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T*
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T*
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ET
348.81 622.269 6.652 -0.399 re
f
BT
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f
BT
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(X)Tj
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[(ma)27.2(y)-326.4(b)-27.2(e)-326.4(reparametrized)-326.5(in)-326.4(the)-326.4(form)]TJ
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[(,)-330(whic)27.2(h)]TJ
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3.407 0 TD
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4.1801 0 TD
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[(tion)-310.1(pro)27.1(vided)-310.1(b)27.1(y)-310.1(the)-310.1(data)]TJ
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11.2334 0 TD
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[(with)-310.1(an)27.1(y)-310.1(other)-310.2(information)-310.3(ab)-27.2(out)]TJ
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14.6604 0 TD
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[(con)27.2(tained)-310.1(in)]TJ
-27.7669 -1.2083 TD
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7.4597 0 TD
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[(\).)-327(In)27.2(tuitiv)27.2(ely)81.6(,)-327(the)]TJ
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7.6171 0 TD
[(r)50(efer)50(enc)49.9(e)-350.5(prior)-350.6(function)]TJ
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10.4282 0 TD
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()Tj
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[(,)-326.9(giv)27.2(en)]TJ
-30.1708 -1.2083 TD
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(\()Tj
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(x)Tj
/F2 1 Tf
0.659 0 TD
[(\))-412.8(and)]TJ
/F10 1 Tf
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(2)Tj
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(x)Tj
/F2 1 Tf
0.659 0 TD
[(\))-412.8(h)0(a)27.2(v)27.2(e)-412.8(strictly)]TJ
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T*
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T*
[(div)27.1(ergence.)-326.4(Th)27.2(us,)-326.4(if)]TJ
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(i)Tj
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[(,)-326.3(then)]TJ
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()Tj
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(i)Tj
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(j)Tj
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(j)Tj
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(|)Tj
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(.)Tj
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[(The)-401.6(in)27.2(trinsic)-401.7(discrepancy)-401.7(is)]TJ
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[(information)-419.2(additive)]TJ
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[(.)-401.6(T)0(h)27.2(us,)-401.7(if)]TJ
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[(consists)-401.7(of)]TJ
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-32.4155 -1.2083 TD
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(j)Tj
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(\),)Tj
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(1)Tj
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[(.)-357.1(This)-357.1(statistically)-357.2(imp)-27.3(ortan)27.2(t)-357(additiv)27.1(e)-357.1(prop)-27.2(ert)27.2(y)-357.1(i)0(s)]TJ
-11.6878 -1.2083 TD
[(essen)27.2(tially)-395.6(unique)-395.6(to)-395.6(logarithmic)-395.6(discrepancies;)-395.7(it)-395.6(is)-395.5(basically)-395.6(a)-395.6(consequence)]TJ
T*
[(of)-466.2(the)-466.2(fact)-466.3(that)-466.2(the)-466.2(join)27.1(t)-466.2(densit)27.2(y)-466.2(o)0(f)-466.2(indep)-27.3(enden)27.2(t)-466.2(random)-466.3(quan)27.2(tities)-466.3(is)-466.2(the)]TJ
T*
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T*
[(whic)27.2(h)-326.4(transforms)-326.4(pro)-27.3(ducts)-326.4(in)27.2(to)-326.4(sums.)]TJ
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0.8333 -1.6826 TD
[(Example)-375(1)]TJ
/F9 1 Tf
6.4516 0 TD
[(Intrinsic)-398(discr)49.9(ep)50(ancy)-398(b)50(etwe)50(en)-398(Binomial)-398.1(distributions)]TJ
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[(.)-378.6(The)]TJ
-28.9964 -1.2083 TD
[(in)27.2(trinsic)-326.5(discrepancy)]TJ
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()Tj
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()Tj
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(1)Tj
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(,)Tj
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[(b)-27.2(e)0(t)27.1(w)27.2(een)-326.4(the)-326.4(t)27.2(w)27.2(o)-326.4(Binomial)-326.5(distributions)]TJ
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(Figure)Tj
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(1)Tj
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[(Intrinsic)-357.7(discr)51.1(ep)51.1(ancy)-357.7(b)51.1(etwe)51.1(en)-357.8(Bernoul)-51(li)-357.8(variables.)]TJ
ET
0 G
1 J 1 j 0.25 w 10 M []0 d
1 i
122.285 308.074 m
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131.042 304.645 m
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S
BT
/F22 1 Tf
10 0 0 10 112.6484 297.087 Tm
0.0001 Tc
(0.1)Tj
ET
168.582 289.945 m
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S
BT
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(0.5)Tj
ET
209.986 273.734 m
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BT
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()Tj
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ET
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S
BT
/F22 1 Tf
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0.0001 Tc
(0.1)Tj
ET
244.408 305.421 m
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S
BT
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(0.5)Tj
ET
259.904 329.125 m
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S
BT
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ET
122.285 308.074 m
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S
BT
/F22 1 Tf
10 0 0 10 115.3114 307.8221 Tm
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(0)Tj
ET
117.542 338.005 m
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S
BT
10 0 0 10 110.6906 336.7887 Tm
(6)Tj
ET
122.285 308.074 m
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122.285 308.074 l
220.899 269.46 m
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S
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b
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b
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b
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b
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b
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184.299 365.618 l
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b
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184.299 365.618 l
182.707 363.349 l
b
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188.349 359.656 m
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187.107 363.608 l
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b
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b
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b
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194.02 356.638 l
b
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198.412 357.413 l
196.875 355.261 l
b
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b
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b
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207.03 353.537 l
205.527 351.418 l
b
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209.934 352.313 l
208.444 350.203 l
b
0.689 0.701 0.856 rg
214.329 347.836 m
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212.855 351.113 l
211.378 349.01 l
b
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b
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218.752 348.761 l
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b
0.684 0.705 0.863 rg
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224.722 346.462 l
221.727 347.606 l
220.289 345.528 l
b
0.683 0.707 0.866 rg
226.325 343.264 m
227.736 345.325 l
224.722 346.462 l
223.297 344.391 l
b
0.682 0.708 0.868 rg
229.373 342.145 m
230.769 344.196 l
227.736 345.325 l
226.325 343.264 l
b
0.681 0.71 0.87 rg
232.441 341.033 m
233.821 343.073 l
230.769 344.196 l
229.373 342.145 l
b
0.68 0.712 0.873 rg
235.53 339.927 m
236.895 341.956 l
233.821 343.073 l
232.441 341.033 l
b
0.678 0.714 0.876 rg
238.64 338.828 m
239.989 340.844 l
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235.53 339.927 l
b
0.677 0.717 0.879 rg
241.771 337.737 m
243.103 339.736 l
239.989 340.844 l
238.64 338.828 l
b
0.676 0.719 0.882 rg
244.927 336.655 m
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b
0.674 0.722 0.885 rg
248.105 335.585 m
249.398 337.537 l
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b
0.672 0.725 0.89 rg
251.308 334.534 m
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b
0.667 0.729 0.896 rg
254.537 333.517 m
255.785 335.379 l
252.579 336.449 l
251.308 334.534 l
b
0.658 0.733 0.905 rg
257.8 332.573 m
259.019 334.351 l
255.785 335.379 l
254.537 333.517 l
b
0.632 0.734 0.921 rg
261.115 331.821 m
262.3 333.504 l
259.019 334.351 l
257.8 332.573 l
b
0.705 0.624 0.763 rg
175.491 364.237 m
177.083 367.431 l
174.289 369.265 l
172.693 366.016 l
b
0.696 0.623 0.771 rg
178.291 362.651 m
179.88 365.789 l
177.083 367.431 l
175.491 364.237 l
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b
q
116.661 269.46 151.346 122.763 re
W n
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223 305.647 m
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131.042 304.645 m
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BT
10 0 0 10 112.6484 297.087 Tm
0 g
(0)Tj
ET
Q
BT
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0 g
0.0001 Tc
(.1)Tj
ET
0.25 w
168.582 289.945 m
169.231 290.697 l
S
BT
10 0 0 10 151.3806 282.1748 Tm
(0.5)Tj
ET
209.986 273.734 m
210.552 274.548 l
S
q
116.661 269.46 151.346 122.763 re
W n
BT
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0.6002 Tc
(09)Tj
ET
Q
BT
/F24 1 Tf
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0 0 0 rg
0 Tc
()Tj
/F23 1 Tf
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(1)Tj
/F24 1 Tf
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()Tj
/F23 1 Tf
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(1)Tj
/F25 1 Tf
10 0 0 10 130.4006 383.2779 Tm
()Tj
/F24 1 Tf
0.325 0 TD
()Tj
/F23 1 Tf
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(1)Tj
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(,)Tj
/F24 1 Tf
0.5 0 TD
()Tj
/F23 1 Tf
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(2)Tj
/F25 1 Tf
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()Tj
ET
0.25 w
321.827 308.075 m
420.441 269.46 l
330.584 304.645 m
331.297 305.337 l
S
BT
/F22 1 Tf
10 0 0 10 312.1713 297.087 Tm
0 g
0.0001 Tc
(0.1)Tj
ET
368.123 289.945 m
368.773 290.697 l
S
BT
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(0.5)Tj
ET
409.527 273.734 m
410.093 274.548 l
S
BT
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(0.9)Tj
/F24 1 Tf
0 0 0 rg
-4.3552 0.6086 TD
0 Tc
()Tj
/F23 1 Tf
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(1)Tj
ET
420.441 269.46 m
462.91 334.424 l
425.542 277.265 m
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S
BT
/F22 1 Tf
10 0 0 10 426.3815 272.301 Tm
0 g
0.0001 Tc
(0.1)Tj
ET
443.949 305.421 m
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S
BT
10 0 0 10 444.8123 300.6533 Tm
(0.5)Tj
ET
459.445 329.125 m
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S
BT
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(0.9)Tj
/F24 1 Tf
0 0 0 rg
0.6905 -2.7975 TD
0 Tc
()Tj
/F23 1 Tf
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(2)Tj
ET
321.827 308.075 m
316.203 343.564 l
321.703 308.86 m
322.627 308.5 l
S
BT
/F22 1 Tf
10 0 0 10 314.8342 307.8221 Tm
0 g
(0)Tj
ET
317.084 338.005 m
318.02 337.673 l
S
BT
10 0 0 10 310.2135 336.7887 Tm
(6)Tj
ET
321.827 308.075 m
316.203 343.564 l
376.419 392.223 l
377.542 360.109 l
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420.441 269.46 m
462.91 334.424 l
467.548 368.365 l
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316.203 343.564 l
422.596 306.606 l
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377.542 360.109 m
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S
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377.735 384.975 m
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386.42 376.847 m
388.01 380.142 l
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383.527 379.481 l
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386.42 376.847 l
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b
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b
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b
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b
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447.106 340.876 l
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b
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b
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b
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b
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b
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b
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b
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b
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b
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b
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b
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b
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b
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b
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b
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b
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b
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b
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b
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b
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387.962 303.392 l
384.523 303.602 l
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b
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b
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b
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404.001 302.664 l
b
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413.436 304.152 l
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b
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415.54 303.993 l
b
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425.282 305.78 l
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419.525 304.621 l
b
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429.382 306.514 l
425.282 305.78 l
423.589 305.349 l
b
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331.521 314.257 l
328.506 315.575 l
326.281 313.293 l
b
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332.327 310.84 m
334.546 313.005 l
331.521 314.257 l
329.297 312.034 l
b
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335.369 309.711 m
337.586 311.819 l
334.546 313.005 l
332.327 310.84 l
b
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338.428 308.648 m
340.639 310.697 l
337.586 311.819 l
335.369 309.711 l
b
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343.71 309.642 l
340.639 310.697 l
338.428 308.648 l
b
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344.598 306.721 m
346.799 308.654 l
343.71 309.642 l
341.503 307.651 l
b
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349.906 307.731 l
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347.713 305.857 l
b
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356.19 306.089 l
353.036 306.876 l
350.85 305.063 l
b
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357.201 303.676 m
359.368 305.368 l
356.19 306.089 l
354.012 304.335 l
b
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362.574 304.718 l
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357.201 303.676 l
b
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365.809 304.137 l
362.574 304.718 l
360.418 303.088 l
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369.075 303.626 l
365.809 304.137 l
363.665 302.57 l
b
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369.075 303.626 l
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b
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372.376 303.188 l
370.259 301.748 l
b
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379.087 302.529 l
375.712 302.821 l
373.611 301.449 l
b
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380.437 301.073 m
382.503 302.311 l
379.087 302.529 l
377.003 301.223 l
b
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383.915 301.002 m
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382.503 302.311 l
380.437 301.073 l
b
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389.465 302.105 l
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383.915 301.002 l
b
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391.019 301.099 m
393.018 302.122 l
389.465 302.105 l
387.441 301.01 l
b
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394.65 301.272 m
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393.018 302.122 l
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b
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400.284 302.399 l
396.623 302.219 l
394.65 301.272 l
b
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404.001 302.664 l
400.284 302.399 l
398.337 301.527 l
b
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407.782 303.017 l
404.001 302.664 l
402.084 301.872 l
b
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409.774 302.832 m
411.626 303.458 l
407.782 303.017 l
405.895 302.307 l
b
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415.54 303.993 l
411.626 303.458 l
409.774 302.832 l
b
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417.75 304.173 m
419.525 304.621 l
415.54 303.993 l
413.724 303.454 l
b
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421.856 304.992 m
423.589 305.349 l
419.525 304.621 l
417.75 304.173 l
b
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426.045 305.916 m
427.734 306.175 l
423.589 305.349 l
421.856 304.992 l
b
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327.032 309.853 m
329.297 312.034 l
326.281 313.293 l
324.014 311.056 l
b
0.659 0.736 0.907 rg
330.065 308.716 m
332.327 310.84 l
329.297 312.034 l
327.032 309.853 l
b
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333.11 307.646 m
335.369 309.711 l
332.327 310.84 l
330.065 308.716 l
b
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336.173 306.641 m
338.428 308.648 l
335.369 309.711 l
333.11 307.646 l
b
0.627 0.751 0.936 rg
339.253 305.704 m
341.503 307.651 l
338.428 308.648 l
336.173 306.641 l
b
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342.354 304.833 m
344.598 306.721 l
341.503 307.651 l
339.253 305.704 l
b
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345.475 304.029 m
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344.598 306.721 l
342.354 304.833 l
b
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350.85 305.063 l
347.713 305.857 l
345.475 304.029 l
b
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354.012 304.335 l
350.85 305.063 l
348.62 303.295 l
b
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357.201 303.676 l
354.012 304.335 l
351.79 302.628 l
b
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360.418 303.088 l
357.201 303.676 l
354.988 302.031 l
b
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363.665 302.57 l
360.418 303.088 l
358.216 301.505 l
b
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366.944 302.122 l
363.665 302.57 l
361.475 301.051 l
b
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370.259 301.748 l
366.944 302.122 l
364.768 300.668 l
b
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370.259 301.748 l
368.096 300.36 l
b
0.372 0.742 0.99 rg
374.873 299.968 m
377.003 301.223 l
373.611 301.449 l
371.464 300.126 l
b
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380.437 301.073 l
377.003 301.223 l
374.873 299.968 l
b
0.293 0.715 0.972 rg
381.823 299.89 m
383.915 301.002 l
380.437 301.073 l
378.326 299.89 l
b
0.25 0.697 0.957 rg
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387.441 301.01 l
383.915 301.002 l
381.823 299.89 l
b
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391.019 301.099 l
387.441 301.01 l
385.372 299.97 l
b
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394.65 301.272 l
391.019 301.099 l
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b
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398.337 301.527 l
394.65 301.272 l
392.628 300.383 l
b
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402.084 301.872 l
398.337 301.527 l
396.343 300.719 l
b
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405.895 302.307 l
402.084 301.872 l
400.121 301.146 l
b
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409.774 302.832 l
405.895 302.307 l
403.964 301.664 l
b
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411.864 302.988 m
413.724 303.454 l
409.774 302.832 l
407.877 302.276 l
b
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417.75 304.173 l
413.724 303.454 l
411.864 302.988 l
b
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420.079 304.715 m
421.856 304.992 l
417.75 304.173 l
415.93 303.799 l
b
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424.315 305.739 m
426.045 305.916 l
421.856 304.992 l
420.079 304.715 l
b
0.658 0.736 0.907 rg
324.722 307.716 m
327.032 309.853 l
324.014 311.056 l
321.703 308.86 l
b
0.649 0.741 0.917 rg
327.757 306.638 m
330.065 308.716 l
327.032 309.853 l
324.722 307.716 l
b
0.638 0.746 0.926 rg
330.805 305.626 m
333.11 307.646 l
330.065 308.716 l
327.757 306.638 l
b
0.627 0.751 0.936 rg
333.871 304.68 m
336.173 306.641 l
333.11 307.646 l
330.805 305.626 l
b
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336.957 303.801 m
339.253 305.704 l
336.173 306.641 l
333.871 304.68 l
b
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340.062 302.989 m
342.354 304.833 l
339.253 305.704 l
336.957 303.801 l
b
0.583 0.762 0.964 rg
343.191 302.246 m
345.475 304.029 l
342.354 304.833 l
340.062 302.989 l
b
0.565 0.764 0.972 rg
346.343 301.571 m
348.62 303.295 l
345.475 304.029 l
343.191 302.246 l
b
0.544 0.766 0.98 rg
349.522 300.967 m
351.79 302.628 l
348.62 303.295 l
346.343 301.571 l
b
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352.729 300.433 m
354.988 302.031 l
351.79 302.628 l
349.522 300.967 l
b
0.497 0.765 0.991 rg
355.967 299.97 m
358.216 301.505 l
354.988 302.031 l
352.729 300.433 l
b
0.47 0.763 0.994 rg
359.236 299.579 m
361.475 301.051 l
358.216 301.505 l
355.967 299.97 l
b
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362.543 299.263 m
364.768 300.668 l
361.475 301.051 l
359.236 299.579 l
b
0.407 0.751 0.994 rg
365.885 299.023 m
368.096 300.36 l
364.768 300.668 l
362.543 299.263 l
b
0.372 0.742 0.99 rg
369.269 298.856 m
371.464 300.126 l
368.096 300.36 l
365.885 299.023 l
b
0.333 0.73 0.982 rg
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374.873 299.968 l
371.464 300.126 l
369.269 298.856 l
b
0.293 0.715 0.971 rg
376.164 298.761 m
378.326 299.89 l
374.873 299.968 l
372.694 298.768 l
b
0.25 0.697 0.957 rg
379.683 298.833 m
381.823 299.89 l
378.326 299.89 l
376.164 298.761 l
b
0.205 0.676 0.938 rg
383.253 298.989 m
385.372 299.97 l
381.823 299.89 l
379.683 298.833 l
b
0.159 0.653 0.916 rg
386.877 299.23 m
388.973 300.135 l
385.372 299.97 l
383.253 298.989 l
b
0.112 0.626 0.89 rg
390.559 299.558 m
392.628 300.383 l
388.973 300.135 l
386.877 299.23 l
b
0.064 0.598 0.861 rg
394.302 299.976 m
396.343 300.719 l
392.628 300.383 l
390.559 299.558 l
b
0.017 0.567 0.829 rg
398.108 300.486 m
400.121 301.146 l
396.343 300.719 l
394.302 299.976 l
b
0 0.535 0.794 rg
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403.964 301.664 l
400.121 301.146 l
398.108 300.486 l
b
0 0.502 0.758 rg
405.933 301.792 m
407.877 302.276 l
403.964 301.664 l
401.984 301.09 l
b
0 0.468 0.72 rg
409.957 302.596 m
411.864 302.988 l
407.877 302.276 l
405.933 301.792 l
b
0.159 0 0 rg
414.064 303.504 m
415.93 303.799 l
411.864 302.988 l
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b
0.198 0 0 rg
418.257 304.519 m
420.079 304.715 l
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414.064 303.504 l
b
q
316.203 269.46 151.346 122.762 re
W n
0.234 0 0 rg
422.541 305.647 m
424.315 305.739 l
420.079 304.715 l
418.257 304.519 l
b
0.25 w
420.441 269.46 m
462.91 334.424 l
467.548 368.365 l
422.596 306.606 l
420.441 269.46 l
321.827 308.075 m
316.203 343.564 l
422.596 306.606 l
420.441 269.46 l
321.827 308.075 l
420.441 269.46 l
330.584 304.645 m
331.297 305.337 l
S
BT
10 0 0 10 312.1713 297.087 Tm
0 g
(0)Tj
ET
Q
BT
10 0 0 10 318.173 297.087 Tm
0 g
0.0001 Tc
(.1)Tj
ET
0.25 w
368.123 289.945 m
368.773 290.697 l
S
BT
10 0 0 10 350.9034 282.1749 Tm
(0.5)Tj
ET
409.527 273.734 m
410.093 274.548 l
S
q
316.203 269.46 151.346 122.762 re
W n
BT
10 0 0 10 393.8481 265.8356 Tm
0.6003 Tc
(09)Tj
ET
Q
BT
/F24 1 Tf
10 0 0 10 350.2964 271.9216 Tm
0 0 0 rg
0 Tc
()Tj
/F23 1 Tf
7.125 0 0 7.125 354.6714 270.3596 Tm
(1)Tj
10 0 0 10 320.1914 382.9335 Tm
(c)Tj
/F25 1 Tf
0.4438 0 TD
()Tj
/F24 1 Tf
0.3187 0 TD
()Tj
/F23 1 Tf
7.125 0 0 7.125 332.1914 381.3715 Tm
(1)Tj
/F24 1 Tf
10 0 0 10 336.7534 382.9335 Tm
-0.0002 Tc
()Tj
/F23 1 Tf
7.125 0 0 7.125 347.5664 381.3715 Tm
0 Tc
(2)Tj
/F25 1 Tf
10 0 0 10 352.1294 382.9335 Tm
()Tj
/F23 1 Tf
7.125 0 0 7.125 355.3164 386.8715 Tm
(2)Tj
/F2 1 Tf
11.9552 0 0 11.9552 101.8879 221.3344 Tm
0 g
[(with)-326.5(common)-326.4(v)54.4(alue)-326.4(for)]TJ
/F10 1 Tf
10.1723 0 TD
(n)Tj
/F2 1 Tf
0.5845 0 TD
(,)Tj
/F10 1 Tf
0.5983 0 TD
(p)Tj
/F7 1 Tf
7.9701 0 0 7.9701 243.5168 219.5412 Tm
(1)Tj
/F2 1 Tf
11.9552 0 0 11.9552 248.2491 221.3344 Tm
(\()Tj
/F10 1 Tf
0.3808 0 TD
(r)Tj
/F2 1 Tf
0.4685 0 TD
[(\))-277.7(=)-277.8(Bi\()]TJ
/F10 1 Tf
3.044 0 TD
(r)Tj
/F11 1 Tf
0.6352 0 TD
(|)Tj
/F10 1 Tf
0.4444 0 TD
[(n,)-166.7()]TJ
/F7 1 Tf
7.9701 0 0 7.9701 325.3868 219.5412 Tm
(1)Tj
/F2 1 Tf
11.9552 0 0 11.9552 330.1191 221.3344 Tm
[(\))-326.4(and)]TJ
/F10 1 Tf
2.6111 0 TD
(p)Tj
/F7 1 Tf
7.9701 0 0 7.9701 367.211 219.5412 Tm
(2)Tj
/F2 1 Tf
11.9552 0 0 11.9552 371.9432 221.3344 Tm
(\()Tj
/F10 1 Tf
0.3807 0 TD
(r)Tj
/F2 1 Tf
0.4685 0 TD
0.0001 Tc
[(\))-277.6(=)-277.7(Bi\()]TJ
/F10 1 Tf
3.044 0 TD
0 Tc
(r)Tj
/F11 1 Tf
0.6352 0 TD
(|)Tj
/F10 1 Tf
0.4444 0 TD
[(n,)-166.7()]TJ
/F7 1 Tf
7.9701 0 0 7.9701 449.081 219.5412 Tm
(2)Tj
/F2 1 Tf
11.9552 0 0 11.9552 453.8132 221.3344 Tm
[(\),)-326.4(is)]TJ
/F10 1 Tf
-27.1907 -2.0948 TD
()Tj
/F11 1 Tf
0.4712 0 TD
({)Tj
/F10 1 Tf
0.5 0 TD
(p)Tj
/F7 1 Tf
7.9701 0 0 7.9701 146.2296 194.4971 Tm
(1)Tj
/F10 1 Tf
11.9552 0 0 11.9552 150.9619 196.2903 Tm
0.1667 Tc
(,p)Tj
/F7 1 Tf
7.9701 0 0 7.9701 162.0812 194.4971 Tm
0 Tc
(2)Tj
/F11 1 Tf
11.9552 0 0 11.9552 166.8134 196.2903 Tm
(})Tj
/F2 1 Tf
0.6667 0 TD
(=)Tj
/F10 1 Tf
0.9282 0 TD
()Tj
/F11 1 Tf
0.4712 0 TD
({)Tj
/F10 1 Tf
0.5 0 TD
()Tj
/F7 1 Tf
7.9701 0 0 7.9701 202.947 194.4971 Tm
(1)Tj
/F10 1 Tf
11.9552 0 0 11.9552 207.6792 196.2903 Tm
0.1667 Tc
(,)Tj
/F7 1 Tf
7.9701 0 0 7.9701 218.3781 194.4971 Tm
0 Tc
(2)Tj
/F11 1 Tf
11.9552 0 0 11.9552 225.1029 196.2903 Tm
(|)Tj
/F10 1 Tf
0.4445 0 TD
(n)Tj
/F11 1 Tf
0.5844 0 TD
(})Tj
/F2 1 Tf
0.7778 0 TD
(=)Tj
/F10 1 Tf
1.0393 0 TD
0.1666 Tc
(n)Tj
/F7 1 Tf
7.9701 0 0 7.9701 273.2932 194.4971 Tm
0 Tc
(1)Tj
/F11 1 Tf
11.9552 0 0 11.9552 278.0254 196.2903 Tm
({)Tj
/F10 1 Tf
0.5 0 TD
()Tj
/F7 1 Tf
7.9701 0 0 7.9701 289.4576 194.4971 Tm
(1)Tj
/F10 1 Tf
11.9552 0 0 11.9552 294.1898 196.2903 Tm
0.1667 Tc
(,)Tj
/F7 1 Tf
7.9701 0 0 7.9701 304.8897 194.4971 Tm
0 Tc
(2)Tj
/F11 1 Tf
11.9552 0 0 11.9552 309.6219 196.2903 Tm
(})Tj
/F10 1 Tf
0.5 0 TD
(,)Tj
/F2 1 Tf
12.2061 0 TD
(\(7\))Tj
/F10 1 Tf
-28.1238 -1.3333 TD
()Tj
/F7 1 Tf
7.9701 0 0 7.9701 130.4847 178.5568 Tm
(1)Tj
/F11 1 Tf
11.9552 0 0 11.9552 135.2169 180.3502 Tm
({)Tj
/F10 1 Tf
0.5 0 TD
()Tj
/F7 1 Tf
7.9701 0 0 7.9701 146.6501 178.5568 Tm
(1)Tj
/F10 1 Tf
11.9552 0 0 11.9552 151.3823 180.3502 Tm
0.1666 Tc
(,)Tj
/F7 1 Tf
7.9701 0 0 7.9701 162.0812 178.5568 Tm
0 Tc
(2)Tj
/F11 1 Tf
11.9552 0 0 11.9552 166.8134 180.3502 Tm
(})Tj
/F2 1 Tf
0.6667 0 TD
[(=)-166.7(min[)]TJ
/F10 1 Tf
2.9988 0 TD
()Tj
/F11 1 Tf
0.5637 0 TD
({)Tj
/F10 1 Tf
0.5 0 TD
()Tj
/F7 1 Tf
7.9701 0 0 7.9701 228.806 178.5568 Tm
(1)Tj
/F11 1 Tf
11.9552 0 0 11.9552 235.5308 180.3502 Tm
(|)Tj
/F10 1 Tf
0.4445 0 TD
()Tj
/F7 1 Tf
7.9701 0 0 7.9701 246.2994 178.5568 Tm
(2)Tj
/F11 1 Tf
11.9552 0 0 11.9552 251.0316 180.3502 Tm
(})Tj
/F10 1 Tf
0.5 0 TD
0.3333 Tc
(,)Tj
/F11 1 Tf
1.169 0 TD
0 Tc
({)Tj
/F10 1 Tf
0.5 0 TD
()Tj
/F7 1 Tf
7.9701 0 0 7.9701 282.4179 178.5568 Tm
(2)Tj
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0.3334 Tc
(,p)Tj
/F14 1 Tf
7.6513 0 0 7.9701 464.2292 388.392 Tm
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(x)Tj
/F17 1 Tf
7.9701 0 0 7.9701 471.211 388.392 Tm
(|)Tj
/F14 1 Tf
7.6513 0 0 7.9701 474.9749 388.392 Tm
()Tj
/F11 1 Tf
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(})Tj
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-32.5 -1.2083 TD
[(b)-27.2(e)0(t)27.2(w)27.2(een)-471(the)-471(estimated)-471.1(mo)-27.2(del)-471(and)-471.1(the)-471(true)-471.1(mo)-27.2(del)-471(measures,)-471.2(as)-471(a)-471(function)]TJ
T*
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()Tj
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[(,)-349.7(the)-349.7(loss)-349.7(whic)27.1(h)-349.7(w)27.2(ould)-349.7(b)-27.3(e)-349.7(suered)-349.8(if)-349.7(mo)-27.2(del)]TJ
/F10 1 Tf
18.7758 0 TD
(p)Tj
/F2 1 Tf
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/F12 1 Tf
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(x)Tj
/F11 1 Tf
0.8257 0 TD
(|)Tj
/F2 1 Tf
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()Tj
/F12 1 Tf
-0.1479 -0.2639 TD
()Tj
/F2 1 Tf
0.5937 0 TD
[(\))-349.6(w)27.2(ere)-349.7(used)-349.8(as)-349.7(a)-349.8(pro)27.2(xy)]TJ
-23.2442 -1.2083 TD
[(for)-408.3(mo)-27.1(del)]TJ
/F10 1 Tf
4.5699 0 TD
(p)Tj
/F2 1 Tf
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(x)Tj
/F11 1 Tf
0.8257 0 TD
(|)Tj
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()Tj
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0.5938 0 TD
[(\).)-408.2(Notice)-408.3(that)-408.2(this)-408.3(directly)-408.3(measures)-408.3(ho)27.2(w)-408.2(dieren)27.1(t)-408.2(the)-408.2(t)27.2(w)27.2(o)]TJ
/F9 1 Tf
-7.306 -1.2083 TD
[(mo)50(dels)]TJ
/F2 1 Tf
3.2489 0 TD
[(are,)-398.9(as)-398.9(opp)-27.2(osed)-398.9(to)-398.9(measuring)-398.9(ho)27.1(w)-398.8(dieren)27.1(t)-398.9(their)]TJ
/F9 1 Tf
21.5937 0 TD
[(lab)50(els)]TJ
/F2 1 Tf
2.6488 0 TD
[(are,)-398.9(whic)27.2(h)-398.9(i)0(s)]TJ
-27.4914 -1.2083 TD
[(what)-456(con)27.1(v)27.2(e)0(n)27.2(tional)-456(loss)-455.9(functions�lik)27.1(e)-455.9(the)-456(quadratic)-456(loss�t)27.1(ypically)-456(do.)-456(As)]TJ
T*
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T*
[(ticular)-476.3(parametrization)-476.4(used;)-476.3(indeed,)]TJ
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16.7066 0 TD
()Tj
/F11 1 Tf
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/F2 1 Tf
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()Tj
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-0.1479 -0.2639 TD
()Tj
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0.5937 0 TD
(,)Tj
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()Tj
/F11 1 Tf
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(})Tj
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0.9763 0 TD
[(pro)27.1(vides)-476.3(a)-476.3(natural,)]TJ
/F9 1 Tf
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/F2 1 Tf
-29.1125 -1.2083 TD
[(loss)-360.2(function)-360.2(for)-360.1(estimation,)-360.2(the)]TJ
/F9 1 Tf
14.1108 0 TD
[(intrinsic)-381.1(loss)]TJ
/F2 1 Tf
5.5186 0 TD
[(.)-360.1(The)]TJ
/F9 1 Tf
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[(intrinsic)-381.1(estimate)]TJ
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7.8787 0 TD
[(is)-360.1(that)]TJ
-30.1866 -1.2083 TD
[(v)54.4(alue)]TJ
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()Tj
/F17 1 Tf
7.9701 0 0 7.9701 130.1021 264.5773 Tm
()Tj
/F2 1 Tf
11.9552 0 0 11.9552 139.5736 260.2386 Tm
[(whic)27.1(h)-396.4(minimizes)]TJ
/F10 1 Tf
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()Tj
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()Tj
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[(,)-396.5(the)-396.4(p)-27.3(osterior)-396.5(ex-)]TJ
-25.1143 -1.2083 TD
[(p)-27.2(ected)-407(in)27.2(trinsic)-407(loss,)-407(among)-407(all)]TJ
14.1122 0.2639 TD
()Tj
/F12 1 Tf
-0.1479 -0.2639 TD
()Tj
/F11 1 Tf
1.0087 0 TD
()Tj
/F1 1 Tf
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()Tj
/F2 1 Tf
0.875 0 TD
[(.)-407(Since)]TJ
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()Tj
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()Tj
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/F2 1 Tf
0.9069 0 TD
[(is)-407(in)27.1(v)54.4(arian)27.1(t)-407(under)-407(re-)]TJ
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[(parametrization,)-305(the)-304.8(in)27.2(trinsic)-304.9(estimate)-304.9(of)-304.7(an)27.1(y)-304.8(one-to-one)-304.9(transformation)-304.9(of)]TJ
/F12 1 Tf
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()Tj
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()Tj
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()Tj
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0.7125 0 TD
(\()Tj
/F12 1 Tf
0.3808 0 TD
()Tj
/F2 1 Tf
0.5937 0 TD
[(\),)-326.3(is)-326.5(simply)]TJ
/F12 1 Tf
5.097 0 TD
()Tj
/F17 1 Tf
7.9701 0 0 7.9701 205.8122 221.2398 Tm
()Tj
/F2 1 Tf
11.9552 0 0 11.9552 213.866 216.9011 Tm
(=)Tj
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1.0393 0 TD
()Tj
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(\()Tj
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()Tj
/F17 1 Tf
7.9701 0 0 7.9701 246.4598 221.2398 Tm
()Tj
/F2 1 Tf
11.9552 0 0 11.9552 251.192 216.9011 Tm
[(\))-326.4(\(Bernardo)-326.5(and)-326.4(Ju�)]TJ
8.3225 0 TD
[(arez,)-326.4(2003\).)]TJ
-20.8112 -1.6939 TD
[(The)-337.8(p)-27.3(osterior)-337.8(exp)-27.3(ected)-337.8(loss)-337.8(function)]TJ
/F10 1 Tf
15.9575 0 TD
(d)Tj
/F2 1 Tf
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(\()Tj
0.5288 0.2639 TD
()Tj
/F12 1 Tf
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()Tj
/F11 1 Tf
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(|)Tj
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(x)Tj
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0.659 0 TD
[(\))-337.8(m)0(a)27.2(y)-337.8(further)-337.9(b)-27.2(e)-337.8(used)-337.8(to)-337.7(de�ne)]TJ
-19.5443 -1.2083 TD
[(p)-27.2(osterior)]TJ
/F9 1 Tf
4.2336 0 TD
(intrinsic)Tj
/F10 1 Tf
4.0489 0 TD
(p)Tj
/F9 1 Tf
0.4914 0 TD
[(-cr)50(e)50(dible)-461.4(r)50(e)50(gions)]TJ
/F10 1 Tf
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(R)Tj
/F16 1 Tf
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(p)Tj
/F2 1 Tf
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(=)Tj
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({)Tj
/F2 1 Tf
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()Tj
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-0.1479 -0.2639 TD
()Tj
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(;)Tj
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(d)Tj
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()Tj
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()Tj
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(|)Tj
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(x)Tj
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(\))Tj
/F10 1 Tf
0.8648 0 TD
0.4839 Tc
(