561
Views
10
CrossRef citations to date
0
Altmetric
Applications and Case Studies

A New Bayesian Test to Test for the Intractability-Countering Hypothesis

ORCID Icon
Pages 561-577 | Received 01 Dec 2015, Accepted 01 Aug 2016, Published online: 13 Jul 2017

References

  • Aitkin, M. (1991), “Posterior Bayes Factors,” Journal of the Royal Statistical Society , Series B, 53, 111–142.
  • Barbieri, M. , and Berger, J. (2004), “Optimal Predictive Model Selection,” The Annals of Statistics , 32, 870–897.
  • Bell, E. F. , and de Jong, R. S. (2001), “Stellar Mass-to-Light Ratios and the Tully-Fisher Relation,” AstrophysicalJournal , 550, 212--229.
  • Berger, J. O. , and Pericchi, L. R. (2001), “Objective Bayesian Methods for Model Selection: Introduction and Comparison,” in Model Selection , Lecture Notes–Monograph Series (Vol. 38), ed. P. Lahiri, Beachwood, OH: Institute of Mathematical Statistics, pp. 135–207.
  • ——— (1996a), “The Intrinsic Bayes Factor for Model Selection and Prediction,” Journal of the American Statistical Association , 57, 109–122.
  • ——— (1996b), “The Intrinsic Bayes Factor for Linear Models,” in Bayesian Statistics (Vol. 5), eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Oxford, UK: Oxford University Press, pp. 25–44.
  • ——— (2004), “Training Samples in Objective Bayesian Model Selection,” The Annals of Statistics , 32, 841–869.
  • Bergond, G. , Zepf, S. E. , Romanowsky, A. J. , Sharples, R. M. , and Rhode, K. L. (2006), “Wide-Field Kinematics of Globular Clusters in the Leo I Group,” Astronomy & Astrophysics , 448, 155–164.
  • Casella, G. , Girón, F. J. , Martínez, M. L. , and Moreno, E. (2009), “Consistency of Bayesian Procedures for Variable Selection,” Annals of Statistics , 37, 3, 1207–1228.
  • Chakrabarty, D. , and Raychaudhury, S. (2008), “The Distribution of Dark Matter in the Halo of the Early-Type Galaxy NGC 4636,” Astronomical Journal , 135, 2350–2357.
  • Chib, S. , and Jeliazkov, I. (2001), “Marginal Likelihood From the Metropolis-Hastings Output,” Journal of the American Statistical Association , 96, 453, 270–281.
  • Chipman, H. , George, E. , and McCulloch, R. E. (2001), “The Practical Implementation of Bayesian Model Selection” (with discussion), in Model Selection, IMS Lecture Series—Monograph Series (Vol. 38), ed. P. Lahiri, Beachwood, OH: Institute of Mathematical Statistics, pp. 67–134.
  • Coccato, L. , Gerhard, Arnaboldi , M., Das, P., Douglas, N. G., Kuijken, K., Merrifield, M. R., Napolitano, N. R., Noordermeer, E., Romanowsky, A. J., Capaccioli, M., Cortesi, A., de Lorenzi, F., and Freeman, K. C. (2009), “Kinematic Properties of Early-Type Galaxy Haloes Using Planetary Nebulae,” Monthly Notices of theRoyal Astronomical Society , 394, 1249--1283.
  • Côté, P. , McLaughlin, D. E. , Hanes, D. A. , Bridges, T. J. , Geislerand D. Merritt, D. , Hesser, J. E. , Harris, G. L. H. , and Lee, M. G. (2001), “Dynamics of the Globular Cluster System Associated With M87 (NGC 4486). II. Analysis,” Astrophysical Journal , 559, 828–850.
  • Dalal, S. R. , Fowlkes, E. B. , and Hoadley, B. (1989), “Risk Analysis of the Space Shuttle: Pre-Challenger Prediction of Failure,” Journal of the American Statistical Association , 84, 945–957.
  • de Blok, W. J. G. , Bosma, A. , and McGaugh, S. (2003), “Simulating Observations of Dark Matter Dominated Galaxies: Towards the Optimal Halo Profile,” Monthly Notices of the Royal Astronomical Society , 340, 657–678.
  • Dekel, A. , Stoehr, F. , Mamon, G. A. , Cox, T. J. , Novak, G. S. , and Primack, J. R. (2005), “Lost and Found Dark Matter in Elliptical Galaxies,” Nature , 437, 707–710.
  • Douglas, N. G. , Napolitano, N. R. , Romanowsky, A. J. , Coccato, L. , Kuijken, K. , Merrifield, M. R. , Arnaboldi, M. , Gerhard, O. , Freeman, K. C. , Merrett, H. , Noordermeer, E. , and Capaccioli, M. (2007), “The PN.S Elliptical Galaxy Survey: Data Reduction, Planetary Nebula Catalog, and Basic Dynamics for NGC 3379,” Astrophysical Journal , 664, 257–276.
  • Fouskakis, D. , Ntzoufrasy, I. , and Draper, D. (2015), “Power-Expected-Posterior Priors for Variable Selection in Gaussian Linear Models,” Bayesian Analysis , 10, 75–107.
  • Gallazzi, A. , and Bell, E. F. (2009), “Stellar Mass-to-Light Ratios from Galaxy Spectra: How Accurate Can They Be?” Astrophysical Journal Supplement , 185, 253–272.
  • Genzel, R. , Schödel, R. , Ott, T. , Eisenhauer, F. , Hofmann, R. , Lehnert, M. , Eckart, A. , Alexander, T. , Sternberg, A. , Lenzen, R. , Clénet, Y. , Lacombe, F. , Rouan, D. , Renzini, A. , and Tacconi-Garman, L. E. (2003), “The Stellar Cusp Around the Supermassive Black Hole in the Galactic Center,” Astrophysical Journal , 594, 812–832.
  • Ghosh, J. K. , and Samanta, T. (2001), “Model Selection—A Overview,” Current Statistics , 80, 1135–1144.
  • Han, C. , and Carlin, B. P. (2000), “MCMC Methods for Computing Bayes Factors: A Comparative Review,” Journal of the American Statistical Association , 96, 1122–1132.
  • Hayashi, E. , Navarro, J. F. , and Springel, V. (2007), “The Shape of the Gravitational Potential in Cold Dark Matter Haloes,” Monthly Notices of the Royal Astronomical Society , 377, 50–62.
  • Kalinova, V. (2014), “Mass Distributions of Galaxies from SAURON and CALIFA Stellar Kinematic Maps,” Doctoral thesis, Max-Planck-Institut fur Astronomie.
  • Kass, R. E. , and Raftery, A. E. (1995), “Bayes Factors,” Journal of the American Statistical Association , 90, 773–795.
  • Leone, F. , Nottingham, R. B. , and Nelson, L. S. (1961), “The Folded Normal Distribution,” Technometrics , 3, 543--550.
  • Link, W. A. , and Barker, R. J. (2006), “Model Weights and the Foundations of Multimodal Inference,” Ecology , 87, 2626–2635.
  • Liu, I.-S. (2002), Continuum Mechanics , New York: Springer-Verlag.
  • Madruga, M. , Pereira, C. , and Stern, J. (2003), “Bayesian Evidence Test for Precise Hypotheses,” Journal of Statistical Planning and Inference , 117, 185–198.
  • Neal, R. M. (1998), “Regression and Classification Using Gaussian Process Priors” (with discussion), in Bayesian Statistics (Vol. 6), ed. J. M. Bernardo, Oxford, UK: Oxford University Press, pp. 475–501.
  • O’Hagan, A. (1995), “Fractional Bayes Factors for Model Comparisons,” Journal of Royal Statistical Society , Series B, 57, 99–138.
  • Pereira, C. , Stern, J. M. , and Wechsler, S. (2008), “Can a Significance Test be Genuinely Bayesian?” Bayesian Analysis , 3, 79–100.
  • Pierce, M. , Beasley, M. A., Forbes, D. A., Bridges, T., Gebhardt, K., Faifer, F. R., Forte, J. C., Zepf, S. E., Sharples, R., Hanes, D. A., and Proctor, R. (2006), “Gemini/GMOS Spectra of Globular Clusters in the Leo Group Elliptical NGC 3379,” Monthly Notices of the Royal Astronomical Society , 366, 1253--1264.
  • Robert, C. (2001), The Bayesian Choice , New York: Springer.
  • Robert, C. P. , and Casella, G. (2004), Monte Carlo Statistical Methods , New York: Springer-Verlag.
  • Roberts, M. S. , and Whitehurst, R. N. (1975), “The Rotation Curve and Geometry of M31 at Large Galactocentric Distances,” Astrophysical Journal , 201, 327–346.
  • Romanowsky, A. J. , Douglas, N. G. , Arnaboldi, M. , Kuijken, K. , Merrifield, M. R. , Napolitano, N. R. , Capaccioli, M. , and Freeman, K. C. (2003), “A Dearth of Dark Matter in Ordinary Elliptical Galaxies,” Science , 301, 1696–1698.
  • Salucci, P. , and Burkert, A. (2000), “Dark Matter Scaling Relations,” Astrophysical Journal Letters , 537, L9–L12.
  • Sawyer Hogg, H. (1947), “Out of Old Books-Catalogues of Nebulous Objects in the Eighteenth Century,” Journal of the Royal Astronomical Society of Canada , 41, 265--273.
  • Sofue, Y. , and Rubin, V. (2001), “Rotation Curves of Spiral Galaxies,” Annual Review of Astronomy & Astrophysics , 39, 137–174.
  • Truesdell, C. , Noll, W. , and Antman, S. S. (2004), The Non-Linear Field Theories of Mechanics (Vol. 3), New York: Springer-Verlag.
  • Wang, C. C. (1969), “On Representations for Isotropic Functions,” Archive for Rational Mechanics and Analysis , 33, 249–267.
  • Weijmans, A. M. , Cappellari, M., Bacon, R., de Zeeuw, P. T., Emsellem, E., Falcón-Barroso, J., Kuntschner, H., McDermid, R. M., van den Bosch, R. C. E., and van de Ven, G. (2009), “Stellar Velocity Profiles and Line Strengths Out to Four Effective Radii in the Early-Type Galaxies NGC 3379 and NGC 821,” Monthly Notices of the Royal Astronomical Society , 398, 561--574.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.