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Table 4 CPs (in \(\%\)), \(\hbox {W}_{\mathrm{mean}}\)’s and \(\hbox {W}_{\mathrm{median}}\)’s of BN, BU, PF and Fieller’s methods

From: BEXCIS: Bayesian methods for estimating the degree of the skewness of X chromosome inactivation

Trait

n

MAF

\({\rho }\)

CP

\(\hbox {W}_{\mathrm{mean}}\)

\(\hbox {W}_{\mathrm{median}}\)

BN

BU

PF

Fieller

BN

BU

PF

Fieller

BN

BU

PF

Fieller

Qualitative

500

0.3

0

93.8

95.2

95.2

95.0

1.4390

1.4643

1.5113

1.5358

1.4936

1.5353

1.5846

1.6362

− 0.05

95.6

95.8

94.2

93.6

1.4303

1.4521

1.5007

1.5045

1.4857

1.5273

1.5724

1.5897

0.05

94.2

95.0

95.4

95.4

1.4116

1.4336

1.4919

1.4895

1.4634

1.5004

1.5497

1.5643

0.1

0

94.0

96.2

89.0

98.6

1.6371

1.6737

1.5841

1.8346

1.6772

1.7290

1.9183

2.0000

− 0.05

93.2

96.2

84.6

98.8

1.6705

1.7130

1.5560

1.8369

1.6951

1.7445

1.9838

2.0000

0.05

92.4

93.4

86.2

95.6

1.6060

1.6382

1.5602

1.7794

1.6638

1.7109

1.8887

2.0000

2000

0.3

0

95.2

95.6

95.6

95.8

0.9647

0.9714

1.0063

1.0133

0.9654

0.9696

0.9956

1.0017

− 0.05

94.6

95.0

95.6

95.4

0.9527

0.9571

0.9879

0.9958

0.9508

0.9492

0.9829

0.9854

0.05

95.8

95.0

95.2

94.8

0.9451

0.9486

0.9808

0.9864

0.9599

0.9619

1.0080

1.0105

0.1

0

93.8

95.0

94.8

95.4

1.3822

1.4041

1.4935

1.5069

1.3978

1.4251

1.5794

1.5657

− 0.05

94.4

95.2

90.8

96.6

1.4304

1.4551

1.4554

1.5630

1.4556

1.4982

1.6570

1.6652

0.05

95.8

96.4

96.6

97.2

1.3416

1.3602

1.4218

1.4338

1.3451

1.3737

1.4454

1.4678

Quantitative

500

0.3

0

96.0

96.4

96.2

95.8

1.1254

1.1333

1.1642

1.1741

1.1202

1.1270

1.1655

1.1715

− 0.05

95.2

95.0

96.6

95.4

1.1289

1.1343

1.1528

1.1661

1.1248

1.1248

1.1388

1.1290

0.05

95.6

95.6

95.8

95.4

1.1014

1.1061

1.1334

1.1455

1.0910

1.0907

1.1143

1.1135

0.1

0

93.2

94.8

85.6

87.6

1.4866

1.5134

1.4382

1.4685

1.5045

1.5415

1.6191

1.5739

− 0.05

94.4

95.6

81.2

88.6

1.5206

1.5505

1.3497

1.4928

1.5501

1.5844

1.5969

1.6238

0.05

94.2

95.4

90.2

92.8

1.4616

1.4865

1.4489

1.4995

1.4926

1.5261

1.5868

1.6013

2000

0.3

0

94.8

95.4

93.6

93.6

0.6563

0.6592

0.6694

0.6704

0.6684

0.6673

0.6792

0.6803

− 0.05

94.6

95.8

96.2

96.2

0.6605

0.6632

0.6747

0.6760

0.6798

0.6793

0.6855

0.6877

0.05

94.8

94.8

94.2

94.2

0.6356

0.6374

0.6508

0.6514

0.6464

0.6493

0.6613

0.6609

0.1

0

96.8

96.6

95.8

93.4

1.1567

1.1687

1.2006

1.2012

1.1513

1.1698

1.2144

1.1945

− 0.05

93.6

95.4

91.8

90.0

1.2586

1.2726

1.2996

1.2817

1.2726

1.2979

1.3801

1.3191

0.05

93.8

95.4

95.0

93.6

1.1202

1.1319

1.1419

1.1616

1.1257

1.1353

1.1558

1.1859

  1. Coverage probability (CP, in \(\%\)) and the mean and median of the widths of the highest posterior density intervals or confidence intervals (respectively denoted as \(\hbox {W}_{\mathrm{mean}}\) and \(\hbox {W}_{\mathrm{median}}\)) of Bayesian method with normal prior (BN), Bayesian method with uniform prior (BU), penalized Fieller’s (PF) and Fieller’s methods among 500 replicates are given under qualitative trait and quantitative trait when \((\sigma _{0}^{2},\ \sigma _{1}^{2},\ \sigma _{2}^{2})=(1,\ 1.2,\ 1)\). The empirical CP should be between \(93.05\%\) and \(96.95\%\) (\(0.95 \pm 2 \times \sqrt{\frac{0.95\times 0.05}{500}}\)) with \(95\%\) probability
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BMC Bioinformatics

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