Table 4 Posterior values of each parameter \(\vartheta \in \{\varepsilon ,\sigma ,p,{\sigma }_{n}\}\) of LJ 6-\(p\): MPV \(b(\vartheta )\) and 5–95% quantiles \(q(\vartheta )\). The values are rounded from 16-digit precision.

From: Data driven inference for the repulsive exponent of the Lennard-Jones potential in molecular dynamics simulations

  

\({\boldsymbol{b}}({\boldsymbol{\varepsilon }})\)

\({\boldsymbol{q}}({\boldsymbol{\varepsilon }})\)

\({\boldsymbol{b}}({\boldsymbol{\sigma }})\)

\({\boldsymbol{q}}({\boldsymbol{\sigma }})\)

\({\boldsymbol{b}}({\boldsymbol{p}})\)

\({\boldsymbol{q}}({\boldsymbol{p}})\)

\({\boldsymbol{b}}({{\boldsymbol{\sigma }}}_{n})\)

\({\boldsymbol{q}}({{\boldsymbol{\sigma }}}_{{\boldsymbol{n}}})\)

\({B}_{p,R}\)

\({L}_{1}\)

2.286

[2.193, 4.794]

3.431

[3.422, 3.464]

6.644

[6.292, 6.647]

0.157

[0.185, 0.302]

\({L}_{2}\)

3.134

[0.712, 4.416]

3.369

[3.319, 3.428]

6.370

[6.293, 8.313]

0.222

[0.215, 0.518]

\({L}_{3}\)

1.250

[0.914, 2.700]

3.322

[3.301, 3.395]

6.715

[6.332, 7.068]

0.098

[0.080, 0.159]

\({L}_{4}\)

0.337

[0.322, 1.060]

3.325

[3.325, 3.398]

9.501

[6.900, 9.842]

0.057

[0.066, 0.153]

\({L}_{5}\)

5.928

[0.794, 7.318]

3.328

[3.190, 3.395]

6.116

[6.102, 7.126]

0.164

[0.168, 0.326]

\(V\)

1.065

[0.625, 3.611]

3.117

[3.037, 3.122]

6.604

[6.151, 6.923]

0.100

[0.099, 0.190]

\(H{B}_{p,R}\)

\({L}_{1}\)

4.561

[3.890, 4.626]

3.454

[3.408, 3.471]

6.302

[6.296, 6.366]

0.422

[0.450, 0.602]

\({L}_{2}\)

2.081

[1.333, 3.515]

3.387

[3.335, 3.424]

6.565

[6.340, 7.051]

0.211

[0.178, 0.351]

\({L}_{3}\)

2.506

[0.941, 4.325]

3.345

[3.295, 3.382]

6.324

[6.198, 6.996]

0.093

[0.081, 0.186]

\({L}_{4}\)

2.588

[0.892, 3.676]

3.403

[3.358, 3.432]

6.339

[6.226, 7.063]

0.082

[0.075, 0.146]

\({L}_{5}\)

2.055

[0.992, 4.281]

3.252

[3.194, 3.382]

6.364

[6.169, 6.837]

0.183

[0.159, 0.316]

\(V\)

1.371

[0.582, 1.896]

3.129

[3.082, 3.194]

6.422

[6.277, 7.025]

0.111

[0.103, 0.233]

\({B}_{p,Q}\)

 

0.252

[0.239, 0.261]

3.370

[3.367, 3.375]

12.703

[12.333, 13.309]

0.006

[0.006, 0.010]