section.

Reviving the Tcl tutorial
Reviving the Tcl tutorial

Arjen Markus. July 2017. How it started …. A question on . comp.lang.tcl. :. Somebody had stumbled over an error/unclear explanation in the online tutorial. I felt responsible. Current URL: . https://www.tcl.tk/man/tcl8.5/tutorial/tcltutorial.html.

The Estimation Problem
The Estimation Problem

How would we select parameters in the limiting case where we had . ALL. the data? .  . k. . →. l . k. . →. l . . S. l. ’ . k→ l’ . Intuitively, the . actual frequencies . of all the transitions would best describe the parameters we seek .

Department of Psychology
Department of Psychology

Messiah College. . What is Psychology? . Psychology is “the systematic/scientific study of the behavior and mental processes of humans.”. http://graduate.carleton.ca/wp-content/uploads/psychology2.jpg.

linear mixed effects analyses (Tutorial 2) Bodo Winter1 University o
linear mixed effects analyses (Tutorial 2) Bodo Winter1 University o

http://www.bodowinter.com/tutorial/bw_LME_tutorial1.pdf This tutorial will take you about 1 hour (possibly a bit more). 1 For updates and other tut

Basics of Statistical Estimation
Basics of Statistical Estimation

Alan Ritter. rittera@cs.cmu.edu. 1. Parameter Estimation. How to . estimate parameters . from data?. 2. Maximum Likelihood Principle:. Choose the parameters that maximize the probability of the observed data.

Department of Psychology
Department of Psychology

Messiah College. . What is Psychology? . Psychology is “the systematic/scientific study of the behavior and mental processes of humans.”. http://graduate.carleton.ca/wp-content/uploads/psychology2.jpg.

Parameter Estimation
Parameter Estimation

Maximum. Likelihood. Estimation. Probabilistic. Graphical. Models. Learning. Biased Coin Example. Tosses are independent of each other. Tosses are sampled from the same distribution (identically distributed).

The Literature of Psychology: Where do you find
The Literature of Psychology: Where do you find

it?. Encyclopedias. Created by Andrea . Dottolo. , Ph.D., Department of Psychology, University of Massachusetts, Lowell. 1. Steps in this tutorial. 1) State goal of this tutorial. 2) Why use encyclopedias.

References: Online Sources
References: Online Sources

APA format. Created by Andrea Dottolo, Ph.D., Department of Psychology, University of Massachusetts, Lowell. 1. Steps in this tutorial. 1) State goals of this tutorial. 2) Difference between a citation and a reference.

335K - views

Journal of Mathematical Psychology Tutorial Tutorial on maximum likelihood estimation In Jae Myung Department of Psychology Ohio State University Neil Avenue Mall Columbus OH USA Received Novem

Published bycalandra-battersby

Theintendedaudienceofthistutorialare researchers who practice mathematical modeling of cognition but are unfamiliar with the estimation method 1nlike least2squares estimation which is primarily a descriptive tool M is a preferred method of parameter

Tags : Theintendedaudienceofthistutorialare researchers who practice mathematical
Embed :
Pdf Download Link

Download Pdf - The PPT/PDF document "Journal of Mathematical Psychology Tu..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.

Journal of Mathematical Psychology Tutorial Tutorial on maximum likelihood estimation In Jae Myung Department of Psychology Ohio State University Neil Avenue Mall Columbus OH USA Received Novem






Presentation on theme: "Journal of Mathematical Psychology Tutorial Tutorial on maximum likelihood estimation In Jae Myung Department of Psychology Ohio State University Neil Avenue Mall Columbus OH USA Received Novem"— Presentation transcript:

          !    " #DepartmentofPsychology,OhioStateUniversity,1885NeilAvenueMall,Columbus,OH43210-1222,USA$  % !&% ' ( % !)* ' " ++ ,"+%!    +      !     -./  ! !!      �#?B)22C)/ /D/ !/2)EEF2   . % 4  145/5   % !/�!/)E42)A2 "   ++ ," !     !     !    ! 2/ ++ 0    0  + %% ! +0 !+'  +   G //JournalofExperimentalPsychology' ! ! / ++  ! !  %  ++   !    % ' !   +  -4.    ! !  ,  ' +!   +         , + 2  ! / ++  ++  +%! ! + !  ! !0   + /?2! + ,         +,  ! !  !    //,@ :H  ,,= +/(= :@  ,,= +/(H 7 :4 % ,,= +/)(4+,,= +//   2.1.Probabilitydensityfunction?     !+ , ! %  !  +   0++ / !  !   ++        %    !  + /"   ,  ++ !  6 !' +!+'' ! ' /5 !0  +'' ! ' 3 %  ! I+ /5 +   % ,!   +'' ! '     !/?2 , ! ! 6 !  +'' ! ' !  !' ! I+ /!  probabilitydensityfunctionH?  + 6  +'' ' %! %  +    ++ 0 0 + %   //! 0 '+ %      /// + %  ! 6 !  2! + + /"!%!'2 % ,I,    ! + !    , !  +'' , H? ! %  + ' +  !  + H?!%!' % ,  ! H?,!   +   0  ' % ! + ,  ,4++  !  +     '    3  @   //   !  +''   , +   !' + // H?  % ' yyyAyyy ?//@ +'' ! '  + !+'' +  +!'  /I.J.Myung/JournalofMathematicalPsychology47(2003)90100 0   0 ' ! ' 0 + &   ' !  !+ /  +  H? 0 ++ ?//" + %   !  0H?'  ! 0   +  0 '  + ?// 0    +  H? ' ! ' ' %  0   + 6  +'' ! % %     H?   !'% +     ! 6  ! /2.2.Likelihoodfunction7%  + % ,  +!H?0 0   !   +''  ! /" + %  + , H?0      C/%//)/"  , 0 % ,0 %  !' % ! ! /5!,0   !0 %  +' �7%  ' % !! ! !    ,6!  H?,  +'' !     ! + ' ,       % +! ! ! /% %  +' ,0 ! 6 likelihoodfunction' %    ! %  ! + %   +      ! + %  ' % !! !  ?  2+ '   + .3/,   ! !% '   +    !  0?/    +  !   ' 0  H?!   ! 5  !?/!, 0  ! 6 !!    ,!     !   +'    /4+ 6, H??/  ! % +  + % ,! 6 ! datascale/*   !,   !   + % +  ' % !! ,! 6 ! parameterscale/"  ,?/  +'' + ! % 6 !+ ,0  ?/    !JJ +''2 II+ + % 6 !!  /&    !  6 % ?//   ! % ' % !! ! +   2+  ! ! ' !  /I.J.Myung/JournalofMathematicalPsychology47(2003)90100 '    + ' ! 0   ! ' 0/" !   0+ ,   ! 0'   '% + + /"  , ! 0 + ,   !     + 2!   JJ II '% 2! + + + !' + %     * !  % '   !!   !  ! %  ! !   !, +          ' ++ ,  , +'' ! '   !   ! /7%   !   + % ! !   +'' ! ' ?/,0     !6! + %   2+!  !  !+'' ! ' / ++ maximumlikelihoodestimation -.,! % + !'$/5/?  ,    !  !+'' ! '      ' % !! JJ   ,II0       %  + %        !    + %  ,0   '    2! + + , ! MLEestimate,!!  !'?  + ,?/, -.    0    2 !%  +'' ! '  +!   -.     0 '  + ?/5!  -.++ ,  ++        %    ! ' % !!  ,     !   2  !  +'' ! '     ' % !!    /3.1.Likelihoodequation -.     !  ' 3 /"   ,0  0 0  + -.    0    ! 3 /? +  % 2  , -.    '  !'   2  ! , '  0 ,    !      -.    '  !'     /5   2  ! ,!   ' ,  ,    0+ !    3  0 likelihoodequation  '  ! 6        !   '   +    6 ! % % %   + /   ! 3  +     2!     -.    /5!! !   '  6 !       !    , 6 ! % %   %  /'    ,  +  2  !  !' %    +   +  , %    ' ! '   !'   !! % %  2  !! 00     %    -.+ ! , !  + % 2+ '   + % 6 !% ? ,'       ! .3/),0 '  2  ! &  , 6 ! % %  2  ! ! dLwnydw w w @ 3  3  ' !  ! -.    '  !      +      ,    ,  !! % %  2  ! !! % ! dLwnydw w 0    % ,!  !/"+  , 0 % ,  +' '     -.    , + 0  ! %%  + ! H?  2 /"   , -.     '   2 +    / '! 2 +    3 6!+  +     2  !/ ! ' =!  9   ! 6 !       %  !  3   !   negativedenite  , 2 '  !%  !   + I.J.Myung/JournalofMathematicalPsychology47(2003)90100       '2   2! 2+ +      %   2 0  + + ,0  '    '   ' +   / JJ   II  + !' ! %       %  +/4+ 6,    ,'       + %  , 0 + % '  !'!!     + %+  0   0+     !  +% !+   /H   +    !  0 +!   ! !/   % + , 0'  0?/,    +  G! !  % %  !/ /,+ @?/ +   + +++ + ! 6 ! /. +   ++ !    '   0 !       + % ' 0  0 %   /3.2.Localmaxima" 0    +    !       + %   3    2  !0' !/?!+   +      + 0  +       +% +  +   ++ !'  /" + %       ! ' /H + !+     + % ,  !+    +! '2+   + % /  ! localmaxima+' /5  + ,?/      + %  + 0 !  +  + @ ! globalmaximum,   + %  + 0 ! + 5,0  '2+   /4 ,   + %  0 !  '2+    + =/1  ,           +' /" !,%   23  % ' ! % + ! + %! +' ,        %  /?  + ,   !     % %   +    + ! !        0    '  ! +  !/;   ++ , ! 0  6!   '   ' !/ ?//5  +  2  ! 6   2+  ! / @ '   0  + 5!= 0  /   0! +   % +   + / 5   +    0  ! K +  ,7  ,:L  ,A%    +' ,    ,    '  ' + +         6! I.J.Myung/JournalofMathematicalPsychology47(2003)90100 3.3.Relationtoleast-squaresestimation$    -.0  + %   mostlikely  % +! ! ! /"-4.,   !,0  + %   +%! mostaccurate! +  ! ,  !   0  ! 6  ! !  3 2 /? ,-4.,sumofsquareserror44.' 0 ' % !+ !  &#x !00; !   ! I+ !  ' % /&    + %  5 -.,6! + %     44.   3  2 +    /   -4.'G     +' , + 0  ! 2 0  +   + /   ' 0  0 !     % 2 % 3  /"  ,-4.     ! !  -.    , + !      ! ' ! ++   ! +  /5 +     +'%  !   '  !  ! + !+0  !     + ! ! /;  , -. !' +   ! -4.,  +'' !    0!6 '   + '  ,  , ! !    $ ,A    , 0 % ,0  0 !   / 0 ' %  ! + !    !  ! ' !0   % /"  ,    2  ! 3%     44.,!   ,  + %  '  !!    -.-4./ "   ,"+   ++   +      !    /  !,"   ! %           + //$':;  ,); ,A; !:.''  ,5  2!     % ' ++ !!  ! + ,"+%!   +  -. 0 ,+0 ! +  /- ' + %  ,  ,! ! I+ !  +'2'       0 !  ! 6 !+0  ! &#x -5;7.2; +   ! &#x -5;7.2;4++  !  ' % 0   +   '2 % !++      ;     !   %'   ! /; ! '6   ' % !! !   ! 6 /5++  -. 3 + 6  H? ! undereachmodel/! ,6 0    ' % !++ '  !'!%!  '    + '   ' ! + !  ;    ' ! ' !0 +''   H? +0  ! ! +   !  '  !+0 &#x -5;7.2; +  � 0     0+  ' !  ! H? '% 3 /? , +'' + ' +'' ! ' / /.3/'  !  !/   , H?  ! .3/'  !' + + +'' + .3/0 !  3 ,.3//4 !,    ! '6 !  ,5 ,    !++' !     +     /"+ , H?'  !' + +&0,   I    ! + !    , !  !2  !  +0  ! % ' ?  ! , H? +  !6    !   /I.J.Myung/JournalofMathematicalPsychology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yung/JournalofMathematicalPsychology47(2003)90100  ++ !  ' ! ' !,  ! ' !/? ,   %  +2  3 ! 3%  ' 0  -.!-4.!  !' ! 0  % ,! + !+++   4.1.MLEinterpretation;  !  0  ! 6  ! '  !  +   ! M"  +   G +      ! ! ' G'+  ! + !    +    ++     !      ! ! /5!6   ,'  6  ,!  /5+ 6 / /,  %   !2  !  +  !  !! !  !  / '   !   % + 6   +     %   !0 ! I6!    ! + /?  + , 0   ' !      +  ! 0 + 6 ! '   + ! 0  0+ , %         ! ! /   3    0  !! !    +  ! /5  0    !  !'    !' !   ' ,0  ! 6 ! ! I'  6   ! '  + !   ! /?      !  !  !    ,  !    !  0   //-  :N ,A) ,? ,:@0 , , ,:N ,       +%!    +  2    !    / -.!   +      !'      3    , -4.,0  + ! + % /" ++ ,"+%!  + ,  % +  !   !  % +  '++ /" +  ! 0++ !      !   + 0! %' -.2' !  //@  ! :=0 ,LN! ,' +  !! ,  '       ! +'   !   + ! %   /    0 0++ !'   7 $ 9C & "     9  /       ,$ !4 0   ,! 0  % 0 %'     %  ++ /   ++ !+     '!  +   -.!-4.   + ! ' !  / ! "#                       !        " #      "$      %&  '(% ((&  (% (% )(*#+% , (*#+%&  (% (% "! (-.. / (% ($       *..$      0     *1+2*-*3                                    6       6*  % 6 (  678787878 6 6 678 $I.J.Myung/JournalofMathematicalPsychology47(2003)90100     6      #        # 9     "   # 6*:   *: " #   "*:      "*.   6,!;' (!;! �    � �?=     "        #    6  - 6    "    - "       $     $  - 76*6- -8@$      - 7*-"*"-8@$              �=  #    6     "$ 6        .   #             #       )=  #   "       "$"        .   #             #    ! "$#     /                  !          9    $      %&  '(% (%&  (% (% )(*#+% , (*#+%&  #(% (% "! (-..% / (% ($                   *1+2*-*3         I.J.Myung/JournalofMathematicalPsychology47(2003)90100 %! 5  ,9//"   !       !++ /�" ,@/&/,:= ,Secondinternationalsymposiumoninformationtheory++/)A/�@!+  5 ! K!/@  ! ,;/9/,:=0 ,=/4//   +   !    /JournalofMathematical,CCC/@ ,//,:H  ,K/5//Mathematicalstatistics* !,&#x12.; =59! 2!,"/= ,7/,:@  ,$/-//Statisticalinference! !//67% ,&#x12.; =5H' /H 7 , /9/,:4 % , ///Probabilityandstatistics! !//@ ,&#x12.;  55!!2;  /K +  ,4/,7  ,=/H/,:L  , //A/*+   '  ! /,))A/- '  ,K//"  2   + ! !  /PsychologicalReview,)/-  ,9/,:N ,;/A)/Modelselection/& 0O ,&#x12.; &O ! /,@/@/)/   !%! /JournalofExperimentalPsychology,)A)C/ ,"//,? , /,:@0 , /;//4+   !    /JournalofMathematicalPsychology , /5/, ,"//,:N ,4//0! !     +   !  /Psychological,/$ ,$/A/5    %/Psychological,CA/$',H/=/,9 ,4/,:; 5// +      /JournalofExperimentalPsychology:Learning,Memory,andCognition,))/                     6       "*9  % 6   6 6 6     6  6*:/ *: //   *:         "*:      "*.   6"-9    6 6 6     "    - 6  - "       $  - 76*6- -8@$       - 7*-"*"-8@$              �= /  6       6    $ 6      6      9  6     )= /  6      "      $"        6      9  6  I.J.Myung/JournalofMathematicalPsychology47(2003)90100 $',H/=/,:; 5/./)/* ! !  &#x ,-;ٕ.; 53   % ! +   /Psychological,)/4 07/A/.    !  ! /Annalsof,))/4+,5//Probabilitytheoryandstatisticalinference/= 2'! ,&#x,-37;䀀1K= '! 1%   /1 , /,: = !,/-//   +  +   (   , +    ! /Psychological,CCC/LN! ,//90 6  +  ! ' /PsychonomicBulletin&Review,)C/; ,/H/A/*     &#x,-37;䀀 =  $'!; &#x -2;p.8;)53   % ! +   /PsychologicalReview,A)/; !,//,:.''  ,./@//*   /PsychologicalScience,C/I.J.Myung/JournalofMathematicalPsychology47(2003)90100