References - Springer978-1-4684-9296-5/1.pdf · 4. F. Reif, Statistical Physics, Berkeley Physics Course -Volume 5, ... 244 References 16. R. ... Volume 2, Inference and ...

References

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Index

A a posteriari probability 3, 4 a priari probability 1, 3, 4,

119-122 acceptance rejection method

69-71,79 arcsine law 88 arrangements 30,39,40 asymptotic efficiency of an esti-

mate 149, 151 asymptotically normal distribu­

tion 151, 203-207, 212 B background 13, 27, 43, 77, 139,

179, 191-194, 198, 200, 216, 219

background subtraction 27, 179, 198, 200, 216

Bartlett S function 168, 201, 202, 212

Bayes' Theorem 119-122, 130, 132-137, 140

Bernoulli trials 35, 42, 61, 62, 115 betting odds for A against B 207 biased estimate 167 binomial coefficient 29, 30, 40 binomial distribution (see distri-

butions, binomial) birth and death problem 84 Breit-Wigner distribution (see

distributions, Breit-Wigner) bridge hands of cards 30, 32, 40 Brownian motion 17 bubble chamber 167 Buffon's Needle 13 C Cauchy distribution (see distribu­

tions, Breit-Wigner)

central limit theorem 44, 52, 62, 65, 107, 110, 112, 114, 116, 117

central moment 7, 13,27 CERN v, 25, 70, 77, 188, 198, 199 CERN library v change of variable 19, 22, 212,

226 characteristic functions 58, 62-65,

98,102, 103 Chauvenet's criterion 89 chi-square distribution (see distri­

butions, chi-square) chi-square fitting 146-148, 153,

154,163,174,178, 179, 183, 186-190, 193, 194, 198, 200, 213, 221, 223

cofactor 100, 196 coin toss 1, 3, 35, 238 combinatorials 29, 31 combining probability estimates

162 combining several measurements

23-26, 161-163, 166, 240 composition 58, 59, 67 compound probability 58, 59, 61,

65 computer program v, 1, 2, 13, 71,

77,79,170,198,199 computing v, 13,66, 70, 71,

75-77,108,117,145,164, 170,195, 198-200,219224, 230, 240

conditional probability 6, 38, 68, 94,119, 133

confidence interval 119, 122-129, 132

248 Index

conditional confidence interval 132, 134, 137

confidence level 123, 126-128, 143-145,178,191

confidence limit 119, 123, 130, 132, 140, 144, 145, 191, 207

constraints 147, 153, 173, 221, 224, 230

convergence in probability 147, 150

convolution 58, 59, 61, 63-65 correlated 9, 19, 20, 70, 101, 103,

109,151,170,173,183,188, 190, 221-224,226, 228-231

correlation coefficient 9, 18, 19, 21, 92, 100, 106, 155, 162

correlation matrix 99, 224, 226 counting rate 27 covariance 92, 93 covariance mapping 106 covariance matrix 179, 182, 189 coverage 128-131, 134, 137

conditional coverage 135, 138 conventional coverage 134, 137 overcoverage and undercoverage

131 credible region 134, 137, 138 cross section 42 cross-entropy 183 curve fitting 49, 170-200, 212,

221 D data set with signal and back­

ground 191, 194 dead time 13 degrees of freedom 25, 49, 50, 64,

103-105, 128, 148, 151, 154, 155, 174, 179, 186, 190,208

density function 1, 4, 5, 8, 13, 16, 40, 47-50, 56, 57, 59, 62, 66, 67, 69, 75-77, 80, 92, 97, 101,

102, 105, 106, 112, 121, 123, 148, 150, 153, 154, 200, 209, 216

dependence 8, 19, 22, 221 detector efficiency 216 die 1-4, 9, 62 differential probability function

(see density function) diffusion 17, 39 direct probability 119 discrete probability 5, 6, 31,

35-43 distribution function 1, 3-5, 53,

64, 66, 67, 76, 111, 112, 163, 164, 201, 202, 211, 212, 231-233, 235, 237

distributions arcsine distribution 88 binomial distribution 35, 37,

39,42-44,47,57,61,62,64, 115, 118, 127, 129, 145, 238

Breit-Wigner distribution 53, 54,64,65,77,114,200,219

Cauchy distribution (see Breit-Wigner distribution)

chi-square distribution 44, 47, 49, 54, 64, 103-105, 146, 148, 151,154,155, 174, 178, 183, 186, 189, 190, 208

exponential distribution 64, 79, 80

F distribution 49, 51, 178 gamma distribution 41, 64, 129,

145 gaussian distribution (see dis­

tributions, normal) geometric distribution 61, 62 hypergeometric distribution 39,

40, 129 Kolmogorov-Smirnov Distribu­

tion 235, 237, 241

log-normal 52, 53, 110 multi-dimensional normal dis­

tribution 101-103, 175 multinomial distribution 39 negative binomial distribution

39, 42, 64, 130, 145 normal distribution 8, 12-15,

38, 44-57, 64, 65, 76, 77, 79, 80, 92, 98, 103-105, 107-110, 114, 116-118, 120, 126-129, 140, 141, 153-156, 165, 166, 168, 169, 194, 195, 201, 211, 219, 223, 229, 240

Poisson distribution 35, 37-40, 42-44,47,59,61,62,64,77, 108, 118, 122, 126, 128, 129, 138, 142-145, 163-165

Rayleigh probability distribu­tion 56

runs distribution 237, 238 Smirnov-Cramer-Von Mises

distribution 233-235 Student's distribution 51, 56,

128, 194 two dimensional normal distri-

bution 97-99, 105, 106 dividing data in half 140 drunkard's walk 17 E effective variance method 184,

185 efficiency of an estimate 149, 151 efficiency of detector 78, 79 elitist method 164 ellipse of concentration 97 ellipsoid of concentration 100, 102 equations of constraint 221-223,

225 error estimate 17, 24, 27, 51, 56,

57,122,142,173-177,189, 197, 198, 204, 225

Index 249

errors in quadrature 20 excess (see kurtosis) expectation value 6, 7, 26, 93,

168,171,172,203,205,226 exponential distribution (see dis-

tributions, exponential) extrapolated point 197 F F distribution (see distributions,

F) factorials 29, 31, 32, 136, 137 fair coin 57, 212 Feller, W. 3, 238 Fisher's lemma (see lemma of

Fisher) fluctuations 106, 107 frequency function (see density

function) frequentist approach 122, 124,

132, 138 G gambler's ruin 89, 90 games of chance 87,90 gamma distribution (see distribu­

tions, gamma) gamma function 55 gaussian distribution (see distri­

butions, normal) generating functions 58, 60-62, 65 geometric distribution (see distri-

butions, geometric) Gibbs phenomenon 178-180, 217 H HBOOK 77, 199 histograms 47, 77-79,218, 219,

231-233,238-240 histogram package v, 77 hypergeometric distribution (see

distributions, hypergeomet-ric)

hypothesis of desperation 122, 123, 126, 127, 143, 144

250 Index

hypothesis testing 49, 209, 212, 231, 235, 238, 240

I identical trials 2 importance sampling 69, 79 independence 2, 3, 9, 13, 17-19,

22-26,35,39,47,50,51, 58,59,62,63,65,76,92,93, 100, 102-105, 107, 108, 148, 155, 163, 170, 173, 205, 209, 210,222

input buffer 81, 82 integral probability (see distribu­

tion function) interpolated point 176, 177, 197 interpolating functions 213-216,

219 inverse probability 119, 239 iterated logarithm 115 iterations to find minima/maxima

187, 188, 200, 224, 225, 229, 230

J jacknife 201, 212 James, F. 71, 114, 190 K Khintchine, A. 115 Kolmogorov-Smirnov Distri-

bution (see distributions, Kolmogorov-Smirnov)

Kolmogorov-Smirnov test 234 Kroneker 8 104 kurtosis 7, 8, 194, 195, 206 L Lagrange multipliers 221 least squares 146, 147, 152, 164,

174, 194, 215, 231, 240 lemma of Fisher 104, 105 likelihood contour 190, 191 likelihood ratio 201, 208, 209,

211,212

linear least squares 215 linear regression 94, 95, 98, 100 LOREN 78, 79 M machine repair line 86 Mann, H.B. and Whitney, D.R.

240 MAPLE v, 198 Marbe, K. 3 marginal probability 5 Markov chains 84 maximum entropy 182 maximum likelihood 146, 148,

174, 189, 199,200,202 estimates 154, 163, 165, 168,

202 method 148, 151, 164-168, 170,

200 method extended 157, 158 theorem 148

mean 7, 8,13, 17, 19,23-26,35, 38-40,43,46,47,49,51,57, 64, 76, 94, 97, 103-105, 113, 122, 123, 127, 142, 145, 155, 165-168, 194, 204, 206, 207, 211,223,229

measurement error 19, 120, 132-135,169, 176,204

median 8 MINUIT 188, 190, 198, 199, 223 mode 8 modified chi-squared minimum

method 147, 148, 153, 174, 223

moment 7, 13,49,54, 61,65,92 moment matrix 92, 99, 102-104,

170,175,176,186,189,221, 226-228

Monte Carlo efficiency 66, 75, 80 Monte Carlo simulation 66-80,

114, 164 199, 212, 218, 219

multi-dimensional distribution 92, 99

multi-dimensional normal dis­tribution (see distributions, multi-dimensional normal)

multinomial coefficients 39 multinomial distribution (see dis­

tributions, multinomial) multiple correlation coefficient

101 multiple scattering 15-17, 22, 23,

27,45,93,96,99, 110-112, 116, 169, 210

N negative binomial distribution

(see distributions, negative binomial)

non-linear parameters 170, 186-191, 195

normal distribution (see distribu-tions, normal)

not-a-knot condition 214, 216 P Parratt, L.G. 122 partial correlation coefficient 101 PCSAS v permutations 39 pivotal quantity 128 plural scattering 112 Poisson distribution (see distribu-

tions, Poisson) Poisson postulate 38 Poisson trials 62 population mean 154 prior probability 132 probability 1-3 probability of causes 119 propagation of errors 19, 22, 114 pseudorandom number v, 13,

66-71, 73, 75-80, 108, 109, 199

Index 251

Q quality function 192, 194 quadratic form 93, 94, 99, 100

semi-positive definite quadratic form 93, 99, 100

queueing theory 81-83 quickline 85, 86 R radioactive decay chain 84 random number (see pseudo-random

number) random variable 5-7, 19,36,59,

63, 65, 66, 92, 107, 108, 168 random walk 17 randomization test 240 randomness I, 2 RANMAR 71-73 Rayleigh probability distribution

(see distributions, Rayleigh) regression analysis 146, 173-178 regression line 94, 95, 98, 100 regression plane 100 regular estimate 149 regularization method 180, 218 regularization parameter 181 relative frequency 2, 3 Renyi theorem 237 resolution function 218, 219 RMARIN 72, 73 robust 194 root N law 15, 22 runs 238 runs distribution (see distribu-

tions, runs) Rutherford scattering 17, 110-113 S sagitta 204 sample correlation coefficient 162,

169 sample mean 26, 168, 240 sample space 4, 14, 19, 132

252 Index

sampling 40, 69, 79, 123, 129, 154, 166, 168, 232, 235, 237, 240

sampling with replacement 34, 39

sampling without replacement 29, 34, 40

SAS v servicing factor 86 Sheppard's corrections for group­

ing 157 significance level 233 significance of a signal 138-141,

178,181, 182,219,233 skewness 7, 8, 206-208 Smirnov theorem 237 Smirnov-Cramer-Von Mises dis-

tribution (see distributions, Smirnov-Cramer-Von Mises distribution)

Smirnov-Cramer-Von Mises goodness of fit test 163, 232-235, 241

spline functions 213, 215, 219 B-splines 215-220 complete splines 214 cubic B-splines 215, 216, 218,

220 cubic splines 213, 219 natural splines 213, 214

standard deviation 7, 8, 19, 35, 65, 97, 114, 117, 120, 122, 138, 189, 190, 211, 212

stochastic matrix 84 straggling 112, 166, 167 Student's distribution (see distri-

butions, Student's) sufficient statistic 128, 150, 151,

155, 208 sum of squares 103, 147

symmetric tails for confidence intervals 123, 125, 131, 158

T telephone exchange 86 Tikhonov regularization method

181 total correlation coefficient 100 traffic intensity 82, 83, 85 two dimensional distribution

92-99, 105, 106 two dimensional normal distribu­

tion (see distributions, two dimensional no

U unbiased estimate 149 uncorrelated 9, 93, 102, 106 unfolding 213, 216, 219, 220 uniform distribution 10, 51, 52 unphysical region 124-126, 131,

144 V variance 7, 8, 10-12, 19-27,36,

38,46,47,49,51,55-57,61, 63, 64, 76, 95, 97, 103-105, 107,112-114,116, 117, 120, 123, 127, 141, 142, 148, 149, 151, 154, 155, 165, 166, 168-170,172-180, 190, 194, 197, 204-206, 209-211, 218, 223, 229, 233, 240

Von Neumann, J. 69 W Wang's theorem 237 weighted events 178 weighted mean 142, 155 weights 26, 69, 113, 142, 147, 155,

173,174,178-180,218 Wilcoxon, F. 240 Y Yost, G.P. 67, 114