%!PS-Adobe-1.0 %%Creator: Ross Cartlidge %%Title: Multiple pages on one page %%CreationDate: Tue Apr 10 09:37:26 EST 1990 %%Pages: 0 %%DocumentFonts: %%BoundingBox: 0 0 0 0 %%EndComments % % Uncomment the next line if you wish to load multi into the "exitserver" % state of the PostScript device % % serverdict begin 0 exitserver % % make each operator to overlay a procedure so a bind in % a prolog will not stop the overlaying by "multi" % [ /gsave /grestore /grestoreall /initgraphics /initmatrix /currentmatrix /setmatrix % Path construction operators /initclip % Virtual memory operators /save % ones which needed special overloading /showpage /erasepage /copypage /restore % ignore these /letter /legal /a4 /b5 /lettersmall /note ] { % if exists check if operator else define {} dup where { pop % If operator then make into procedure dup load type /operatortype eq { 1 array cvx dup 0 3 index cvx % /n -> n put % {}[0] -> n bind def } { pop } ifelse } { {} def } ifelse } forall % % Initialise endmulti to execute an error % /endmulti { count array astore /ostack exch def 250 array execstack /estack exch def 20 array dictstack /dstack exch def $error /newerror true put $error /errorname (No matching multi) cvn put $error /command (endmulti) put $error /ostack ostack put $error /estack estack put $error /dstack dstack put stop } bind def % % Put multiple logical pages on one physical page % until "endmulti" called % % landscape nrows ncols left_right up_down row_major dividers multi - % landscape nrows ncols up_down row_major dividers multi - % landscape nrows ncols row_major dividers multi - % landscape nrows ncols dividers multi - % landscape nrows ncols multi - % % Go into multi page representation % % landscape boolean:true - divide page in landscape orientation % false- divide page in portrait orirntation % nrows integer:number of logical pages down physical page % ncols integer:number of logical pages across physical page % left_right(*) boolean:true - rows fill left to right % false- rows fill right to left % up_down(*) boolean:true - columsn fill top to bottom % false- columns fill bottom to top % row_major(*) boolean:true - fill rowwise % false- fill columnwise % dividers(*) boolean:true - divide logical pages by lines % false- don't divide logical pages % % NB: Optional parameters(*) default to true. % /multi { currentdict 64 dict begin /initdict exch def % store initial dict for backward reference % % Initialise the Optional Parameters (right to left) % [ /dividers /row_major /up_down /left_right ] { exch dup type /booleantype ne { exch % put non bool back true def % default to true } { def } ifelse } forall /cols exch def /rows exch def % % get size of current page % initgraphics clippath pathbbox /Y exch def % Max Y /X exch def % Max X /y exch def % Min Y /x exch def % Min X /W X x add def % Width of Page /H Y y add def % Height of page % % functions to turn page# into row and column % depending on whether rows or cols fill first % row_major { /tocol { cols mod } def /torow { cols idiv } def } { /tocol { rows idiv } def /torow { rows mod } def } ifelse % if landscape { % % Note: x and y are reversed % /w Y y sub def % Width of imageable region /h X x sub def % Height of imageable region /ox y def % origin of physical page /oy x def /L % Map to landscape -90 matrix rotate 0 H matrix translate matrix concatmatrix def } { /w X x sub def /h Y y sub def /ox x def /oy y def /L matrix def } ifelse % % Calculate origin fudge so that scaled margin = fudge % This means that the clippath of the logical page % will align with the physical clippath. % (wf/W)x = xf where, % wf = new width = w + 2xf, % x = margin xf = scaled margin % so xf = wx/(COLS.W-2x) /xf w x mul W cols mul 2 x mul sub div def /yf h y mul H rows mul 2 y mul sub div def /w w 2 xf mul add def /h h 2 yf mul add def % % CTM (multi) = C x T x M x L x I % CTM (normal) = C x I % CTM (normal) = CTM (multi) x (T x M x L x I)-1 x I % M = (Scale rows/cols) x (Scale logical to physical) x % (Translate to physical clip origin + fudge) % T = (Convert logical page to spot and physical) % L = (Convert to landscape) % I = Initial Physical CTM % C = Random transform on logical page /M w W div cols div h H div rows div matrix scale ox xf sub oy yf sub matrix translate % Move to origin matrix concatmatrix def /I matrix currentmatrix def /I_inv I matrix invertmatrix def % matrix T /T { page# tocol left_right not { cols 1 sub exch sub } if W mul page# torow up_down { rows 1 sub exch sub } if H mul 3 -1 roll translate } def % % Utility functions % NB: *_t1 are temporary variables % % matrix fromcanon /From_t1 matrix def /From_t2 matrix def /From_t3 matrix def /From_t4 matrix def /fromcanon { I_inv From_t1 T M L I From_t2 concatmatrix From_t3 concatmatrix From_t4 concatmatrix 3 -1 roll concatmatrix } def % /n {} mkmulti - % makes a new function called "n" in previous dict with:- % {}[0] = /n % {}[1] = currentdict % currentdict.n = prevdict.n % /mkmulti { 1 index dup load def %define old val in current dict 5 array cvx dup 3 4 -1 roll put % A[3] = {} dup 0 3 index put % A[0] = /n dup 1 currentdict put % A[1] = currentdict dup 2 /begin cvx put % A[2] = begin dup 4 /exec cvx put % A[4] = exec initdict 3 1 roll put % define initdict.n to multi function } def % % path_to_proc {} % make proc represenation of current path % /path_to_proc { { [ /newpath cvx { /moveto cvx} { /lineto cvx} { /curveto cvx} { /closepath cvx } pathforall ] cvx exch pop } stopped { $error /errorname get /invalidaccess eq { cleartomark $error /newerror false put (%%Warning%% charpath in path - path nulled) = cvx exec } { stop } ifelse } if } def /path_def { { currentpoint } stopped { $error /newerror false put { newpath } } { /newpath cvx 3 1 roll /moveto cvx 4 array astore cvx } ifelse } cvlit def % % Draw lines round logical pages % /draw_dividers { initgraphics L concat M concat 1 1 cols 1 sub { W mul dup 0 moveto rows H mul lineto } for 1 1 rows 1 sub { H mul dup 0 exch moveto cols W mul exch lineto } for stroke } def % % for each graphics operator which affects absolute state % /M1 matrix def /M3 matrix def /M2 matrix def [ /gsave /grestore /grestoreall /initgraphics /initmatrix /currentmatrix /setmatrix % Path construction operators /initclip % Virtual memory operators /save ] { { % Save paths path_def path_to_proc clippath { {} } path_to_proc % % CTM <- CTM x Tocano (canon mode) % M1 currentmatrix Tocanon M2 concatmatrix setmatrix % Restore paths initclip exec clip exec load exec % Save paths path_def path_to_proc clippath { {} } path_to_proc % % CTM <- CTM x Fromcanon (Non canon mode) % M1 currentmatrix Fromcanon M2 concatmatrix setmatrix % Restore paths initclip exec clip exec end } mkmulti } forall % % Define the operators which can't use the standard template % /showpage { /page# page# 1 add def % Update the transform matrices page# npages eq { dividers { draw_dividers } if load exec % the previous showpage /page# 0 def } { pop } ifelse /Fromcanon Fromcanon fromcanon def /Tocanon Fromcanon Tocanon invertmatrix def end initgraphics % the new initgraphics } mkmulti /copypage { pop end gsave showpage grestore } mkmulti /erasepage { pop end gsave initclip clippath 1 setgray fill grestore } mkmulti [ /letter /legal /a4 /b5 /lettersmall /note ] { { pop end (%%Warning%% Device change ignored) = } mkmulti } forall % % Define restore separately as it affects the value of page#, etc % /restore { pop % Push the values to restore after restore mark exch % put mark under -save- page# Fromcanon aload pop Tocanon aload pop counttomark -1 roll % get -save- to the top restore % Restore popped values Tocanon astore pop Fromcanon astore pop /page# exch def pop % mark % Save paths path_def path_to_proc clippath { { } } path_to_proc % % CTM <- CTM x Fromcanon (Non canon mode) % M1 currentmatrix Fromcanon M2 concatmatrix setmatrix % Restore paths initclip exec clip exec end } mkmulti % % procedure to undo the effect of multi % /endmulti { pop % don't need /endmulti [ /gsave /grestore /grestoreall /initgraphics /initmatrix /currentmatrix /setmatrix % Path construction operators /initclip % Virtual memory operators /save % ones which needed special overloading /showpage /erasepage /copypage /restore % ignore these /letter /legal /a4 /b5 /lettersmall /note % /endmulti ] { initdict exch dup load % get old value put % restore old value } forall page# 0 ne % if not at new page show uncomplete page { dividers { draw_dividers } if showpage } if end } mkmulti % % Set up in multi(non canon) mode % /page# 0 def /npages rows cols mul def /Fromcanon matrix fromcanon def /Tocanon Fromcanon matrix invertmatrix def end initgraphics } bind def true 1 2 false multi %------------------------------------------------------------------------------- % Define eof-hook for dvips so odd numbered dvi files work O.K. % % D.A. Green --- MRAO --- 1994 January 7th % /end-hook {endmulti} def %------------------------------------------------------------------------------- %!PS-Adobe-2.0 %%Creator: dvips 5.519 Copyright 1986, 1993 Radical Eye Software %%Title: lang4.dvi %%CreationDate: Wed Aug 23 11:39:53 1995 %%Pages: 19 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSCommandLine: dvips lang4.dvi %DVIPSSource: TeX output 1995.08.23:1132 %%BeginProcSet: tex.pro /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR matrix currentmatrix dup dup 4 get round 4 exch put dup dup 5 get round 5 exch put setmatrix}N /@landscape{/isls 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-3438 0 R (0.1) Rshow 672 2570 M 31 0 V 3386 0 R -31 0 V 672 2788 M 31 0 V 3386 0 R -31 0 V 672 2900 M 31 0 V 3386 0 R -31 0 V 672 2953 M 63 0 V 3354 0 R -63 0 V -3438 0 R (1) Rshow 672 211 M 0 63 V 0 2679 R 0 -63 V 672 71 M (1) Cshow 1015 211 M 0 31 V 0 2711 R 0 -31 V 1215 211 M 0 31 V 0 2711 R 0 -31 V 1358 211 M 0 31 V 0 2711 R 0 -31 V 1468 211 M 0 31 V 0 2711 R 0 -31 V 1558 211 M 0 31 V 0 2711 R 0 -31 V 1635 211 M 0 31 V 0 2711 R 0 -31 V 1701 211 M 0 31 V 0 2711 R 0 -31 V 1759 211 M 0 31 V 0 2711 R 0 -31 V 1811 211 M 0 63 V 0 2679 R 0 -63 V 1811 71 M (10) Cshow 2154 211 M 0 31 V 0 2711 R 0 -31 V 2354 211 M 0 31 V 0 2711 R 0 -31 V 2497 211 M 0 31 V 0 2711 R 0 -31 V 2607 211 M 0 31 V 0 2711 R 0 -31 V 2697 211 M 0 31 V 0 2711 R 0 -31 V 2774 211 M 0 31 V 0 2711 R 0 -31 V 2840 211 M 0 31 V 0 2711 R 0 -31 V 2898 211 M 0 31 V 0 2711 R 0 -31 V 2950 211 M 0 63 V 0 2679 R 0 -63 V 2950 71 M (100) Cshow 3293 211 M 0 31 V 0 2711 R 0 -31 V 3493 211 M 0 31 V 0 2711 R 0 -31 V 3636 211 M 0 31 V 0 2711 R 0 -31 V 3746 211 M 0 31 V 0 2711 R 0 -31 V 3836 211 M 0 31 V 0 2711 R 0 -31 V 3913 211 M 0 31 V 0 2711 R 0 -31 V 3979 211 M 0 31 V 0 2711 R 0 -31 V 4037 211 M 0 31 V 0 2711 R 0 -31 V 4089 211 M 0 63 V 0 2679 R 0 -63 V 4089 71 M (1000) Cshow 672 211 M 3417 0 V 0 2742 V -3417 0 V 672 211 L LT0 3606 2750 M (0.1) Rshow 3690 2750 M 252 0 V 672 2953 M 1015 902 L 52 -691 V LT1 3606 2610 M (1) Rshow 3690 2610 M 252 0 V 672 2821 M 343 -205 V 200 -265 V 143 -87 V 110 -136 V 90 -260 V 77 -269 V 66 -485 V 58 -29 V 52 -192 V 31 -682 V LT2 3606 2470 M (10) Rshow 3690 2470 M 252 0 V 672 2550 M 343 -92 V 200 -26 V 143 -27 V 110 -48 V 90 -125 V 77 -29 V 66 -44 V 58 -19 V 52 -23 V 47 -50 V 43 -47 V 40 -5 V 36 -8 V 35 -61 V 31 -33 V 30 -22 V 29 -70 V 27 -4 V 25 -39 V 24 -7 V 23 -33 V 22 -19 V 21 -47 V 20 -35 V 20 -60 V 18 -12 V 18 -10 V 18 -24 V 16 -22 V 17 -57 V 15 -4 V 16 -38 V 14 -34 V 15 -40 V 14 -2 V 13 -6 V 13 -15 V 13 -19 V 13 -18 V 12 -24 V 12 -83 V 12 -3 V 11 -18 V 11 -26 V 11 -4 V 11 -37 V 10 -7 V 10 -42 V 10 -8 V 10 -19 V 10 -58 V 9 -50 V 9 -5 V 9 -1 V 9 -11 V 9 -17 V 9 -61 V 8 -30 V 8 -14 V 8 -3 V 9 0 V 7 -8 V 8 -10 V 8 -53 V 7 -46 V 8 -10 V 7 -35 V 7 -3 V 8 -55 V 7 -13 V 7 -18 V 6 -12 V 7 -18 V 7 -31 V 6 -23 V 7 -12 V 6 -7 V 6 -6 V 7 -39 V 6 0 V 6 -43 V 6 -10 V 6 -39 V 6 -15 V 5 -14 V 6 -4 V 4 -20 V LT3 3606 2330 M (100) Rshow 3690 2330 M 252 0 V 672 2157 M 343 -50 V 200 -15 V 143 -14 V 110 -9 V 90 -4 V 77 -57 V 66 -10 V 58 -21 V 52 -7 V 47 -15 V 43 -14 V 40 -1 V 36 -20 V 35 -9 V 31 -6 V 30 -20 V 29 -1 V 27 -10 V 25 -2 V 24 -9 V 23 -16 V 22 -7 V 21 -6 V 20 -4 V 20 -7 V 18 -4 V 18 -2 V 18 -1 V 16 -1 V 17 -9 V 15 -2 V 16 -11 V 14 -1 V 15 -14 V 14 -11 V 13 -3 V 13 -15 V 13 -1 V 13 -5 V 12 -1 V 12 -8 V 12 -3 V 11 -2 V 11 -4 V 11 -4 V 11 -1 V 10 -4 V 10 -2 V 10 -1 V 10 -4 V 10 0 V 9 -1 V 9 -4 V 9 0 V 9 -1 V 9 -6 V 9 -4 V 8 -2 V 8 -3 V 8 -2 V 9 -4 V 7 -8 V 8 -1 V 8 0 V 7 -7 V 8 -2 V 7 -4 V 7 -1 V 8 -1 V 7 -6 V 7 -3 V 6 -2 V 7 -1 V 7 -3 V 6 -4 V 7 -4 V 6 -2 V 6 -1 V 7 -2 V 6 -2 V 6 -1 V 6 -10 V 6 -6 V 6 0 V 5 -3 V 6 -3 V 6 -5 V 5 0 V 6 -5 V 5 0 V 6 -3 V 5 0 V 5 -8 V 6 -6 V 5 -4 V 5 -2 V 5 -3 V 5 -1 V 5 -1 V 5 -7 V 5 -1 V 5 -4 V 4 -5 V 5 0 V 5 -4 V 4 0 V 5 -1 V 5 -8 V 4 -4 V 5 -1 V 4 -5 V 4 -1 V 5 -1 V 4 0 V 4 -3 V 5 -5 V 4 -3 V 4 -4 V 4 -3 V 4 -4 V 4 -13 V 4 0 V 4 -1 V 4 -6 V 4 -2 V 4 -5 V 4 -3 V 4 -2 V 4 -1 V 4 -2 V 3 0 V 4 -1 V 4 -2 V 3 -3 V 4 0 V 4 0 V 3 -2 V 4 -1 V 3 -1 V 4 -3 V 3 0 V 4 -1 V 3 -2 V 4 -1 V 3 -9 V 4 0 V 3 -9 V 3 -5 V 4 -2 V 3 -1 V 3 -3 V 3 -4 V 4 0 V 3 -4 V 3 -10 V 3 -2 V 3 -4 V 3 -1 V 3 -1 V 4 -4 V 3 -4 V 3 -1 V 3 0 V 3 -2 V 3 -2 V 3 -4 V 3 -1 V 3 -4 V 2 -2 V 3 0 V 3 -6 V 3 -7 V 3 -6 V 3 -4 V 3 -1 V 2 0 V 3 -3 V 3 -11 V 3 -1 V 2 0 V 3 -2 V 3 -4 V 3 -2 V 2 -3 V 3 -2 V 3 0 V 2 0 V 3 -2 V 3 -2 V 2 -6 V 3 -10 V 2 -1 V 3 -1 V 2 -5 V 3 -7 V 2 -6 V 3 -9 V 2 -15 V 3 -1 V 2 -10 V 3 0 V 2 -1 V 3 -3 V 2 0 V 2 -5 V 3 -4 V 2 -1 V 3 -15 V 2 -1 V 2 -5 V 3 -2 V 2 -8 V 2 -2 V 3 -2 V 2 -14 V 2 -5 V 3 -2 V 2 -2 V 2 -4 V 2 0 V 2 -20 V 3 0 V 2 -2 V 2 -2 V 2 -14 V 3 -4 V 2 -1 V 2 -3 V 2 -2 V 2 -3 V 2 -6 V 2 -1 V 3 -5 V 2 -3 V 2 -8 V 2 -9 V 2 -2 V 2 -2 V 2 -16 V 2 -7 V 2 -2 V 2 -1 V 2 -2 V 2 -14 V 2 -5 V 2 -1 V 2 -4 V 2 -5 V 2 -2 V 2 -1 V 2 -1 V 2 -1 V 2 -1 V 2 -10 V 2 -1 V 2 -12 V 2 -3 V 2 -1 V 2 -2 V 2 -5 V 1 -1 V 2 -1 V 2 -2 V 2 -1 V 2 0 V 2 -3 V 2 -2 V 1 -4 V 2 -7 V 2 -2 V 2 -1 V 2 -2 V 2 -7 V 1 -1 V 2 -2 V 2 -17 V 2 -4 V 2 0 V 1 -5 V 2 -4 V 2 -1 V 2 -2 V 1 -2 V 2 -2 V 2 -3 V 2 -9 V 1 -1 V 2 0 V 2 -2 V 1 -20 V 2 -2 V 2 -3 V 1 -3 V 2 -2 V 2 -4 V 1 -14 V 2 -1 V 2 -4 V 1 -1 V 2 -19 V 2 -7 V 1 0 V 2 -2 V 2 0 V 1 -1 V 2 -1 V 1 -1 V 2 -3 V 2 0 V 1 0 V 2 -1 V 1 -22 V 2 -2 V 2 0 V 1 -4 V 2 -6 V 1 -3 V 2 -13 V 1 -1 V 2 -1 V 1 -2 V 2 -8 V 2 -3 V 1 -1 V 2 -3 V 1 -2 V 2 -7 V 1 0 V 2 -5 V 1 0 V 2 -4 V 1 -4 V 2 -6 V 1 -4 V 2 -1 V 1 0 V 1 -5 V 2 -2 V 1 -1 V 2 -2 V 1 -7 V 2 0 V 1 -5 V 2 -3 V 1 -1 V 1 0 V 2 -5 V 1 -2 V 2 -1 V 1 -1 V 2 -8 V 1 -1 V 1 0 V 2 -4 V 1 -2 V 1 -1 V 2 -5 V 1 -1 V 2 -3 V 1 -7 V 1 -1 V 2 0 V 1 -5 V 1 -6 V 2 -6 V 1 -9 V 2 0 V 1 0 V 1 -3 V 2 -11 V 1 -2 V 1 -3 V 2 -1 V 1 -6 V 1 -1 V 1 -3 V 2 -1 V 1 -4 V 1 -1 V 2 0 V 1 -2 V 1 -4 V 2 -1 V 1 -2 V 1 -2 V 1 -1 V 2 -7 V 1 -8 V 1 -1 V 1 -5 V 2 -1 V 1 -1 V 1 -3 V 2 -4 V 1 0 V 1 -5 V 1 0 V currentpoint stroke M 2 -14 V 1 -1 V 1 -9 V 1 -7 V 1 -4 V 2 -2 V 1 -18 V 1 -13 V 1 -14 V 2 -2 V 1 -3 V 1 -1 V 1 -3 V 1 -17 V 2 -6 V 1 -8 V 1 -1 V 1 0 V 1 -6 V 2 -1 V 1 -2 V 1 0 V 1 -3 V 1 -2 V 1 -12 V 2 -1 V 1 -3 V 1 -2 V 1 -13 V 1 -2 V 1 -8 V 2 -3 V 1 -4 V 1 -2 V 1 0 V 1 -13 V 1 -12 V 1 -4 V 2 -1 V 1 -9 V 1 0 V 1 0 V 1 -8 V 1 -2 V 1 -10 V 1 -1 V 1 0 V 2 -3 V 1 -2 V 1 -1 V 1 -8 V 1 -1 V 1 -4 V 1 -1 V 1 -4 V 1 -3 V 1 -6 V 2 0 V 1 0 V 1 -9 V 1 -11 V 1 -15 V 1 -1 V 0 -2 V LT4 3606 2190 M (1000) Rshow 3690 2190 M 252 0 V 672 1813 M 343 -3 V 200 -33 V 143 -18 V 110 -5 V 90 -10 V 77 -15 V 66 -7 V 58 -14 V 52 -14 V 47 -12 V 43 -9 V 40 -2 V 36 -1 V 35 -1 V 31 -4 V 30 0 V 29 -3 V 27 -2 V 25 -9 V 24 -3 V 23 -8 V 22 -3 V 21 -6 V 20 0 V 20 -2 V 18 0 V 18 -5 V 18 -2 V 16 -7 V 17 -2 V 15 -2 V 16 -5 V 14 -2 V 15 -5 V 14 -2 V 13 -6 V 13 0 V 13 -2 V 13 -2 V 12 0 V 12 -1 V 12 -2 V 11 0 V 11 0 V 11 -3 V 11 -1 V 10 0 V 10 -1 V 10 -2 V 10 0 V 10 -1 V 9 -1 V 9 -2 V 9 -1 V 9 -4 V 9 -1 V 9 -2 V 8 -2 V 8 -1 V 8 0 V 9 -3 V 7 -2 V 8 -1 V 8 0 V 7 0 V 8 -3 V 7 -1 V 7 -1 V 8 -2 V 7 -4 V 7 -1 V 6 -1 V 7 0 V 7 -2 V 6 -2 V 7 0 V 6 -5 V 6 -6 V 7 0 V 6 -1 V 6 -2 V 6 0 V 6 -1 V 6 -1 V 5 0 V 6 -9 V 6 -1 V 5 -1 V 6 -3 V 5 0 V 6 -1 V 5 0 V 5 0 V 6 -2 V 5 0 V 5 -1 V 5 -2 V 5 -1 V 5 0 V 5 -1 V 5 -1 V 5 0 V 4 -1 V 5 -2 V 5 0 V 4 -1 V 5 0 V 5 0 V 4 -1 V 5 -1 V 4 0 V 4 0 V 5 0 V 4 0 V 4 0 V 5 0 V 4 -2 V 4 -1 V 4 -1 V 4 -1 V 4 -1 V 4 -5 V 4 0 V 4 -1 V 4 -1 V 4 -2 V 4 -2 V 4 -1 V 4 0 V 4 -2 V 3 0 V 4 -2 V 4 0 V 3 0 V 4 -1 V 4 -1 V 3 0 V 4 -1 V 3 0 V 4 -1 V 3 -1 V 4 -1 V 3 0 V 4 -2 V 3 -1 V 4 -1 V 3 0 V 3 -1 V 4 0 V 3 -1 V 3 -4 V 3 -1 V 4 -1 V 3 -5 V 3 -1 V 3 0 V 3 -2 V 3 -3 V 3 0 V 4 -1 V 3 0 V 3 0 V 3 -1 V 3 -1 V 3 -1 V 3 -2 V 3 -2 V 3 0 V 2 -1 V 3 -1 V 3 -3 V 3 -1 V 3 -1 V 3 0 V 3 -1 V 2 0 V 3 -1 V 3 0 V 3 0 V 2 -1 V 3 -1 V 3 -1 V 3 -1 V 2 0 V 3 -1 V 3 0 V 2 0 V 3 -2 V 3 -1 V 2 -3 V 3 -1 V 2 0 V 3 -1 V 2 0 V 3 0 V 2 0 V 3 -1 V 2 0 V 3 0 V 2 -2 V 3 0 V 2 -1 V 3 0 V 2 -1 V 2 0 V 3 0 V 2 -1 V 3 -1 V 2 0 V 2 0 V 3 -2 V 2 -1 V 2 -1 V 3 0 V 2 -1 V 2 -1 V 3 0 V 2 -1 V 2 -1 V 2 -1 V 2 -2 V 3 0 V 2 0 V 2 0 V 2 -1 V 3 0 V 2 0 V 2 -2 V 2 0 V 2 0 V 2 -1 V 2 0 V 3 -1 V 2 -1 V 2 -1 V 2 0 V 2 0 V 2 -1 V 2 0 V 2 -1 V 2 -2 V 2 0 V 2 -1 V 2 0 V 2 -1 V 2 -1 V 2 -1 V 2 -1 V 2 0 V 2 0 V 2 -1 V 2 0 V 2 0 V 2 -2 V 2 -1 V 2 0 V 2 0 V 2 -2 V 2 -1 V 2 -1 V 1 -1 V 2 0 V 2 -2 V 2 0 V 2 0 V 2 -1 V 2 -1 V 1 0 V 2 -1 V 2 0 V 2 -1 V 2 -1 V 2 0 V 1 0 V 2 0 V 2 -1 V 2 0 V 2 0 V 1 -2 V 2 -1 V 2 -1 V 2 0 V 1 -2 V 2 0 V 2 0 V 2 -1 V 1 0 V 2 -2 V 2 0 V 1 -1 V 2 0 V 2 0 V 1 -2 V 2 0 V 2 0 V 1 -2 V 2 0 V 2 0 V 1 0 V 2 -1 V 2 0 V 1 -1 V 2 -2 V 2 0 V 1 -2 V 2 0 V 1 -1 V 2 -1 V 2 0 V 1 0 V 2 -1 V 1 -1 V 2 0 V 2 0 V 1 -1 V 2 0 V 1 0 V 2 -2 V 1 0 V 2 0 V 1 -1 V 2 -1 V 2 0 V 1 0 V 2 0 V 1 -1 V 2 0 V 1 0 V 2 -1 V 1 0 V 2 0 V 1 -1 V 2 -1 V 1 0 V 2 0 V 1 -2 V 1 0 V 2 0 V 1 0 V 2 0 V 1 -1 V 2 0 V 1 -1 V 2 -2 V 1 -1 V 1 -1 V 2 0 V 1 -1 V 2 -1 V 1 0 V 2 -1 V 1 0 V 1 0 V 2 -1 V 1 0 V 1 -1 V 2 0 V 1 -1 V 2 0 V 1 -1 V 1 -1 V 2 -1 V 1 0 V 1 0 V 2 -1 V 1 -2 V 2 -1 V 1 0 V 1 0 V 2 -1 V 1 -1 V 1 0 V 2 0 V 1 -1 V 1 0 V 1 -1 V 2 -3 V 1 -1 V 1 -2 V 2 -1 V 1 0 V 1 0 V 2 -1 V 1 0 V 1 -1 V 1 -1 V 2 0 V 1 0 V 1 -3 V 1 -1 V 2 0 V 1 -2 V 1 0 V 2 0 V 1 -1 V 1 -1 V 1 0 V currentpoint stroke M 2 -1 V 1 0 V 1 0 V 1 -1 V 1 0 V 2 0 V 1 -2 V 1 0 V 1 0 V 2 0 V 1 -1 V 1 -1 V 1 0 V 1 -1 V 2 0 V 1 0 V 1 0 V 1 -1 V 1 -1 V 2 -1 V 1 0 V 1 0 V 1 -2 V 1 0 V 1 0 V 2 -1 V 1 0 V 1 0 V 1 0 V 1 0 V 1 -2 V 2 0 V 1 0 V 1 0 V 1 -1 V 1 -1 V 1 0 V 1 -1 V 2 -1 V 1 0 V 1 0 V 1 0 V 1 -1 V 1 0 V 1 -1 V 1 -1 V 1 0 V 2 -2 V 1 0 V 1 -1 V 1 0 V 1 -1 V 1 0 V 1 -2 V 1 -1 V 1 0 V 1 -1 V 2 0 V 1 -1 V 1 0 V 1 -2 V 1 -1 V 1 0 V 1 -2 V 1 0 V 1 -2 V 1 0 V 1 0 V 1 -1 V 1 -1 V 1 0 V 2 -3 V 1 0 V 1 0 V 1 -1 V 1 0 V 1 -1 V 1 -1 V 1 0 V 1 0 V 1 -3 V 1 0 V 1 -3 V 1 -1 V 1 0 V 1 -2 V 1 -1 V 1 0 V 1 -2 V 1 -1 V 1 0 V 1 0 V 1 -1 V 1 0 V 1 -1 V 1 -2 V 1 -1 V 1 0 V 1 0 V 1 -1 V 1 -1 V 1 -1 V 1 -1 V 1 0 V 1 -1 V 1 0 V 1 -1 V 1 0 V 1 -1 V 1 -3 V 1 0 V 1 0 V 1 -3 V 1 0 V 1 0 V 1 -3 V 1 0 V 1 -1 V 1 0 V 1 0 V 1 -1 V 1 -2 V 0 -1 V 1 0 V 1 0 V 1 -2 V 1 0 V 1 -2 V 1 -1 V 1 -2 V 1 -1 V 1 -1 V 1 0 V 1 0 V 1 -1 V 1 0 V 1 -1 V 1 0 V 1 -1 V 1 -1 V 1 0 V 1 -2 V 1 0 V 1 -2 V 1 -1 V 1 -1 V 1 0 V 1 0 V 1 -1 V 1 -2 V 1 0 V 1 -2 V 1 0 V 1 -2 V 1 0 V 1 -1 V 1 -2 V 0 -1 V 1 -1 V 1 0 V 1 -1 V 1 0 V 1 -1 V 1 -1 V 1 0 V 0 -1 V 1 -2 V 1 0 V 1 -1 V 1 -1 V 1 0 V 1 -2 V 1 -1 V 0 -1 V 1 -1 V 1 -1 V 1 0 V 1 -1 V 1 -1 V 1 0 V 1 -2 V 1 0 V 1 -1 V 1 0 V 1 -2 V 0 -1 V 1 -1 V 1 -1 V 1 0 V 1 0 V 1 -1 V 1 -1 V 1 -1 V 1 0 V 1 -1 V 1 -1 V 0 -1 V 1 -1 V 1 0 V 1 -2 V 1 0 V 1 0 V 1 -1 V 1 0 V 1 0 V 1 -1 V 1 -2 V 1 -1 V 1 0 V 1 -2 V 1 0 V 1 0 V 1 -1 V 1 -1 V 1 -1 V 1 -3 V 1 -3 V 1 0 V 1 0 V 0 -1 V 1 -1 V 1 0 V 1 -2 V 0 -1 V 1 0 V 1 0 V 1 0 V 1 -1 V 0 -1 V 1 -1 V 1 0 V 1 -2 V 0 -1 V 1 0 V 1 0 V 1 -1 V 1 0 V 0 -2 V 1 -1 V 1 -1 V 1 -1 V 0 -1 V 1 -1 V 1 -1 V 1 0 V 1 -1 V 1 -1 V 1 -4 V 0 -1 V 1 -1 V 1 0 V 1 0 V 0 -1 V 1 0 V 1 -2 V 1 -1 V 0 -1 V 1 -1 V 1 -1 V 1 0 V 0 -1 V 1 0 V 1 -2 V 1 -1 V 1 -1 V 1 0 V 1 -1 V 0 -1 V 1 0 V 1 0 V 0 -1 V 1 -7 V 1 0 V 1 0 V 0 -2 V 1 -2 V 1 -2 V 1 -1 V 1 -1 V 1 -3 V 1 -1 V 1 0 V 1 -1 V 1 -3 V 1 -2 V 1 0 V 1 -1 V 1 -1 V 0 -1 V 1 -4 V 1 -1 V 1 -1 V 1 0 V 1 0 V 1 -1 V 1 0 V 0 -4 V 1 -1 V 1 0 V 0 -2 V 1 0 V 1 -2 V 0 -1 V 1 0 V 1 -1 V 1 -1 V 0 -2 V 1 -3 V 1 -1 V 0 -2 V 1 -1 V 1 -3 V 0 -2 V 1 -2 V 1 -1 V 1 -1 V 1 -1 V 0 -2 V 1 0 V 1 -2 V 0 -2 V 1 -1 V 1 -2 V 0 -1 V 1 0 V 1 -3 V 0 -1 V 1 -2 V 1 -1 V 0 -1 V 1 -2 V 1 0 V 1 -1 V 1 0 V 0 -1 V 1 -1 V 1 -1 V 1 -6 V 1 -1 V 0 -4 V 1 0 V 1 -3 V 0 -2 V 1 0 V 1 -2 V 0 -1 V 1 0 V 0 -1 V 1 0 V 1 0 V 1 -2 V 1 -1 V 1 0 V 1 -1 V 1 -1 V 1 0 V 0 -1 V 1 -1 V 0 -1 V 1 0 V 1 -1 V 0 -1 V 1 -1 V 1 -3 V 1 -2 V 1 0 V 0 -3 V 1 -2 V 0 -5 V 1 -3 V 1 -1 V 0 -1 V 1 0 V 1 -2 V 1 -2 V 0 -1 V 1 -1 V 1 -3 V 1 0 V 0 -1 V 1 -1 V 1 -1 V 0 -1 V 1 -1 V 1 -1 V 0 -3 V 1 -4 V 0 -1 V 1 -2 V 1 -2 V 0 -1 V 1 -1 V 0 -1 V 1 -5 V 1 -1 V 1 0 V 0 -5 V 1 -1 V 1 -1 V 1 -5 V currentpoint stroke M 0 -5 V 1 -2 V 1 -1 V 1 -2 V 0 -1 V 1 0 V 1 -1 V 0 -1 V 1 -1 V 0 -2 V 1 -2 V 1 -3 V 0 -1 V 1 -1 V 0 -2 V 1 -6 V 1 -2 V 1 -3 V 0 -2 V 1 0 V 0 -1 V 1 -1 V 1 -5 V 0 -5 V 1 -1 V 1 -1 V 1 -3 V 0 -1 V 1 -2 V 0 -1 V 1 -2 V 0 -4 V 1 -2 V 1 -7 V 1 -2 V 0 -1 V 1 -1 V 0 -9 V 1 -4 V 1 -3 V 1 -1 V 0 -1 V 1 -4 V 0 -7 V 1 -2 V 1 -2 V 0 -1 V 1 -2 V 0 -1 V 1 -1 V 1 -3 V 1 -7 V 1 -2 V 1 0 V 0 -3 V 1 0 V 1 -1 V 0 -1 V 1 -2 V 1 -3 V 1 -3 V 0 -7 V 1 -1 V 0 -3 V 1 0 V 0 -1 V 1 -1 V 1 0 V 0 -10 V 1 -2 V 0 -2 V 1 -2 V 0 -2 V 1 0 V 0 -1 V 1 -4 V 0 -1 V 1 -13 V 1 0 V 0 -2 V 1 0 V 0 -10 V 1 -7 V 1 -5 V 0 -4 V 1 -5 V 0 -1 V 1 -9 V 0 -6 V 1 0 V 1 -3 V 0 -1 V 1 -2 V 1 -4 V 0 -1 V 1 -2 V 0 -1 V 1 -1 V 0 -1 V 1 -7 V 0 -8 V 1 -13 V 1 -1 V 0 -6 V 1 -8 V 0 -6 V 1 -3 V 1 0 V 0 -18 V 1 0 V 0 -2 V 1 -5 V 0 -2 V 1 -1 V 0 -2 V 1 -11 V 0 -16 V 1 -9 V 0 -3 V 1 -10 V 0 -3 V 1 -17 V 0 -6 V 1 -7 V 0 -1 V 1 -20 V 1 -9 V 1 -3 V 0 -16 V 1 -32 V 0 -11 V 1 -3 V 0 -4 V 1 -5 V 0 -28 V 1 -3 V 0 -6 V 1 -9 V 1 -21 V 0 -7 V 1 -4 V 0 -46 V 1 -26 V 0 -4 V stroke grestore end showpage %%EndDocument endTexFig 109 965 a Fq(Fig.)j(1.)g(Zipf)h(plots)g(for)f(random)h(samples)g(from) f(Diric)o(hlet)i(distribution)q(s)h(with)d(v)n(arious)i(v)n(alues)f(of) 105 1011 y Fd(\013)c Fq(=)h(0)p Fd(:)p Fq(1)6 b Fd(:)g(:)h(:)f Fq(1000.)13 b(F)m(or)g(eac)o(h)g(giv)o(en)h Fd(I)i Fq(and)e Fd(\013)p Fq(,)e Fd(I)j Fq(samples)g(from)d(a)h(standard)i(gamma)e (distribution)118 1056 y(w)o(ere)g(generated)h(with)f(shap)q(e)h (parameter)g Fd(\013=I)h Fq(and)f(normalized)h(to)e(giv)o(e)h(a)f (sample)h Fc(p)f Fq(from)f(the)129 1102 y(Diric)o(hlet)j(distributio)q (n.)g(The)e(Zipf)h(plot)g(sho)o(ws)g(the)f(probabiliti)q(es)j Fd(p)1161 1106 y Fb(i)1174 1102 y Fq(,)d(rank)o(ed)h(b)o(y)f (magnitude,)693 1148 y(v)o(ersus)h(their)g(rank.)100 1308 y Fw(of)f(the)h(Diric)o(hlet)g(distribution)f(is:)589 1398 y Fl(Z)s Fw(\()p Fl(\013)p Fr(m)p Fw(\))e(=)774 1359 y Fe(Y)795 1447 y Fo(i)834 1398 y Fw(\000\()p Fl(\013m)939 1404 y Fo(i)953 1398 y Fw(\))c(/\000\()p Fl(\013)p Fw(\))12 b Fl(:)435 b Fw(\(9\))100 1521 y(The)14 b(v)o(ector)h Fr(m)e Fw(is)h(the)g(mean)f(of)g(the)i(probabilit)o(y)d(distribution:) 556 1570 y Fe(Z)605 1627 y Fw(Diric)o(hlet)762 1608 y Fj(\()p Fo(I)r Fj(\))807 1627 y Fw(\()p Fr(p)p Fp(j)p Fl(\013)p Fr(m)p Fw(\))c Fr(p)h Fl(d)1011 1610 y Fo(I)1023 1627 y Fr(p)i Fw(=)h Fr(m)375 b Fw(\(10\))100 1732 y(The)11 b(role)g(of)f Fl(\013)h Fw(can)g(b)q(e)h(c)o(haracterized)h(in)d(t)o(w) o(o)h(w)o(a)o(ys.)f(First,)h(the)h(parameter)e Fl(\013)h Fw(measures)g(the)100 1786 y(sharpness)16 b(of)e(the)i(distribution;)e (it)g(measures)h(ho)o(w)g(di\013eren)o(t)g(w)o(e)g(exp)q(ect)i(t)o (ypical)d(samples)100 1840 y Fr(p)j Fw(from)g(the)h(distribution)g(to)g (b)q(e)h(from)d(the)j(mean)e Fr(m)p Fw(.)g(A)i(large)f(v)n(alue)f(of)h Fl(\013)g Fw(pro)q(duces)h(a)100 1894 y(distribution)g(o)o(v)o(er)h Fr(p)f Fw(whic)o(h)h(is)g(sharply)g(p)q(eak)o(ed)g(around)g Fr(m)p Fw(.)f(The)i(e\013ect)g(of)f Fl(\013)f Fw(can)h(b)q(e)100 1948 y(visualized)d(b)o(y)g(dra)o(wing)g(a)g(t)o(ypical)f(sample)h (from)e(the)j(distribution)f(Diric)o(hlet)1401 1930 y Fj(\()p Fo(I)r Fj(\))1446 1948 y Fw(\()p Fr(p)p Fp(j)p Fl(\013)p Fr(m)p Fw(\))n(,)100 2002 y(with)g Fr(m)h Fw(set)h(to)f(the)g (uniform)e(v)o(ector)j Fl(m)780 2008 y Fo(i)813 2002 y Fw(=)g(1)p Fl(=I)s Fw(,)e(and)h(making)d(a)j(Zipf)g(plot,)f(that)h (is,)f(a)100 2056 y(rank)o(ed)h(plot)f(of)h(the)h(v)n(alues)e(of)h(the) g(comp)q(onen)o(ts)g Fl(p)965 2062 y Fo(i)979 2056 y Fw(.)f(It)h(is)g(traditional)f(to)h(plot)f(b)q(oth)h Fl(p)1580 2062 y Fo(i)100 2110 y Fw(\(v)o(ertical)e(axis\))g(and)g(the) h(rank)f(\(horizon)o(tal)g(axis\))g(on)g(logarithmic)e(scales)j(so)f (that)h(p)q(o)o(w)o(er)100 2164 y(la)o(w)e(relationships)i(app)q(ear)g (as)g(straigh)o(t)f(lines.)g(Figure)h(1)f(sho)o(ws)h(these)h(plots)f (for)f(a)g(single)100 2218 y(sample)10 b(from)f(ensem)o(bles)i(with)g Fl(I)k Fw(=)d(100)e(and)h Fl(I)k Fw(=)d(1000)e(and)h(with)g Fl(\013)g Fw(from)e(0.1)i(to)g(1000.)e(F)m(or)100 2272 y(large)j Fl(\013)p Fw(,)g(the)h(plot)f(is)h(shallo)o(w)f(with)g(man)o (y)f(comp)q(onen)o(ts)h(ha)o(ving)g(similar)e(v)n(alues.)i(F)m(or)g (small)100 2326 y Fl(\013)p Fw(,)j(t)o(ypically)h(one)g(comp)q(onen)o (t)g Fl(p)641 2332 y Fo(i)672 2326 y Fw(receiv)o(es)i(an)e(o)o(v)o (erwhelming)f(share)i(of)f(the)i(probabilit)o(y)m(,)100 2380 y(and)g(of)g(the)i(probabilit)o(y)d(that)i(remains)f(to)g(b)q(e)i (shared)f(among)e(the)i(other)h(comp)q(onen)o(ts,)100 2434 y(another)d(comp)q(onen)o(t)g Fl(p)492 2440 y Fo(i)504 2432 y Fg(0)534 2434 y Fw(receiv)o(es)i(a)f(similarly)c(large)j(share.) h(In)f(the)h(limit)d(as)i Fl(\013)g Fw(go)q(es)h(to)100 2488 y(zero,)c(the)g(plot)g(tends)h(to)e(an)h(increasingly)g(steep)h(p) q(o)o(w)o(er)f(la)o(w.)141 2545 y(Second,)h(w)o(e)f(can)h(c)o (haracterize)h(the)f(role)g(of)e Fl(\013)i Fw(in)e(terms)i(of)e(the)i 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496 y Fo(i)837 484 y Fl(p)858 463 y(\013m)921 469 y Fo(i)944 463 y Fp(\000)k Fw(1)858 495 y Fo(i)1008 484 y Fl(\016)r Fw(\()1044 453 y Fe(P)1088 496 y Fo(i)1109 484 y Fl(p)1130 490 y Fo(i)1153 484 y Fp(\000)g Fw(1\))p Fl(=)n(Z)s Fw(\()p Fl(\013)p Fr(m)p Fw(\))p 647 503 734 2 v 927 541 a Fl(P)c Fw(\()p Fr(F)p Fp(j)p Fl(\013)p Fr(m)p Fw(\))1520 513 y(\(12\))568 646 y(=)647 586 y Fe(Q)686 629 y Fo(i)707 617 y Fl(p)728 596 y(F)755 602 y Fo(i)777 596 y Fw(+)k Fl(\013m)882 602 y Fo(i)905 596 y Fp(\000)f Fw(1)728 628 y Fo(i)969 617 y Fl(\016)r Fw(\()1005 586 y Fe(P)1049 629 y Fo(i)1070 617 y Fl(p)1091 623 y Fo(i)1114 617 y Fp(\000)g Fw(1\))p 647 636 546 2 v 768 674 a Fl(P)d Fw(\()p Fr(F)p Fp(j)p Fl(\013)p Fr(m)p Fw(\))p Fl(Z)s Fw(\()p Fl(\013)p Fr(m)p Fw(\))1520 646 y(\(13\))568 741 y(=)42 b(Diric)o(hlet)799 723 y Fj(\()p Fo(I)r Fj(\))844 741 y Fw(\()p Fr(p)p Fp(j)p Fr(F)9 b Fw(+)g Fl(\013)p Fr(m)p Fw(\))p Fl(:)446 b Fw(\(14\))100 833 y(The)14 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y(dominate)c(o)o(v)o(er)i(the) g(prior)g(in)f(subsequen)o(t)j(predictions.)e(If)f Fl(\013)h Fp(\035)1137 1129 y Fe(P)1181 1173 y Fo(i)1202 1160 y Fl(F)1229 1166 y Fo(i)1253 1160 y Fw(then)h Fl(P)6 b Fw(\()p Fl(i)p Fp(j)p Fr(F)p Fl(;)h(\013)p Fr(m)p Fw(\))j Fp(')100 1214 y Fl(m)136 1220 y Fo(i)150 1214 y Fw(;)j(if)g Fl(\013)f Fp(\034)305 1183 y Fe(P)348 1227 y Fo(i)369 1214 y Fl(F)396 1220 y Fo(i)424 1214 y Fw(then)i Fl(P)6 b Fw(\()p Fl(i)p Fp(j)p Fr(F)p Fl(;)h(\013)p Fr(m)p Fw(\))j Fp(')i Fl(F)806 1220 y Fo(i)819 1214 y Fl(=)p Fw(\()856 1183 y Fe(P)900 1227 y Fo(i)912 1218 y Fg(0)932 1214 y Fl(F)959 1220 y Fo(i)971 1212 y Fg(0)984 1214 y Fw(\).)141 1271 y(Finally)c(w)o(e)i(note)h(from)d(equations)i(\(9\))f(and)h (\(14\))g(that)g(the)g(`evidence')g(for)g Fl(\013)p Fr(m)p Fw(,)f Fl(P)d Fw(\()p Fr(F)p Fp(j)p Fl(\013)p Fr(m)p Fw(\),)100 1325 y(is:)344 1413 y Fl(P)g Fw(\()p Fr(F)p Fp(j)p Fl(\013)p Fr(m)p Fw(\))k(=)577 1385 y Fl(Z)s Fw(\()p Fr(F)g Fw(+)f Fl(\013)p Fr(m)p Fw(\))p 577 1403 211 2 v 617 1441 a Fl(Z)s Fw(\()p Fl(\013)p Fr(m)p Fw(\))804 1413 y(=)853 1353 y Fe(Q)892 1397 y Fo(i)913 1384 y Fw(\000\()p Fl(F)982 1390 y Fo(i)1005 1384 y Fw(+)g Fl(\013m)1109 1390 y Fo(i)1123 1384 y Fw(\))p 853 1403 287 2 v 876 1441 a(\000\()918 1410 y Fe(P)962 1454 y Fo(i)983 1441 y Fl(F)1010 1447 y Fo(i)1032 1441 y Fw(+)h Fl(\013)p Fw(\))1205 1385 y(\000\()p Fl(\013)p Fw(\))p 1150 1403 196 2 v 1150 1410 a Fe(Q)1189 1454 y Fo(i)1210 1441 y Fw(\000\()p Fl(\013m)1315 1447 y Fo(i)1329 1441 y Fw(\))1520 1413 y(\(16\))100 1513 y(The)i(imp)q(ortan)o(t)f(role)h(of)f(the)i (evidence)g(\(also)f(kno)o(wn)f(as)i(the)f(marginalized)e(lik)o(eliho)q (o)q(d\))g(will)100 1567 y(b)q(ecome)k(clear)h(shortly)m(.)f (Additional)f(useful)i(form)o(ulae)e(and)h(appro)o(ximations)e(are)j (found)f(in)100 1621 y(app)q(endix)g(A.)390 1795 y Fk(2.5)23 b(De\014nition)17 b(of)f(the)h(hier)n(ar)n(chic)m(al)d(mo)n(del)j Fp(H)1274 1801 y Fo(D)100 1879 y Fw(W)m(e)9 b(no)o(w)h(de\014ne)h(the)f 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Fw(\))17 b(on)h(the)h(measure)e Fl(\013)p Fr(m)h Fw(\(to)g(b)q(e)g(precise,)h(a) f(\015at)g(prior)f(on)h Fr(m)g Fw(and)g(a)f(broad)p eop %%Page: 8 8 8 7 bop 100 178 a Fw(8)351 b Fm(D.)15 b(J.)f(C.)g(MacKay)i(and)g(L.)e (C.)g(Bauman)i(Peto)100 278 y Fw(gamm)o(a)11 b(prior)j(o)o(v)o(er)g Fl(\013)p Fw(\).)f(The)h(prior)g(on)f Fl(Q)h Fw(de\014ned)h(b)o(y)f (this)g(hierarc)o(hical)f(mo)q(del)g(is)h(then:)347 381 y Fl(P)6 b Fw(\()p Fl(Q)p Fp(jH)476 387 y Fo(D)505 381 y Fw(\))12 b(=)577 325 y Fe(Z)625 342 y(Y)644 430 y Fo(j)685 335 y Fe(h)705 381 y Fw(Diric)o(hlet)862 363 y Fj(\()p Fo(I)r Fj(\))907 381 y Fw(\()p Fr(q)948 388 y Fi(j)p Fo(j)976 381 y Fp(j)p Fl(\013)p Fr(m)p Fw(\))1070 335 y Fe(i)1097 381 y Fl(P)6 b Fw(\()p Fl(\013)p Fr(m)p Fw(\))p Fl(d)1251 364 y Fo(I)1268 381 y Fl(\013)p Fr(m)p Fl(:)173 b Fw(\(18\))100 505 y(When)19 b(w)o(e)h(use)h(this)f(hierarc)o(hical)f (mo)q(del)f(w)o(e)i(can)g(e\013ectiv)o(ely)h(\014nd)f(out)f(from)f(the) i(data)100 559 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Fr(q)15 b Fw(of)f(a)h(single)g(die)g(as)g (coming)e(from)g(a)i(Diric)o(hlet)g(prior)g(with)f(unkno)o(wn)h(h)o(yp) q(erparameters)100 2653 y Fr(u)c Fw(=)g Fl(\013)p Fr(m)i Fw(that)h(c)o(haracterize)h(the)f(factory)m(.)e(The)i(data)f(are)g(the) h(outcomes)f(of)g(rolls)g(of)f Fl(J)18 b Fw(dice)p eop %%Page: 11 11 11 10 bop 485 178 a Fm(Hier)n(ar)n(chic)n(al)14 b(Dirichlet)f(L)n (anguage)k(Mo)n(del)372 b Fw(11)100 278 y(lab)q(eled)13 b(b)o(y)g Fl(j)r Fw(.)h(Eac)o(h)f(die)h Fl(j)h Fw(is)f(rolled)f(a)g(n)o (um)o(b)q(er)f(of)h(times)g Fl(F)1070 284 y Fo(j)1087 278 y Fw(,)g(and)g(w)o(e)h(are)f(told)g(the)h(coun)o(ts)100 332 y(of)i(the)h(outcomes,)f Fl(F)448 339 y Fo(i)p Fi(j)p Fo(j)487 332 y Fw(,)g(whic)o(h)h(giv)o(e)f(us)h(imp)q(erfect)g (information)d(ab)q(out)j(the)g(parameters)100 386 y Fl(Q)g Fw(=)h Fp(f)p Fl(q)240 393 y Fo(i)p Fi(j)p Fo(j)278 386 y Fp(g)p Fw(.)f(Giv)o(en)g(these)i(measuremen)o(ts,)d(our)h(task)h (is)f(to)h(infer)f(the)h(h)o(yp)q(erparameters)100 440 y Fr(u)d Fw(=)i 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Fo(i)1188 1981 y Fl(<)c Fw(1)17 b Fk(and)f Fl(\013)11 b(>)h Fw(1)100 2059 y(W)m(e)j(no)o(w)g (assume)g(that)g Fl(\013)f(>)g Fw(1)i(and)f Fl(u)727 2065 y Fo(i)754 2059 y Fl(<)g Fw(1)g(to)g(deriv)o(e)h(an)f(algorithm)e (sp)q(ecialized)j(for)f(the)100 2113 y(parameter)c(regimes)g(exp)q (ected)j(in)d(language)g(mo)q(delling.)e(W)m(e)i(exp)q(ect)j Fl(\013)d Fw(to)h(b)q(e)g(greater)h(than)100 2167 y(1)g(b)q(ecause)j Fl(\013)d Fw(corresp)q(onds)j(to)d(the)i(rough)e(n)o(um)o(b)q(er)g(of)g (data)h(p)q(oin)o(ts)f(needed)j(to)d(o)o(v)o(erwhelm)100 2221 y(the)e(Diric)o(hlet)g(prior.)f(Ho)o(w)h(man)o(y)e(times)h Fl(F)784 2227 y Fo(j)812 2221 y Fw(do)h(w)o(e)h(exp)q(ect)g(w)o(e)f (need)h(to)f(see)i(con)o(text)e Fl(j)j Fw(for)d(us)100 2275 y(to)i(ha)o(v)o(e)g(learn)o(t)g(the)h(principal)f(prop)q(erties)h (of)f Fr(q)873 2281 y Fo(j)891 2275 y Fw(?)g(If)g(w)o(e)g(ha)o(v)o(e)g (only)g(seen)h(a)f(con)o(text)h(one)g(or)100 2329 y(t)o(w)o(o)f(times,) 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y(Bro)o(wn,)e(P)m(.)g(F.,)f(Della)h(Pietra,)g(S.)g(A.,) g(Della)f(Pietra,)i(V.)f(J.,)g(Lai,)f(J.)h(C.,)g(and)g(Mercer,)i(R.)e (L.)141 2039 y(\(1992\))h(An)e(estimate)f(of)g(an)g(upp)q(er)h(b)q (ound)g(for)f(the)h(en)o(trop)o(y)g(of)f(English.)j Fm(Computational) 141 2089 y(Linguistics)j Fr(18)d Fw(\(1\):)f(31{40.)100 2131 y(Bro)o(wn,)g(P)m(.)g(F.,)f(DellaPietra,)h(S.)g(A.,)g (DellaPietra,)f(V.)h(J.,)g(and)g(Mercer,)i(R.)e(L.)k(\(1993\))h(The)141 2182 y(mathematics)c(of)i(statistical)g(mac)o(hine)f(translation:)g(P)o (arameter)h(estimation.)24 b Fm(Compu-)141 2232 y(tational)15 b(Linguistics)i Fr(19)c Fw(\(2\):)h(263{311.)100 2274 y(Bun)o(tine,)g(W.)j(\(1992\))h(Learning)c(classi\014cation)g(trees.)20 b Fm(Statistics)14 b(and)i(Computing)h Fr(2)p Fw(:)d(63{)141 2325 y(73.)100 2367 y(Co)o(x,)d(R.)k(\(1946\))g(Probabilit)o(y)m(,)10 b(frequency)m(,)j(and)f(reasonable)h(exp)q(ectation.)j Fm(A)o(m.)d(J.)g(Physics)141 2417 y Fr(14)p Fw(:)g(1{13.)100 2459 y(Gale,)j(W.,)g(and)h(Ch)o(urc)o(h,)g(K.)28 b(\(1991\))g(A)18 b(program)d(for)i(aligning)e(sen)o(tences)20 b(in)d(bilingual)141 2510 y(corp)q(ora.)i(In)13 b Fm(Pr)n(o)n(c)n(e)n(e)n(dings)i(of)g(29th) g(A)o(nnual)h(Me)n(eting)f(of)g(the)g(A)o(CL)p Fw(,)d(pp.)i(177{184.) 100 2552 y(Gull,)d(S.)i(F.)k(\(1989\))g(Dev)o(elopmen)o(ts)12 b(in)h(maxim)n(um)c(en)o(trop)o(y)14 b(data)f(analysis.)j(In)d Fm(Maximum)141 2602 y(Entr)n(opy)k(and)g(Bayesian)g(Metho)n(ds,)g (Cambridge)e(1988)6 b Fw(,)16 b(ed.)f(b)o(y)h(J.)f(Skilling,)e(pp.)i (53{71,)141 2653 y(Dordrec)o(h)o(t.)f(Klu)o(w)o(er.)p eop %%Page: 19 19 19 18 bop 485 178 a Fm(Hier)n(ar)n(chic)n(al)14 b(Dirichlet)f(L)n (anguage)k(Mo)n(del)372 b Fw(19)100 278 y(Hanson,)14 b(R.,)f(Stutz,)h(J.,)g(and)g(Cheeseman,)h(P)m(.)k(\(1991\))g(Ba)o(y)o (esian)14 b(classi\014cation)h(with)f(cor-)141 328 y(relation)g(and)g (inheritance.)21 b(In)15 b Fm(Pr)n(o)n(c)n(e)n(e)n(dings)g(of)g(the)h (12th)g(International)f(Joint)h(Confer-)141 378 y(enc)n(e)d(on)g(A)o 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(y)g(net)o(w)o(orks.)j Fm(Nucle)n(ar)141 801 y(Instruments)g(and)h (Metho)n(ds)f(in)g(Physics)g(R)n(ese)n(ar)n(ch,)g(Se)n(ction)g(A)f Fr(354)f Fw(\(1\):)h(73{80.)100 843 y(MacKa)o(y)m(,)f(D.)h(J.)g(C.)21 b(\(1995b\))e(Densit)o(y)c(net)o(w)o(orks)g(and)g(protein)f(mo)q (delling.)k(In)c Fm(Maximum)141 892 y(Entr)n(opy)f(and)h(Bayesian)g (Metho)n(ds,)g(Cambridge)e(1994)6 b Fw(,)12 b(ed.)g(b)o(y)g(J.)f (Skilling)f(and)i(S.)f(Sibisi,)141 942 y(Dordrec)o(h)o(t.)j(Klu)o(w)o (er.)100 984 y(MacKa)o(y)m(,)e(D.)h(J.)g(C.)18 b(\(1995c\))f(Hyp)q (erparameters:)d(Optimize,)e(or)i(in)o(tegrate)g(out?)j(In)d Fm(Maxi-)141 1034 y(mum)e(Entr)n(opy)h(and)g(Bayesian)g(Metho)n(ds,)f (Santa)h(Barb)n(ar)n(a)f(1993)6 b Fw(,)11 b(ed.)g(b)o(y)g(G.)f (Heidbreder,)141 1083 y(Dordrec)o(h)o(t.)k(Klu)o(w)o(er.)100 1125 y(MacKa)o(y)m(,)i(D.)g(J.)h(C.,)f(\(1995d\))28 b(Mo)q(dels)17 b(for)g(dice)g(factories)h(and)f(amino)e(acid)i(probabilit)o(y)141 1175 y(v)o(ectors.)i(In)14 b(preparation.)100 1216 y(Nadas,)i(A.)27 b(\(1984\))f(Estimation)15 b(of)h(probabilities)g(in)g(the)i(language)e (mo)q(del)f(of)h(the)i(IBM)141 1266 y(sp)q(eec)o(h)e(recognition)d (system.)18 b Fm(IEEE)e(T)m(r)n(ans)g Fr(ASSP{32)c Fw(\(4\):)i (859{861.)100 1308 y(Neal,)8 b(R.)h(M.)i(\(1992\))f(Ba)o(y)o(esian)f (mixture)g(mo)q(delling.)f(In)h Fm(Maximum)j(Entr)n(opy)f(and)g (Bayesian)141 1357 y(Metho)n(ds,)j(Se)n(attle)g(1991)6 b Fw(,)12 b(ed.)h(b)o(y)f(C.)g(Smith,)f(G.)h(Eric)o(kson,)g(and)h(P)m (.)f(Neudorfer,)h(pp.)f(197{)141 1407 y(211,)h(Dordrec)o(h)o(t.)h(Klu)o (w)o(er.)100 1449 y(Neal,)e(R.)h(M.)k(\(1993\))g(Probabilistic)c (inference)i(using)e(Mark)o(o)o(v)f(c)o(hain)i(Mon)o(te)f(Carlo)g (meth-)141 1499 y(o)q(ds.)j(T)m(ec)o(hnical)c(Rep)q(ort)h(CR)o (G{TR{93{1,)c(Dept.)j(of)g(Computer)g(Science,)h(Univ)o(ersit)o(y)g(of) 141 1548 y(T)m(oron)o(to.)100 1590 y(P)o(eto,)c(L.)g(B.)i(\(1994\))g(A) f(comparison)e(of)h(t)o(w)o(o)g(smo)q(othing)e(metho)q(ds)j(for)f(w)o (ord)g(bigram)f(mo)q(dels.)141 1640 y(T)m(ec)o(hnical)j(Rep)q(ort)h (CSRI-304,)e(Computer)h(Systems)g(Researc)o(h)i(Institute,)f(Univ)o (ersit)o(y)g(of)141 1689 y(T)m(oron)o(to.)100 1731 y(Press,)i(W.,)e (Flannery)m(,)g(B.,)h(T)m(euk)o(olsky)m(,)e(S.)i(A.,)f(and)h(V)m (etterling,)g(W.)f(T.)17 b(\(1988\))g Fm(Numeric)n(al)141 1781 y(R)n(e)n(cip)n(es)e(in)g(C)6 b Fw(.)18 b(Cam)o(bridge.)100 1822 y(Skilling,)11 b(J.)19 b(\(1989\))f(Classic)c(maxim)n(um)c(en)o (trop)o(y)m(.)18 b(In)c Fm(Maximum)i(Entr)n(opy)f(and)h(Bayesian)141 1872 y(Metho)n(ds,)f(Cambridge)g(1988)6 b Fw(,)14 b(ed.)g(b)o(y)f(J.)h (Skilling,)d(Dordrec)o(h)o(t.)j(Klu)o(w)o(er.)100 1914 y(W)m(est,)g(M.)19 b(\(1992\))g(Hyp)q(erparameter)c(estimation)e(in)g (Diric)o(hlet)h(pro)q(cess)i(mixture)e(mo)q(dels.)141 1963 y(W)m(orking)e(pap)q(er)j(92-A03,)d(Duk)o(e)i(Inst.)g(of)f(Stats.) h(and)g(Decision)g(Sciences.)100 2005 y(William)o(s,)g(C.)i(K.)h(I.,)e (and)i(Hin)o(ton,)f(G.)g(E.)27 b(\(1991\))g(Mean)17 b(\014eld)g(net)o (w)o(orks)g(that)g(learn)g(to)141 2055 y(discriminate)d(temp)q(orally)e (distorted)k(strings.)21 b(In)15 b Fm(Conne)n(ctionist)h(Mo)n(dels:)f (Pr)n(o)n(c)n(e)n(e)n(dings)141 2105 y(of)20 b(the)g(1990)h(Summer)f (Scho)n(ol)t Fw(,)f(ed.)h(b)o(y)f(D.)f(S.)h(T)m(ouretzky)m(,)g(J.)g(L.) g(Elman,)e(and)i(T.)g(J.)141 2154 y(Sejno)o(wski.)13 b(Morgan)h(Kaufmann,)d(San)j(Mateo,)g(CA.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF endmulti