The analysis of cosmic ray data

There has been a number of new statistical results in recent years with application to the particular problems met in analysing cosmic ray particle and -ray data. Some specific statistics have been developed which deal with long-standing problems, such as the scan statistic for detecting bursts of counts and point sources in two dimensions. This review describes the available methods for the problems of detecting signals in time series and two dimensions and recommends the best statistic for each. New approaches to old problems have been developed based on Bayesian methods, which attempt to relieve the concerns often expressed about `degrees of freedom'. The background to these methods is given and some recent results on some of the same problems are given.

[1]  James D. Hamilton.  Time Series Analysis , 1994 .

[2]  J. Glaz,et al.  Approximations for the tail probabilities and moments of the scan statistic. , 1993, Statistics in medicine.

[3]  Joseph Naus,et al.  Probabilities for a $k$th Nearest Neighbor Problem on the Line , 1973 .

[4]  J. Cordes,et al.  A VLA Search for the Geminga Pulsar: A Bayesian Limit on a Scintillating Source , 1999, astro-ph/9912410.

[5]  Joseph Naus,et al.  New recursive methods for scan statistic probabilities , 1997 .

[6]  P. Serlemitsos,et al.  Millisecond temporal structure in Cygnus X-1 , 1974 .

[7]  C. Loader.  Large-deviation approximations to the distribution of scan statistics , 1991, Advances in Applied Probability.

[8]  N Nagarwalla,et al.  A scan statistic with a variable window. , 1996, Statistics in medicine.

[9]  Marianne Månsson,et al.  Poisson approximation in connection with clustering of random points , 1999 .

[10]  W. J. Langford.  Statistical Methods , 1959, Nature.

[11]  W. D. Ray,et al.  Spectral Analysis and Time Series. Vol. 1: Univariate Series. , 1982 .

[12]  J. Glaz.  Approximations for tail probabilities and moments of the scan statistic , 1992 .

[13]  K. J. Orford.  Elimination of red noise in pulsar searches , 1996 .

[14]  L. Scarsi,et al.  Search for pulsed γ-ray emission from radio pulsars in the COS-B data. , 1983 .

[15]  William H. Press,et al.  Numerical recipes , 1990 .

[16]  Emanuel Parzen,et al.  Modern Probability Theory And Its Applications , 1960 .

[17]  K. Mardia.  Statistics of Directional Data , 1972 .

[18]  Robert B. Ash,et al.  Information Theory , 2020, The SAGE International Encyclopedia of Mass Media and Society.

[19]  Steven Kay,et al.  Modern Spectral Estimation: Theory and Application , 1988 .

[20]  Jeffrey D. Scargle.  Studies in Astronomical Time Series Analysis: V. Bayesian Blocks, A New Method to Analyze Structure in , 1998 .

[21]  Ti-Pei Li,et al.  Analysis methods for results in gamma-ray astronomy , 1983 .

[22]  Geoffrey N. Pendleton,et al.  BATSE Observations of the Large-Scale Isotropy of Gamma-Ray Bursts , 1995, astro-ph/9509078.

[23]  Sven Erick Alm.  On the Distributions of Scan Statistics of a Two-Dimensional Poisson Process , 1997, Advances in Applied Probability.

[24]  S. Ikeda.  On bouman-velden-yamamoto’s asymptotic evaluation formula for the probability of visual response in a certain experimental research in quantum-biophysics of vision , 1965 .

[25]  T. Bai,et al.  Methods of periodicity analysis - Relationship between the Rayleigh analysis and a maximum likelihood method , 1992 .

[26]  K. Pearson,et al.  Biometrika , 1902, The American Naturalist.

[27]  George P. H. Styan,et al.  Selected Tables in Mathematical Statistics , 1971 .

[28]  P. Gregory,et al.  Bayesian Periodic Signal Detection. II. Discovery of Periodic Phase Modulation in LS I +61°303 Radio Outbursts , 1999 .

[29]  A. Connors,et al.  A Maximum Entropy Map of the 511 keV Positron Annihilation Line Emission Distribution Near the Galactic Center , 1997 .

[30]  Ronald L. Iman,et al.  On a method for detecting clusters of possible uranium deposits , 1979 .

[31]  D. Leahy,et al.  On searches for periodic pulsed emission - The Rayleigh test compared to epoch folding , 1983 .

[32]  The detection of bursts in UHE and VHE gamma ray data , 1993 .

[33]  Euclid,et al.  Advances in Applied Probability , 1981, Journal of Applied Probability.

[34]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

[35]  K. J. Orford,et al.  Transient emission of ultra-high energy pulsed γ rays from Crab pulsar PSR0531 , 1982, Nature.

[36]  L. Sucheston.  Modern Probability Theory and its Applications. , 1961 .

[37]  Narayanaswamy Balakrishnan,et al.  Advances in the Theory and Practice of Statistics , 1998 .

[38]  Joseph Naus,et al.  Tight Bounds and Approximations for Scan Statistic Probabilities for Discrete Data , 1991 .

[39]  D. L. Bertsch,et al.  The Likelihood Analysis of EGRET Data , 1996 .

[40]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[41]  A. Giles.  An Efficient Algorithm for the Detection of Infrequent Rapid Bursts in Time Series Data , 1997 .

[42]  D. G. Watts,et al.  Spectral analysis and its applications , 1968 .

[43]  Joseph Naus,et al.  Some Probabilities, Expectations and Variances for the Size of Largest Clusters and Smallest Intervals , 1966 .

[44]  Analytical treatment of oversampling , 1990 .

[45]  John Skilling,et al.  Maximum Entropy and Bayesian Methods , 1989 .

[46]  Jie Chen,et al.  Two-dimensional discrete scan statistics☆ , 1996 .

[47]  C. Koen.  Astronomical time series analysis in South Africa , 1995 .

[48]  John L. Stanford,et al.  Statistical methods for physical science , 1994 .

[49]  F. James.  Statistical Methods in Experimental Physics , 1973 .

[50]  J. Scargle.  Studies in astronomical time series analysis. II - Statistical aspects of spectral analysis of unevenly spaced data , 1982 .

[51]  A Simpler Expression for $K$th Nearest Neighbor Coincidence Probabilities , 1975 .

[52]  M. Kulldorff.  A spatial scan statistic , 1997 .

[53]  P. C. Gregory,et al.  Bayesian Periodic Signal Detection: Analysis of ROSAT Observations of PSR 0540-693 , 1996 .

[54]  Jonathan D. Cryer,et al.  Time Series Analysis , 1986 .

[55]  Joseph Naus,et al.  Power of the scan statistic in detecting a changed segment in a Bernoulli sequence , 1994 .

[56]  N. Kalouptsidis,et al.  Spectral analysis , 1993 .

[57]  B. C. Raubenheimer,et al.  A powerful test for weak periodic signals with unknown light curve shape in sparse data. , 1989 .

[58]  De Jager.  On Periodicity Tests and Flux Limit Calculations for Gamma-Ray Pulsars , 1994 .

[59]  D. Hearn.  Consistent analysis of gamma-ray astronomy experiments , 1969 .

[60]  Joseph Naus,et al.  Approximations for Distributions of Scan Statistics , 1982 .

[61]  P. C. Gregory,et al.  Bayesian Periodic Signal Detection. I. Analysis of 20 Years of Radio Flux Measurements of the X-Ray Binary LS I +61°303 , 1999 .

[62]  E. O'mongain.  Application of Statistics to Results in Gamma Ray Astronomy , 1973, Nature.

[63]  Nicholas I. Fisher,et al.  Statistical Analysis of Circular Data , 1993 .