Skip to main content Accessibility help
×
Hostname: page-component-7c8c6479df-nwzlb Total loading time: 0 Render date: 2024-03-19T06:53:46.940Z Has data issue: false hasContentIssue false

5 - A crash course on data analysis in asteroseismology

Published online by Cambridge University Press:  05 December 2013

Thierry Appourchaux
Affiliation:
Institut d'Astrophysique Spatiale
Pere L. Pallé
Affiliation:
Instituto de Astrofísica de Canarias, Tenerife
César Esteban
Affiliation:
Instituto de Astrofísica de Canarias, Tenerife
Get access

Summary

“Throughout human history, as our species has faced the frightening, terrorizing fact that we do not know who we are or where we are going in this ocean of chaos, it has been the authorities – the political, the religious, the educational authorities – who have attempted to comfort us by giving us order, rules, regulations, informing – forming in our minds – their view of reality.

To think for yourself you must question authority and learn how to put yourself in a state of vulnerable open-mindedness, chaotic, confused vulnerability to inform yourself.”

Timothy Leary in Sound Bites from the Counter Culture (1989)

Introduction

This chapter attempts to provide a summary of the course I gave during the XXII Canary Island Winter School of Astrophysics. In no way should this chapter be perceived as the final answer to a problem. I hope that this chapter can serve as a basis for students and fellow scientists to go beyond what is written here. As in many approaches that I have pursued, this work is a snapshot of where I am and hopefully a possible starting point from which one can expand to other paths not yet ventured.

This chapter starts with a short historical introduction on signal processing and statistics or how our forefathers started doing data analysis more than 200 years ago. The second part is related to the sampling and acquisition of continuous physical signals for subsequent analysis in a digital world.

Type
Chapter
Information
Asteroseismology , pp. 123 - 162
Publisher: Cambridge University Press
Print publication year: 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aigrain, S., Favata, F., and Gilmore, G. 2004. Characterising stellar micro-variability for planetary transit searches. A&A, 414, 1139–52.Google Scholar
Anderson, E.R., Duvall, T.L. Jr., and Jefferies, S. M. 1990. Modeling of solar oscillation power spectra. ApJ, 364(Dec.), 699.Google Scholar
Appourchaux, T. 2008. Bayesian approach for g-mode detection, or how to restrict our imagination. Astronomische Nachrichten, 329(June), 485.Google Scholar
Appourchaux, T., Andersen, B.N., Frohlich, C., Jimenez, A., Telljohann, U., and Wehrli, C. 1997. In-flight performance of the VIRGO Luminosity Oscillations Imager aboard SOHO. Sol. Phys., 170, 27–41.Google Scholar
Appourchaux, T., Gizon, L., and Rabello-Soares, M. C. 1998. The art of fitting p-mode spectra. I. Maximum Likelihood Estimation. A&AS, 132(Oct.), 107–19.Google Scholar
Appourchaux, T., Frohlich, C., Andersen, B.N., Berthomieu, G., Chaplin, W., Elsworth, Y., Finsterle, W., Gough, D.O., Hoeksema, J.T., Isaak, G.R., Kosovichev, A.G., Provost, J., Scherrer, P.H., Sekii, T., and Toutain, T. 2000. Observational upper limits for low-degree solar g modes. ApJ, 538, 401–14.Google Scholar
Appourchaux, T., Andersen, B., and Sekii, T. 2002. What have we learnt with the Luminosity Oscillations Imager over the past 6 years? Pages 47–50 of: C., Frohlich and A., Wilson (ed), From Solar Min to Max: Half a Solar Cycle with SOHO. ESA Special Publication, vol. 508.
Appourchaux, T., Berthomieu, G., Michel, E., Aerts, C., Ballot, J., Barban, C., Baudin, F., Boumier, P., de Ridder, J., Floquet, M., Garcia, R.A., Garrido, R., Goupil, M.-J., Lambert, P., Lochard, J., Neiner, C., Poretti, E., Provost, J., Roxburgh, I., Samadi, R., and Toutain, T. 2006a. Data analysis tools for the seismology programme. Page 377 of: M., Fridlung, A., Baglin, J., Lochard and L., Conroy (ed), The CoRoT Mission. ESA Publications Division, ESA Spec. Publ. 1306.
Appourchaux, T., Berthomieu, G., Michel, E., Ballot, J., Barban, C., Baudin, F., Boumier, P., de Ridder, J., Floquet, M., Garcia, R.A., Garrido, R., Goupil, M.-J., Lambert, P., Lochard, J., Mazumdar, A., Neiner, C., Poretti, E., Provost, J., Roxburgh, I., Samadi, R., and Toutain, T. 2006b. Evaluation of the scientific performances for the seismology programme. Page 429 of: M., Fridlung, A., Baglin, J., Lochard and L., Conroy (ed), The CoRoT Mission. ESA Publications Division, ESA Spec. Publ. 1306.
Appourchaux, T., Michel, E., Auvergne, M., Baglin, A., Toutain, T., Baudin, F., Benomar, O., Chaplin, W.J., Deheuvels, S.,Samadi, R.,Verner, G.A., Boumier, P., Garcia, R.A., Mosser, B., Hulot, J.-C., Ballot, J., Barban, C., Elsworth, Y., Jimenez-Reyes, S.J., Kjeldsen, H., Regulo, C., and Roxburgh, I. W. 2008. CoRoT sounds the stars: p-mode parameters of Sun-like oscillations on HD 49933. A&A, 488(Sept.), 705–14.Google Scholar
Appourchaux, T., Samadi, R., and Dupret, M.-A. 2009. On posterior probability and significance level: application to the power spectrum of HD 49 933 observed by CoRoT. A&A, 506 (Oct.), 1–5.Google Scholar
Ballot, J., Garcia, R.A., and Lambert, P. 2006. Rotation speed and stellar axis inclination from p modes: how CoRoT would see other suns. MNRAS, 369(July), 1281–1286.Google Scholar
Ballot, J., Appourchaux, T., Toutain, T., and Guittet, M. 2008. On deriving p-mode parameters for inclined solar-like stars. A&A, 486(Aug.), 867–75.Google Scholar
Barban, C., Deheuvels, S., Baudin, F., Appourchaux, T., Auvergne, M., Ballot, J., Boumier, P., Chaplin, W.J., Garcia, R.A., Gaulme, P., Michel, E., Mosser, B., Regulo, C., Roxburgh, I. W., Verner, G., Baglin, A., Catala, C., Samadi, R., Bruntt, H., Elsworth, Y., and Mathur, S. 2009. Solar-like oscillations in HD 181420: data analysis of 156 days of CoRoT data. A&A, 506(Oct.), 51–6.Google Scholar
Baudin, F., Barban, C., Belkacem, K., Hekker, S., Morel, T., Samadi, R., Benomar, O., Goupil, M., Carrier, F., Ballot, J., Deheuvels, S., De Ridder, J., Hatzes, A.P., Kallinger, T., and Weiss, W. W. 2011. Amplitudes and lifetimes of solar-like oscillations observed by CoRoT. Red-giant versus main-sequence stars. A&A, 535(May), A84.Google Scholar
Bayes, T. 1763. An Essay towards solving a Problem in the Doctrine of Chances. Philosophical Transactions of the Royal Society of London, 53, 370.Google Scholar
Bedding, T.R., Kjeldsen, H., Reetz, J., and Barbuy, B. 1996. Measuring stellar oscillations using equivalent widths of absorption lines. MNRAS, 280(June), 1155–61.Google Scholar
Belkacem, K., Samadi, R., Goupil, M.-J., Lefevre, L., Baudin, F., Deheuvels, S., Dupret, M.-A., Appourchaux, T., Scuflaire, R., Auvergne, M., Catala, C., Michel, E., Miglio, A., Montalban, J., Thoul, A., Talon, S., Baglin, A., and Noels, A. 2009. Solar-like oscillations in a massive star. Science, 324(June), 1540.Google Scholar
Belkacem, K., Dupret, M.A., and Noels, A. 2010. Solar-like oscillations in massive main-sequence stars. I. Asteroseismic signatures of the driving and damping regions. A&A, 510(Jan.), A6.Google Scholar
Belmonte, J.A., Chevreton, M., Mangeney, A., Praderie, F., Saint-Pe, O., Puget, P., Alvarez, M., and Roca Cortes, R. 1991. Rapid photometry of the Delta Scuti variable 63 Herculis and of the F 2V star HD 155543: Observations and analysis of the time series. A&A, 246(June), 71–83.Google Scholar
Benomar, O. 2010. Sismologie stellaire: Méthodes statistiques appliquées aux étoiles de type solaire. Ph.D. thesis, Universite Paris-Sud XI, Orsay, France.
Benomar, O., Baudin, F., Campante, T.L., Chaplin, W.J., Garcia, R.A., Gaulme, P., Toutain, T., Verner, G.A., Appourchaux, T., Ballot, J., Barban, C., Elsworth, Y., Mathur, S., Mosser, B., Regulo, C., Roxburgh, I.W., Auvergne, M., Baglin, A., Catala, C., Michel, E., and Samadi, R. 2009a. A fresh look at the seismic spectrum of HD49933: analysis of 180 days of CoRoT photometry. A&A, 507(Nov.), L13–L16.Google Scholar
Benomar, O., Appourchaux, T., and Baudin, F. 2009b. The solar-like oscillations of HD 49933: a Bayesian approach. A&A, 506(Oct.), 15–32.Google Scholar
Berger, J. O. 1997. Could Fisher, Jeffreys and Neyman have agreed upon testing?Statistical Science, 18, 1–32.Google Scholar
Berger, J.O., and Sellke, T. 1987. Testing of a point null hypothesis: The irreconcilability of significance levels and evidence. Journal of the American Statistical Association, 82(397), 112–39.Google Scholar
Berger, J.O., Boukai, B., and Wang, Y. 1997. Unified frequentist and Bayesian testing of a precise hypothesis. Statistical Science, 12(3), 133–60.Google Scholar
Bernoulli, J. 1713. Ars conjectandi, opus posthumum. Accedit Tractatus de seriebus infinitis, et epistola gallice scripta de ludo pilae reticularis. Thurneysen Brothers, Basel, Switzerland.
Bretthorst, L. G. 1988. Bayesian Spectrum Analysis and Parameter Estimation. Springer-Verlag, Berlin, available electronically at bayes.wustl.edu/glb/book.pdf.
Bretthorst, G. L. 2001a. Generalizing the Lomb-Scargle periodogram. Pages 241–245 of: A., Mohammad-Djafari (ed), Bayesian Inference and Maximum Entropy Methods in Science and Engineering. American Institute of Physics Conference Series, vol. 568.
Bretthorst, G. L. 2001b. Generalizing the Lomb-Scargle periodogram: the nonsinusoidal case. Pages 246–251 of: A., Mohammad-Djafari (ed), Bayesian Inference and Maximum Entropy Methods in Science and Engineering. American Institute of Physics Conference Series, vol. 568.
Brewer, B.J., Bedding, T.R., Kjeldsen, H., and Stello, D. 2007. Bayesian inference from observations of solar-like oscillations. ApJ, 654(Jan.), 551–7.Google Scholar
Broomhall, A.-M., Chaplin, W.J., Elsworth, Y., Appourchaux, T., and New, R. 2010. A comparison of frequentist and Bayesian inference: searching for low-frequency p modes and g modes in Sun-as-a-star data. MNRAS, 406(Aug.), 767–81.Google Scholar
Chaplin, W.J., Elsworth, Y., Howe, R., Isaak, G.R., McLeod, C.P., Miller, B.A., van der Raay, H.B., Wheeler, S.J., and New, R. 1996. BiSON Performance. Sol. Phys., 168(Sept.), 1–18.Google Scholar
Chaplin, W.J., Appourchaux, T., Elsworth, Y., Isaak, G.R., Miller, B.A., and New, R. 2004. On comparing estimates of low-l solar p-mode frequencies from Sun-as-a-star and resolved observations. A&A, 424(Sept.), 713–17.Google Scholar
Christensen-Dalsgaard, J. 1989. The effect of rotation on whole-disc Doppler observations of solar oscillations. MNRAS, 239(Aug.), 977–94.Google Scholar
Christensen-Dalsgaard, J. 2004. An Overview of helio- and asteroseismology. Page 1 of: D., Danesy (ed), SOHO 14 Helio- and Asteroseismology: Towards a Golden Future. ESA Special Publication, vol. 559.
Christensen-Dalsgaard, J., and Gough, D. O. 1982. On the interpretation of five-minute oscillations in solar spectrum line shifts. MNRAS, 198(Jan.), 141–71.Google Scholar
Christensen-Dalsgaard, J., Carpenter, K.G., Schrijver, C.J., Karovska, M., and the Si Team. 2011. The stellar imager (SI): a mission to resolve stellar surfaces, interiors, and magnetic activity. Journal of Physics Conference Series, 271(1), 012085.Google Scholar
Cooley, J.W., and Tuckey, J. W. 1965. An algorithm for the machine calculation of complex Fourier series. Math. Comp., 19, 297–301.Google Scholar
Cramer, H. 1946. Mathematical Methods of Statistics. Princeton University Press, New Jersey.
Cuypers, J. 1987. Medelingen van de Koninklijke Academie voor Wetenschappen, Letteren en Schone Kunsten van Belgi'e, Jg. 49 Nr. 3 (Brussel: Paleis der Academieen), 21.
De Finetti, B. 1937. La prevision: ses lois logiques, ses sources subjectives. Annales de l'Institut Henri Poincare, 7, 1.Google Scholar
De Moivre, A. 1718. The doctrine of chances of a method of calculating the probability of events in play. W. Pearson, London, United Kingdom.
Deheuvels, S., Bruntt, H., Michel, E., Barban, C., Verner, G., Regulo, C., Mosser, B., Mathur, S., Gaulme, P., Garcia, R.A., Boumier, P., Appourchaux, T., Samadi, R., Catala, C., Baudin, F., Baglin, A., Auvergne, M., Roxburgh, I.W., and Perez Hernandez, F. 2010. Seismic and spectroscopic characterization of the solar-like pulsating CoRoT target HD 49385. A&A, 515(June), A87.Google Scholar
Duvall, T.L. Jr., and Harvey, J. W. 1986. Solar Doppler shifts: sources of continuous spectra. Page 105 of: Osaki, Y., and Shibahashi, H. (eds), Seismology of the Sun and the Distant Stars. Lecture Notes in Physics, Springer Verlag, Berlin.
Duvall, T. L. Jr., Jefferies, S.M., Harvey, J.W., Osaki, Y., and Pomerantz, M. A. 1993. Asymmetries of solar oscillation line profiles. ApJ, 410(June), 829–36.Google Scholar
Fisher, R. A. 1912. On an absolute criterion for fitting frequency curves. Messenger of Mathematics, 41, 155–60.Google Scholar
Fisher, R. A. 1925. Theory of statistical estimation. Proc. Cambridge Philos. Soc., 22, 155–60.Google Scholar
Fleischmann, M., and Pons, S. 1989. Electrochemically induced nuclear fusion of deuterium. Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, 261, 301–8.Google Scholar
Fourier, J. 1822. Theorieanalytiquedelachaleur. Firmin-Didot, Paris, France.
Frieden, B. R. 1983. Probability, Statistical Optics, and Data Testing: A Problem Solving Approach. Springer-Verlag, Berlin.
Frohlich, C., Andersen, B.N., Appourchaux, T., Berthomieu, G., Crommelynck, D.A., Domingo, V., Fichot, A., Finsterle, W., Gomez, M.F., Gough, D., Jimenez, A., Leifsen, T., Lombaerts, M., Pap, J.M., Provost, J., Cortes, T.R., Romero, J., Roth, H., Sekii, T., Telljohann, U., Toutain, T., and Wehrli, C. 1997. First results from VIRGO, the experiment for helioseis-mology and solar irradiance monitoring on SOHO. Sol. Phys., 170, 1–25.Google Scholar
Gabriel, M. 1993. The probability-density function of solar p modes and the location of the excitation mechanism. A&A, 274(July), 931.Google Scholar
Gabriel, M. 1994. The probability-density function of a Fourier line. A&A, 287(July), 685–691.Google Scholar
Garcia, R.A., Regulo, C., Samadi, R., Ballot, J., Barban, C., Benomar, O., Chaplin, W.J., Gaulme, P., Appourchaux, T., Mathur, S., Mosser, B., Toutain, T., Verner, G.A., Auvergne, M., Baglin, A., Baudin, F., Boumier, P., Bruntt, H., Catala, C., Deheuvels, S., Elsworth, Y., Jimenez-Reyes, S.J., Michel, E., Perez Hernandez, F., Roxburgh, I.W., and Salabert, D. 2009. Solar-like oscillations with low amplitude in the CoRoT target HD 181906. A&A, 506(Oct.), 41–50.Google Scholar
Gaulme, P., Appourchaux, T., and Boumier, P. 2009. Mode width fitting with a simple Bayesian approach. Application to CoRoT targets HD 181420 and HD 49933. A&A, 506(Oct.), 7–14.Google Scholar
Gauss, C. F. 1809. Theoria motus corporum coelestium in sectionibus conicis solem ambientum. Konigliche Gesellschaft der Wissenschaften, Gottingen, Germany.
Gauss, C. F. 1866. Nachlass: Theoria interpolationis methodo nova tractata: Werke band 3, 265-327. Konigliche Gesellschaft der Wissenschaften, Gottingen, Germany.
Gautschy, A., and Saio, H. 1995. Stellar pulsations across the HR diagram: part 1. ARA&A, 33, 75–114.Google Scholar
Gautschy, A., and Saio, H. 1996. Stellar pulsations across the HR diagram: part 2. ARA&A, 34, 551–606.Google Scholar
Gelly, B., Lazrek, M., Grec, G., Ayad, A., Schmider, F.X., Renaud, C., Salabert, D., and Fossat, E. 2002. Solar p-modes from 1979 days of the GOLF experiment. A&A, 394(Oct.), 285.Google Scholar
Gelman, A., and Meng, X.-L. 1998. Simulating normalizing constants: from importance sampling to bridge sampling to path sampling. Statistical Science, 13(2)(Oct.), 163–185.Google Scholar
Gibbs, J. W. 1898. Fourier series. Nature, 59, 200.Google Scholar
Gibbs, J. W. 1899. Fourier series. Nature, 59, 606.Google Scholar
Gizon, L., and Solanki, S. K. 2003. Determining the inclination of the rotation axis of a sun-like star. ApJ, 589(June), 1009–19.Google Scholar
Goldstine, H. H. 1977. A History of Numerical Analysis from the 16th through the 19th Century. Springer, New York-Heidelberg-Berlin.
Gott, J. R. III 1994. Future Prospects Discussed. Nature, 368, 106–8.Google Scholar
Gregory, P. C. 2005. Bayesian Logical Data Analysis for the Physical Sciences: A Comparative Approach with “Mathematica” Support. Cambridge University Press, Cambridge.
Gruberbauer, M., Kallinger, T., Weiss, W.W., and Guenther, D. B. 2009. On the detection of Lorentzian profiles in a power spectrum: a Bayesian approach using ignorance priors. A&A, 506(Nov.), 1043–53.Google Scholar
Handberg, R., and Campante, T. L. 2011. Bayesian peak-bagging of solar-like oscillators using MCMC: a comprehensive guide. A&A, 527(Mar.), A56.Google Scholar
Harvey, J. 1985. High-resolution helioseismology. Pages 199–208 of: E., Rolfe, and B., Battrick (eds), Future missions in solar, heliospheric and space plasma physics, ESA SP-235. ESA Publications Division, Noordwijk, The Netherlands.
Harvey, J.W., Duvall, T. L. Jr., Jefferies, S.M., and Pomerantz, M. A. 1993. Chromospheric oscillations and the background spectrum. ASP Conference Series, 42, 111.Google Scholar
Hastings, W. K. 1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1)(July), 97.Google Scholar
Heideman, M.T., Johnson, D.H., and Sidney Burrus, C. 1985. Gauss and the history of the fast Fourier transform. Archive for History of Exact Sciences, 34, 265–77.Google Scholar
Hill, F., Stark, P.B., Stebbins, R.T., Anderson, E.R., Antia, H.M., Brown, T.M., Duvall, T. L. Jr., Haber, D.A., Harvey, J.W., Hathaway, D.H., Howe, R., Hubbard, R., Jones, H.P., Kennedy, J.R., Korzennik, S.G., Kosovichev, A.G., Leibacher, J.W., Libbrecht, K.G., Pintar, J.A., Rhodes, E. J. Jr., Schou, J.Thompson, M.J., Tomczyk, S., Toner, C.G., Toussaint, R., and Williams, W. E. 1996. The Solar Acoustic Spectrum and Eigenmode. Science, 272, 1292.Google Scholar
Hogbom, J. A. 1974. Aperture Synthesis with a Non-Regular Distribution of Interferometer Baselines. A&AS, 15(June), 417–26.Google Scholar
Houdek, G., Balmforth, N.J., Christensen-Dalsgaard, J., and Gough, D. O. 1999. Amplitudes of stochastically excited oscillations in main-sequence stars. A&A, 351(Nov.), 582.Google Scholar
Jaynes, E. T. 1987. Bayesian spectrum and chirp analysis. Page 1 of: C. R., Smith and G. J., Erickson (ed), Maximum entropy and Bayesian spectral analysis and estimation problems. D.Reidel, Dordrecht, the Netherlands.
Jaynes, E. T. 2009. Probability Theory: The Logic of Science. 6th edition. Larry, Brethorst (ed). Cambridge University Press, Cambridge, United Kingdom.
Jeffreys, H. 1939. Theory of Probability. Oxford Universitty Press, Oxford, United Kingdom.
Jeffreys, H. 1946. An invariant form for the prior probability in estimation problems. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 186, 155–160.Google Scholar
Keshner, M. S. 1982. 1/f noise. IEEE Proceedings, 70, 212–18.Google Scholar
Khinchin, A. Y. 1934. Korrelationstheorie der stationaren stochastichen Prozesse. Mathematische Annalen, 109, 604.Google Scholar
Koen, C. 1999. The analysis of indexed astronomical time series. V. Fitting sinusoids to highspeed photometry. MNRAS, 309(Nov.), 769–802.Google Scholar
Komm, R.W., Gu, Y., Hill, F., Stark, P.B., and Fodor, I. K. 1999. Multitaper spectral analysis and wavelet denoising applied to helioseismic data. ApJ, 519, 407–21.Google Scholar
Kosovichev, A.G., Schou, J., Scherrer, P.H., Bogart, R.S., Bush, R.I., Hoeksema, J.T., Aloise, J., Bacon, L., Burnette, A., de Forest, C., Giles, P.M., Leibrand, K., Nigam, R., Rubin, M., Scott, K., Williams, S.D., Basu, S., Christensen-Dalsgaard, J., Dappen, W., Rhodes, E.J., Duvall, T.L., Howe, R., Thompson, M.J., Gough, D.O., Sekii, T., Toomre, J., Tarbell, T.D., Title, A.M., Mathur, D., Morrison, M., Saba, J. L. R., Wolfson, C.J., Zayer, I., and Milford, P. N. 1997. Structure and rotation of the solar interior: initial results from the MDI medium-l program. Sol. Phys., 170, 43–61.Google Scholar
Kumar, P., Franklin, J., and Goldreich, P. 1988. Distribution functions for the time-averaged energies of stochastically excited solar p modes. ApJ, 328(May), 879.Google Scholar
Laplace, M. 1774. Memoire sur la probabilité des causes par les événements. Mémoires de Mathématique et de Physique, T6, 621–56.Google Scholar
Legendre, A.-M. 1805. Nouvelles méthodes pour la determination des orbites des cometes. Firmin Didot, Paris, France.
Libbrecht, K. G. 1992. On the ultimate accuracy of solar oscillation frequency measurements. ApJ, 387(Mar.), 712.Google Scholar
Mathur, S., Handberg, R., Campante, T.L., Garcia, R.A., Appourchaux, T., Bedding, T.R., Mosser, B., Chaplin, W.J., Ballot, J., Benomar, O., Bonanno, A., Corsaro, E., Gaulme, P., Hekker, S., Regulo, C., Salabert, D., Verner, G., White, T.R., Brandão, I.M., Creevey, O.L., Dogan, G., Elsworth, Y., Huber, D., Hale, S.J., Houdek, G., Karoff, C., Metcalfe, T.S., Molenda-Zakowicz, J., Monteiro, M. J. P. F. G., Thompson, M.J., Christensen-Dalsgaard, J., Gilliland, R.L., Kawaler, S.D., Kjeldsen, H., Quintana, E.V., Sanderfer, D.T., and Seader, S. E. 2011. Solar-like oscillations in KIC11395018 and KIC11234888 from 8 months of Kepler data. ArXiv e-prints.Google Scholar
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E. 1953. Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21(6) (July), 1087.Google Scholar
Mosser, B., Michel, E., Appourchaux, T., Barban, C., Baudin, F., Boumier, P., Bruntt, H., Catala, C., Deheuvels, S., Garcia, R.A., Gaulme, P., Regulo, C., Roxburgh, I., Samadi, R., Verner, G., Auvergne, M., Baglin, A., Ballot, J., Benomar, O., and Mathur, S. 2009. The CoRoT target HD 175726: an active star with weak solar-like oscillations. A&A, 506(Oct.), 33–40.Google Scholar
Neyman, J., and Pearson, E. 1933. On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society of London. Series A, 231(July), 289.Google Scholar
Nigam, R., and Kosovichev, A. G. 1998. Measuring the Sun's eigenfrequencies from velocity and intensity helioseismic spectra: asymmetrical line profile-fitting formula. ApJ, 505(Sept.), L51.Google Scholar
Nigam, R., Kosovichev, A.G., Scherrer, P.H., and Schou, J. 1998. Asymmetry in velocity and intensity helioseismic spectra: a solution to a long-standing puzzle. ApJ, 495(Mar.), L115.Google Scholar
Nyquist, H. 1924. Certain factors affecting telegraph speed. Bell Syst. Tech. Journal, 3, 324–52.Google Scholar
Parseval des Chênes, M.-A. 1806. Mémoire sur les séries et sur l'intégration complete d'une équation aux differences partielles lineaire du second ordre, a coefficients constants. Mémoires présentés a l'Institut des Sciences, Lettres et Arts, par divers savans, et lus dans ses assemblees. Sciences, mathématiques et physiques, 1, 638.Google Scholar
Peligrad, M., and Wu, W. B. 2010. Central limit theorem for Fourier transforms of stationary processes. The Annals of Probability, 38, 2009.Google Scholar
Poincare, H. 1914. La Science et l'Hypothèse. Editions Flammarion, Paris, France.
Poretti, E., Michel, E., Garrido, R., Lefevre, L., Mantegazza, L., Rainer, M., Rodríguez, E., Uytterhoeven, K., Amado, P.J., Martin-Ruiz, S., Moya, A., Niemczura, E., Suarez, J.C., Zima, W., Baglin, A., Auvergne, M., Baudin, F., Catala, C., Samadi, R., Alvarez, M., Mathias, P., Paparo, M., Papics, P., and Plachy, E. 2009. HD 50844: a new look at delta Scuti stars from CoRoT space photometry. A&A, 506(Oct.), 85–93.Google Scholar
Press, W.H., and Rybicki, G. B. 1989. Fast algorithm for spectral analysis of unevenly sampled data. ApJ, 338(Mar.), 277–80.Google Scholar
Rao, C.R., 1945. Information and the accuracy attainable in the estimation of statistical parameters. Bulletin of the Calcutta Mathematical Society, 37, 81–9.Google Scholar
Ritzwoller, M.H., and Lavely, E. M. 1991. A unified approach to the helioseismic forward and inverse problems of differential rotation. ApJ, 369(Mar.), 557.Google Scholar
Roberts, D.H., Lehar, J., and Dreher, J. W. 1987. Time Series Analysis with clean. Part one: derivation of a spectrum. AJ, 93(Apr.), 968–89.Google Scholar
Samadi, R., and Goupil, M.-J. 2001. Excitation of stellar p-modes by turbulent convection. I. Theoretical formulation. A&A, 370, 136–46.Google Scholar
Scargle, J. D. 1982. Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data. ApJ, 263(Dec.), 835–53.Google Scholar
Schou, J. 1992. On the analysis of helioseismic data. Ph.D. thesis, Arhus Universitet, Denmark.
Schou, J., and Brown, T. M. 1994. Generation of artificial helioseismic time-series. A&AS, 107(Nov.), 541.Google Scholar
Schuster, A. 1897. On lunar and solar periodicities of earthquakes. Proc. Royal Soc. of London, 61, 455.Google Scholar
Scott, J.G., and Berger, J. O. 2010. Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem. The Annals of Statistics, 38(5), 2587–619.Google Scholar
Sellke, T., Bayarri, M.J., and Berger, J. 2001. Calibration of p-values for testing precise null hypotheses. The American Statistician, 55(Mar.), 62–71.Google Scholar
Severino, G., Magrí, M., Oliviero, M., Straus, T., and Jefferies, S. M. 2001. The Solar intensity-velocity cross spectrum: a powerful diagnostic for helioseismology. ApJ, 561(Nov.), 444–9.Google Scholar
Shannon, C. E. 1949. Communication in the presence of noise. Proceedings of the IRE, 37, 10–21.Google Scholar
Slepian, D. 1978. Prolate spheroidal wave functions, Fourier analysis, and uncertainty. V. The discrete case. Bell System Technical Journal, 57, 1371–430.Google Scholar
Stahn, T., and Gizon, L. 2008. Fourier analysis of gapped time series: improved estimates of solar and stellar oscillation parameters. Sol. Phys., 251(Sept.), 31–52.Google Scholar
Sturrock, P.A., and Scargle, J. D. 2009. A Bayesian assessment of p-values for significance estimation of power spectra and an alternative procedure, with application to solar neutrino data. ApJ, 706(Nov.), 393–8.Google Scholar
Tanvir, N.R., Hendry, M.A., Watkins, A., Kanbur, S.M., Berdnikov, L.N., and Ngeow, C. C. 2005. Determination of Cepheid parameters by light-curve template fitting. MNRAS, 363(Nov.), 749–62.Google Scholar
Thomson, D. J. 1982. Spectrum estimation and harmonic analysis. Pages 1055–1096 of: Proc. IEEE, vol. 70.Google Scholar
Toutain, T., and Appourchaux, T. 1994. Maximum likelihood estimators: an application to the estimation of the precision of helioseismic measurements. A&A, 289(Sept.), 649.Google Scholar
Toutain, T., and Frohlich, C. 1992. Characteristics of solar p-modes: results from the IPHIR experiment. A&A, 257(Apr.), 287–97.Google Scholar
Toutain, T., and Gouttebroze, P. 1993. Visibility of solar p-modes. A&A, 268(Feb.), 309–18.Google Scholar
Toutain, T., Appourchaux, T., Baudin, F., Frohlich, C., Gabriel, A.H., Scherrer, P., Andersen, B.N., Bogart, R., Bush, R., Finsterle, W., Garciía, R.A., Grec, G., Henney, C.J., Hoeksema, J. T., Jimenez, A., Kosovichev, A., Roca Cortés, T., Turck-Chiěze, S., Ulrich, R., and Wehrli, C. 1997. Tri-phonic helioseismology: comparison of solar p modes observed by the hélioséismology instruments aboard SOHO. Sol. Phys., 175(Oct.), 311–28.Google Scholar
Wehlau, W., and Leung, K.-C. 1964. The multiple periodicity of Delta Delphini. ApJ, 139(Apr.), 843.Google Scholar
Wiener, N. 1930. Generalized harmonic analysis. Acta Mathematica, 55, 117.Google Scholar
Wilks, S. S. 1938. The large-sample distribution of the likelihood ratio for testing com?posite hypotheses. Annals of Mathematical Statistics, 9(July), 60.Google Scholar
Yoachim, P., McCommas, L.P., Dalcanton, J.J., and Williams, B. F. 2009. A panoply of Cepheid light curve templates. AJ, 137(June), 4697–706.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×