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Kazem Nasserinejad, Joost van Rosmalen, Wim de Kort, Emmanuel Lesaffre
Comparison of Criteria for Choosing the Number of Classes in Bayesian Finite Mixture Models
www.plosone.org
www.plosone.org
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(where)Tj
/F6 1 Tf
2.6476 0 Td
[()]TJ
/F5 1 Tf
(\()Tj
/F6 1 Tf
[()]TJ
/F5 1 Tf
(|)Tj
/F12 1 Tf
()Tj
/F5 1 Tf
(,)Tj
/F6 1 Tf
2.2847 0 Td
[()]TJ
/F5 1 Tf
(,)Tj
/F17 1 Tf
0.9071 0 Td
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(\))Tj
1.0148 0 Td
(is)Tj
0.8504 0 Td
(the)Tj
1.4683 0 Td
(density)Tj
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(observed)Tj
3.7984 0 Td
(data,)Tj
/F6 1 Tf
2.1373 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 409.6062 543.4015 cm
BT
/F6 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 411.5338 545.0456 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F6 1 Tf
[()]TJ
/F5 1 Tf
(|)Tj
/F6 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 426.5007 543.4015 cm
BT
/F6 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 428.4283 545.0456 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
/F17 1 Tf
0.4422 0 Td
(\r)Tj
/F5 1 Tf
(\))Tj
1.0147 0 Td
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0.8504 0 Td
(the)Tj
1.4684 0 Td
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1.0148 0 Td
(the)Tj
1.4683 0 Td
(observed)Tj
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(data)Tj
1.9106 0 Td
(in)Tj
1.0374 0 Td
(latent)Tj
2.4718 0 Td
(class)Tj
/F6 1 Tf
2.041 0 Td
[()]TJ
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(,)Tj
/F6 1 Tf
0.7029 0 Td
[()]TJ
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0.8618 0 Td
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2.6985 0 Td
()Tj
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4.3143 0 Td
(the)Tj
1.474 0 Td
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(which)Tj
2.6532 0 Td
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1.4457 0 Td
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5.4935 0 Td
(and)Tj
1.7291 0 Td
(sum)Tj
1.9276 0 Td
(to)Tj
1.0261 0 Td
(1.)Tj
/F6 1 Tf
0.9184 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 408.7559 517.3795 cm
BT
/F6 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 412.8944 519.0236 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(is)Tj
0.8447 0 Td
(a)Tj
0.6576 0 Td
(vector)Tj
2.6986 0 Td
(of)Tj
1.0148 0 Td
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4.6714 0 Td
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1.389 0 Td
(the)Tj
1.4683 0 Td
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1.0148 0 Td
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1.4683 0 Td
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1.9106 0 Td
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2.0466 0 Td
[()]TJ
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(,)Tj
0.7029 0 Td
(and)Tj
/F17 1 Tf
1.7292 0 Td
(\r)Tj
/F5 1 Tf
0.6746 0 Td
(is)Tj
0.8447 0 Td
(a)Tj
0.6577 0 Td
(vector)Tj
2.6985 0 Td
(of)Tj
1.0148 0 Td
(parameters)Tj
4.6714 0 Td
(common)Tj
3.8437 0 Td
(to)Tj
1.0262 0 Td
(all)Tj
1.1508 0 Td
(classes.)Tj
3.0501 0 Td
(The)Tj
1.7858 0 Td
(observed)Tj
-33.1707 -1.2983 Td
(data)Tj
/F6 1 Tf
1.9105 0 Td
[()]TJ
/F5 1 Tf
0.6577 0 Td
(can)Tj
1.627 0 Td
(be)Tj
1.1452 0 Td
(either)Tj
2.5342 0 Td
(univariate)Tj
4.2463 0 Td
(or)Tj
1.0998 0 Td
(multivariate,)Tj
5.2837 0 Td
(and)Tj
/F6 1 Tf
1.7348 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 405.0708 491.3574 cm
BT
/F6 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 406.9417 493.0582 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F6 1 Tf
[()]TJ
/F5 1 Tf
(|)Tj
/F6 1 Tf
[()]TJ
/F5 1 Tf
(,)Tj
/F17 1 Tf
1.9445 0 Td
(\r)Tj
/F5 1 Tf
(\))Tj
1.0148 0 Td
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1.9275 0 Td
(correspond)Tj
4.7792 0 Td
(to)Tj
1.0262 0 Td
(e.g.)Tj
1.559 0 Td
(a)Tj
0.652 0 Td
(simple)Tj
-33.5959 -1.3039 Td
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3.8664 0 Td
(model)Tj
2.7439 0 Td
(or)Tj
1.0999 0 Td
(a)Tj
0.6519 0 Td
(complex)Tj
3.6227 0 Td
(hierarchical)Tj
4.9379 0 Td
(model.)Tj
-15.7265 -1.2982 Td
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2.3584 0 Td
(we)Tj
1.3323 0 Td
(use)Tj
1.5307 0 Td
(a)Tj
0.6519 0 Td
(Bayesian)Tj
3.7247 0 Td
(setting,)Tj
3.1068 0 Td
(priors)Tj
2.6135 0 Td
(need)Tj
2.143 0 Td
(to)Tj
1.0261 0 Td
(be)Tj
1.1508 0 Td
(chosen)Tj
3.0104 0 Td
(for)Tj
/F17 1 Tf
1.3889 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 457.285 465.3921 cm
BT
/F6 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 459.2125 467.0362 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
/F6 1 Tf
0.4478 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 468.3401 465.3921 cm
BT
/F6 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 472.422 467.0362 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F6 1 Tf
[()]TJ
/F5 1 Tf
0.8163 0 Td
(=)Tj
0.7994 0 Td
(1,)Tj
/F16 1 Tf
0 Tc
0.9241 0 Td
(.)Tj
0.4308 0 Td
(.)Tj
0.4366 0 Td
(.)Tj
/F5 1 Tf
-0.004 Tc
(,)Tj
/F6 1 Tf
0.7143 0 Td
[()]TJ
/F5 1 Tf
(\),)Tj
1.4287 0 Td
(and)Tj
/F17 1 Tf
1.7291 0 Td
(\r)Tj
/F5 1 Tf
(.)Tj
0.9014 0 Td
(A)Tj
-35.4214 -1.2982 Td
(challenging)Tj
4.8132 0 Td
(issue)Tj
2.16 0 Td
(that)Tj
1.7801 0 Td
(arises)Tj
2.4378 0 Td
(in)Tj
1.0375 0 Td
(Bayesian)Tj
3.719 0 Td
(mixture)Tj
3.3959 0 Td
(models)Tj
3.1011 0 Td
(is)Tj
0.8503 0 Td
(the)Tj
1.4684 0 Td
(nonidentifiability)Tj
7.1885 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4683 0 Td
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3.0557 0 Td
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1.7802 0 Td
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3.6113 0 Td
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1.1848 0 Td
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1.4684 0 Td
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4.3936 0 Td
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1.0148 0 Td
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3.8437 0 Td
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4.9662 0 Td
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2.0012 0 Td
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3.0388 0 Td
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5.5899 0 Td
(of)Tj
1.0148 0 Td
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3.3618 0 Td
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2.6135 0 Td
(and)Tj
1.7291 0 Td
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4.2405 0 Td
([)Tj
0.83 0.64 0.02 0 k
(14)Tj
0 g
(].)Tj
2.075 0 Td
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1.9842 0 Td
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2.2167 0 Td
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1.0261 0 Td
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-34.9735 -1.2983 Td
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2.5171 0 Td
(label)Tj
2.0806 0 Td
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4.0592 0 Td
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1.0375 0 Td
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1.4683 0 Td
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3.3336 0 Td
(output,)Tj
3.1237 0 Td
(and)Tj
1.7291 0 Td
(the)Tj
1.4684 0 Td
(posterior)Tj
3.8437 0 Td
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5.329 0 Td
(of)Tj
1.0148 0 Td
(class-specific)Tj
-31.005 -1.2982 Td
(parameters)Tj
/F6 1 Tf
4.6714 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 251.3763 400.3653 cm
BT
/F6 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 255.5149 402.0661 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(will)Tj
1.661 0 Td
(be)Tj
1.1509 0 Td
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3.6567 0 Td
(and)Tj
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1.9389 0 Td
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2.9196 0 Td
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1.389 0 Td
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3.9345 0 Td
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0.83 0.64 0.02 0 k
(17)Tj
0 g
(].)Tj
ET
Q
q
1 j
1 J
0 w
11.9999 0 0 11.9999 200.0125 372.9826 cm
BT
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1 TL
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2.8015 0 Td
(for)Tj
1.3749 0 Td
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ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 355.9748 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
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0.8447 0 Td
(no)Tj
1.2756 0 Td
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3.4242 0 Td
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1.3833 0 Td
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1.4684 0 Td
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4.6771 0 Td
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3.8948 0 Td
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2.4775 0 Td
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1.0262 0 Td
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2.5228 0 Td
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2.2563 0 Td
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5.3291 0 Td
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2.7213 0 Td
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1.2756 0 Td
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1.4683 0 Td
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3.8438 0 Td
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4.9662 0 Td
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1.0148 0 Td
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1.4684 0 Td
(model)Tj
2.7496 0 Td
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0.839 0 Td
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3.8438 0 Td
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1.7744 0 Td
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2.1997 0 Td
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4.5354 0 Td
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2.0523 0 Td
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2.2507 0 Td
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1.3776 0 Td
(the)Tj
1.4627 0 Td
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2.0352 0 Td
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/F17 1 Tf
5.2157 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 480.8125 328.3086 cm
BT
/F6 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 482.7401 330.0094 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
0.4365 0 Td
(is)Tj
0.8447 0 Td
(a)Tj
0.6463 0 Td
(symmetric)Tj
4.4504 0 Td
(Dirich-)Tj
-34.6504 -1.2982 Td
(let)Tj
1.1848 0 Td
(distribution,)Tj
5.1931 0 Td
(i.e.)Tj
/F12 1 Tf
1.3663 0 Td
()Tj
/F5 1 Tf
(|K)Tj
/F18 1 Tf
1.6837 0 Td
(*)Tj
/F5 1 Tf
1.2189 0 Td
(Dirichlet\()Tj
/F17 1 Tf
()Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 350.9858 315.3259 cm
BT
/F5 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 354.5574 317.0267 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
/F16 1 Tf
0 Tc
0.4422 0 Td
(.)Tj
0.4365 0 Td
(.)Tj
0.4308 0 Td
(.)Tj
/F5 1 Tf
-0.004 Tc
(,)Tj
/F17 1 Tf
0.72 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 380.296 315.3259 cm
BT
/F6 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 385.1149 317.0267 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\),)Tj
0.788 0 Td
(and)Tj
/F17 1 Tf
1.7291 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 415.7858 315.3259 cm
BT
/F6 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 421.4551 317.0267 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(=)Tj
/F17 1 Tf
0.7993 0 Td
()Tj
/F5 1 Tf
0.771 0 Td
(for)Tj
/F6 1 Tf
1.3833 0 Td
[()]TJ
/F5 1 Tf
0.686 0 Td
(=)Tj
0.7994 0 Td
(1,)Tj
/F16 1 Tf
0 Tc
0.9241 0 Td
(.)Tj
0.4308 0 Td
(.)Tj
0.4366 0 Td
(.)Tj
/F5 1 Tf
-0.004 Tc
(,)Tj
/F6 1 Tf
0.7143 0 Td
[()]TJ
/F5 1 Tf
(.)Tj
1.0885 0 Td
(Smaller)Tj
3.2371 0 Td
(values)Tj
2.6646 0 Td
(of)Tj
/F17 1 Tf
-36.0791 -1.3039 Td
()Tj
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0.7654 0 Td
(correspond)Tj
4.7792 0 Td
(with)Tj
1.9955 0 Td
(a)Tj
0.6577 0 Td
(less)Tj
1.61 0 Td
(informative)Tj
4.8983 0 Td
(prior.)Tj
2.4831 0 Td
(A)Tj
0.9014 0 Td
(flat)Tj
1.4854 0 Td
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2.2563 0 Td
(distribution)Tj
4.9662 0 Td
(is)Tj
0.8504 0 Td
(obtained)Tj
3.7304 0 Td
(with)Tj
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2.0012 0 Td
()Tj
/F5 1 Tf
0.7654 0 Td
(=)Tj
0.7993 0 Td
(1,)Tj
-34.9452 -1.2982 Td
(whereas)Tj
3.4413 0 Td
(setting)Tj
/F17 1 Tf
2.8856 0 Td
()Tj
/F5 1 Tf
0.7654 0 Td
(=)Tj
0.7993 0 Td
(0)Tj
0.6974 0 Td
(leads)Tj
2.211 0 Td
(to)Tj
1.0261 0 Td
(an)Tj
1.2019 0 Td
(improper)Tj
4.0195 0 Td
(Dirichlet)Tj
3.7757 0 Td
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5.1986 0 Td
(and)Tj
1.7291 0 Td
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1.7689 0 Td
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1.0204 0 Td
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1.2076 0 Td
(improper)Tj
4.0138 0 Td
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-35.7616 -1.2983 Td
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2.4548 0 Td
(result.)Tj
-1.2585 -1.3039 Td
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1.7858 0 Td
(choice)Tj
2.7892 0 Td
(of)Tj
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1.0148 0 Td
()Tj
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0.7711 0 Td
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0.8503 0 Td
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4.5071 0 Td
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1.0148 0 Td
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1.1452 0 Td
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1.6214 0 Td
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3.4751 0 Td
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(the)Tj
1.4683 0 Td
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3.8437 0 Td
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3.0331 0 Td
(Although)Tj
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(large)Tj
2.16 0 Td
(values)Tj
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(of)Tj
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1.0148 0 Td
()Tj
/F5 1 Tf
0.771 0 Td
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1.8482 0 Td
(to)Tj
1.0261 0 Td
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4.8982 0 Td
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2.2564 0 Td
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5.5558 0 Td
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2.33 0 Td
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4.7112 0 Td
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(use)Tj
1.5307 0 Td
(values)Tj
2.6646 0 Td
(larger)Tj
2.5341 0 Td
(than)Tj
2.0296 0 Td
(1)Tj
0.6974 0 Td
(\(e.g.,)Tj
/F17 1 Tf
2.1203 0 Td
()Tj
/F5 1 Tf
0.771 0 Td
(=)Tj
0.7993 0 Td
(4)Tj
0.6974 0 Td
(or)Tj
/F17 1 Tf
1.0941 0 Td
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