Abstract
We assume that a set of events \(x_1, \dots ,x_N\) is given. Neither the mean \(\xi \) nor the standard deviation \(\sigma \) of the data is known. They are to be inferred. It is assumed that the Gaussian model
of Eq. (4.1) applies for the distribution of every \(x_k\).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
J. Neyman, E.L. Scott, Consistent estimates based on partially consistent observations. Econometrica 16, 1–32 (1948)
S.L. Stephenson, J.D. Bowman, B.E. Crawford, P.P.J. Delheij, C.M. Frankle, M. Iinuma, J.N. Knudson, L.Y. Lowie, A. Masaike, Y. Matsuda, G.E. Mitchell, S.I. Pentilä, H. Postma, N.R. Roberson, S.J. Seestrom, E.I. Sharapov, Y.-F. Yen, V.W. Yuan, Parity nonconservation in neutron resonances in \({\rm ^{232}{T}h}\). Phys. Rev. C 58, 1236–1246 (1998)
G.E. Mitchell, J.D. Bowman, S.I. Penttilä, E.I. Sharapov, Parity violation in compound nuclei: experimental methods and recent results. Phys. Rep. — Rev. Sec. Phys. Lett. 354:157–241 (2001) (The original publication on parity violation in \(^{115}{\rm In}\) is [12])
G.E. Mitchell, J.D. Bowman, H.A. Weidenmüller, Parity violation in the compound nucleus. Rev. Mod. Phys. 71, 445–457 (1999)
J. Kiefer, J. Wolfowitz, Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters. Ann. Math. Stat. 27, 887–906 (1956)
A.P. Dawid, N. Stone, J.V. Zidek, Marginalisation paradoxes in Bayesian and structural inference. J. R. Stat. Soc. B 35, 189–233 (1973)
J.M. Bernardo, Reference posterior distributions for Bayesian inference. J. R. Stat. Soc. B 41, 113–147 (1979)
E.T. Jaynes, Marginalization and prior probabilities, in Zellner [13], pp. 43–87
A. Nicolaou, Bayesian intervals with good frequentist behaviour in the presence of nuisance parameters. J. R. Stat. Soc. B 55, 377–390 (1993)
R. Mukerjee, D.K. Dey, Frequentist validity of posteriori quantiles in the presence of nuisance parameter: higher order asymptotic. Biometrika 80(3), 499–505 (1993)
T. Lancaster, The incidental parameter problem since 1948. J. Econ. 95, 391–413 (2000)
S.L. Stephenson, J.D. Bowman, F. Corvi, B.E. Crawford, P.P.J. Delheij,C.M. Frankle, M. Iinuma, J.N. Knudson, L.Y. Lowie, A. Masaike,Y. Masuda, Y. Matsuda, G.E. Mitchell, S.I. Pentilä, H. Postma, N.R. Roberson, S.J. Seestrom, E.I. Sharapov, H.M. Shimizu, Y.-F. Yen, V.W. Yuan, L. Zanini, Parity violation in neutron resonances in \({\rm ^{115}{in}}\). Phys. Rev. C 61, 045501/1–11 (2000)
A. Zellner (ed.), Bayesian Analysis in Econometrics and Statistics: Essays in Honour of H. Jeffreys. Studies in Bayesian Econometrics, vol. 1 (North Holland, Amsterdam, 1980)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Harney, H.L. (2016). Inferring the Mean or the Standard Deviation. In: Bayesian Inference. Springer, Cham. https://doi.org/10.1007/978-3-319-41644-1_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-41644-1_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-41642-7
Online ISBN: 978-3-319-41644-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)