Bolstad W.M. — Introduction to Bayesian Statistics :: Электронная библиотека попечительского совета мехмата МГУ

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Bolstad W.M. — Introduction to Bayesian Statistics

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Название: Introduction to Bayesian Statistics

Автор: Bolstad W.M.

Аннотация:

This textbook is suitable for beginning undergraduates encountering rigorous statistics for the first time. The word "Bayesian" in the title simply indicates that the material is approached from a Bayesian rather than the more traditional frequentist perspective. The basic foundations of statistics are covered: discrete random variables, mean and variance, continuous random variables and common distributions, and so on, as well as a fair amount of specifically Bayesian material, such as chapters on Bayesian inference. As is the norm for elementary statistics books, Bolstad (statistics, University of Waikato, New Zealand) claims this book is suitable for undergraduates with no calculus experience; however, basic familiarity with integral calculus will help students considerably in the sections devoted to continuous random variables.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 2007

Количество страниц: 437

Добавлена в каталог: 22.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Bayes factor      70
Bayes' theorem      66 73
Bayes' theorem using table, binomial observation with discrete prior      110
Bayes' theorem using table, discrete observation with discrete prior      104
Bayes' theorem using table, normal observation with discrete prior      200
Bayes' theorem using table, Poisson observation with discrete prior      112
Bayes' theorem, analyzing the observations all together      106 203
Bayes' theorem, analyzing the observations sequentially      202
Bayes' theorem, binomial observation, beta prior      143
Bayes' theorem, binomial observation, continuous prior      142
Bayes' theorem, binomial observation, discrete prior      108
Bayes' theorem, binomial observation, mixture prior      322
Bayes' theorem, binomial observation, uniform prior      142
Bayes' theorem, discrete random variables      101
Bayes' theorem, events      63 65 68
Bayes' theorem, linear regression model      276
Bayes' theorem, mixture prior      3 19
Bayes' theorem, normal observations known mean, inverse-chi-squared prior for $\sigma^2$       302
Bayes' theorem, normal observations known mean, Jeffreys' prior for $\sigma^2$       302
Bayes' theorem, normal observations known mean, positive uniform prior for $\sigma^2$       301
Bayes' theorem, normal observations with known variance, continuous prior for $\mu$       205
Bayes' theorem, normal observations with known variance, discrete prior for $\mu$       199
Bayes' theorem, normal observations with known variance, flat prior for $\mu$       206
Bayes' theorem, normal observations with known variance, mixture prior      324
Bayes' theorem, normal observations with known variance, normal prior for $\mu$       207
Bayes' theorem, Poisson observation, continuous prior      183
Bayes' theorem, Poisson observation, gamma prior      185
Bayes' theorem, Poisson observation, positive uniform prior      184
Bayes' theorem, Poisson, Jeffreys' prior      185
Bayesian approach to statistics      6 11
Bayesian credible interval      153
Bayesian credible interval, binomial proportion $\pi$       153
Bayesian credible interval, difference between normal means $\mu_1 - \mu_2$ , equal variances      240
Bayesian credible interval, difference between normal means $\mu_1 - \mu_2$ , unequal variances      246
Bayesian credible interval, difference between proportions $\pi_1 - \pi_2$       248
Bayesian credible interval, normal mean $\mu$       21 1
Bayesian credible interval, normal standard deviation $\sigma$       309
Bayesian credible interval, Poisson parameter $\mu$       192
Bayesian credible interval, regression slope $\mu$       280
Bayesian credible interval, used for Bayesian two-sided hypothesis test      176
Bayesian estimator, binomial proportion $\pi$       152
Bayesian estimator, normal $\sigma$       308
Bayesian estimator, normal mean $\mu$       224
Bayesian hypothesis test, one-sided, binomial proportion $\pi$       173
Bayesian hypothesis test, one-sided, difference between normal means $\mu_1 - \mu_2$       242
Bayesian hypothesis test, one-sided, normal mean $\mu$       230
Bayesian hypothesis test, one-sided, normal standard deviation $\sigma$       310
Bayesian hypothesis test, one-sided, Poisson parameter $\mu$       193
Bayesian hypothesis test, one-sided, regression slope $\beta$       280
Bayesian hypothesis test, two-sided, binomial proportion $\pi$       176
Bayesian hypothesis test, two-sided, difference between normal means $\mu_1 - \mu_2$       243 245
Bayesian hypothesis test, two-sided, normal mean $\mu$       234
Bayesian hypothesis test, two-sided, Poisson parameter $\mu$       194
Bayesian hypothesis test, two-sided, regression slope $\beta$       281
Bayesian inference for standard deviation      297
Bayesian universe      66 101 112
Bayesian universe, parameter space dimension      69 74 101 112
Bayesian universe, reduced      67 102 113
Bayesian universe, sample space dimension      69 74 101 112
Beta distribution      127
Beta distribution, density      128
Beta distribution, mean      128
Beta distribution, normal approximation      133
Beta distribution, shape      127
Beta distribution, variance      129
Bias, response      16
Bias, sampling      14
Binomial distribution      83 96 141 353
Binomial distribution, characteristics of      84
Binomial distribution, mean      84
Binomial distribution, probability function      84
Binomial distribution, table      361—363
Binomial distribution, variance      85
Blackjack      71 76
Boxplot      30 48
Boxplot, stacked      37
Central limit theorem      132 199
Chi-squared distribution      359
Conditional probability      73
Conditional random variable, continuous, conditional density      134
Conjugate family of priors, binomial observation      144 155
Conjugate family of priors, Poisson observation      185—181 86
Continuous random variable      121
Continuous random variable, probability density function      123 136
Continuous random variable, probability is area under density      124 136
Correlation, bivariate data set      46 49
Covariance, bivariate data set      46
Cumulative frequency polygon      35 48
Deductive logic      56
Degrees of freedom      43
Degrees of freedom, simple linear regression      280
Degrees of freedom, two samples unknown equal variances      244
Degrees of freedom, two samples unknown unequal variances, Satterthwaite’s adjustment      246
Degrees of freedom, unknown variance      2 13
Derivative      339
Derivative, higher      341
Derivative, partial      349
Designed experiment      18 22
Designed experiment, completely randomized design      18 22 24—25
Designed experiment, randomized block design      19 22 24—25
Differentiation      339
Discrete random variable      77—78 95
Discrete random variable, expected value      80
Discrete random variable, probability distribution      77 80 95
Discrete random variable, variance      81
Dotplot      30
Dotplot, stacked      37
Equivalent sample size, beta prior      147
Equivalent sample size, gamma prior      187
Equivalent sample size, normal prior      209
Estimator, frequentist      163 223
Estimator, mean squared error      164
Estimator, minimum variance unbiased      164 224
Estimator, sampling distribution      163
Estimator, unbiased      164 224
Event      58
Event, complement      58 73
Events, independent      60—61
Events, intersection      58 73
Events, mutually exclusive (disjoint)      58 61 73
Events, partitioning universe      64
Events, union      58 72
Expected value, continuous random variable      125
Expected value, discrete random variable      80 95
Experimental units      17—18 20 24
Finite population correction factor      86
Five number summary      3 1
Frequency table      33
Frequentist approach to statistics      5 11
Frequentist confidence interval      167
Frequentist confidence interval normal mean $\mu$       226
Frequentist confidence interval regression slope $\beta$       280
Frequentist confidence intervals, relationship to frequentist hypothesis tests      175
Frequentist hypothesis test, level of significance      171
Frequentist hypothesis test, null distribution      172
Frequentist hypothesis test, one-sided, binomial proportion $\pi$       171
Frequentist hypothesis test, one-sided, normal mean $\mu$       229
Frequentist hypothesis test, p-value      172
Frequentist hypothesis test, rejection region      172
Frequentist hypothesis test, two-sided, binomial proportion $\pi$       173
Frequentist hypothesis test, two-sided, normal mean $\mu$       232
Frequentist, interpretation of probability and parameters      161
Function      333
Function, antiderivative      342
Function, continuous      337
Function, continuous, maximum and minimum      338
Function, differentiable      339
Function, differentiable, critical points      341
Function, graph      334
Function, limit at a point      335

Fundamental theorem of calculus      346
Gamma distribution      129
Gamma distribution, density      130
Gamma distribution, mean      130
Gamma distribution, shape      129
Gamma distribution, variance      131
histogram      34—35 48
Hypergeometric distribution      85
Hypergeometric distribution, mean      86
Hypergeometric distribution, probability function      86
Hypergeometric distribution, variance      86
Integration      342
Integration, definite integral      342 345 347
Integration, multiple integral      350
Interquartile range, data set      42 49
Interquartile range, posterior distribution      152
Inverse chi-squared distribution      310
Inverse chi-squared distribution, density      298
Jeffreys' prior binomial      145
Jeffreys' prior normal mean      206
Jeffreys' prior normal variance      302
Jeffreys' prior Poisson      185
Joint likelihood, linear regression sample      276
Joint random variables, conditional probability      92
Joint random variables, conditional probability distribution      93
Joint random variables, continuous      134
Joint random variables, continuous and discrete      135
Joint random variables, continuous, joint density      134
Joint random variables, continuous, marginal density      134
Joint random variables, discrete      89
Joint random variables, discrete, joint probability distribution      89
Joint random variables, discrete, marginal probability distribution      89
Joint random variables, independent      91
Joint random variables, joint probability distribution      96
Joint random variables, marginal probability distribution      96
Likelihood, binomial      108
Likelihood, binomial, proportional      111
Likelihood, discrete parameter      103—104
Likelihood, events partitioning universe      66
Likelihood, mean, single normal observation      200
Likelihood, multiplying by constant      67 111
Likelihood, normal mean, random sample of size n      203
Likelihood, normal mean, using density function      201
Likelihood, normal mean, using ordinates table      200
Likelihood, normal sample mean $\bar{y}$       203
Likelihood, normal variance      299
Likelihood, Poisson      184
Likelihood, regression, intercept $\alpha_{\bar{x}}$       277
Likelihood, regression, slope $\beta$       277
Likelihood, sample mean from normal distribution      209
Logic, deductive      72
Logic, inductive      72
Lurking variable      2 10 19—20 25
Marginalization      2 14 282
Marginalizing out the mixture parameter      321
Mean of a linear function      82 96
Mean squared error      225
Mean, continuous random variable      125
Mean, data set      40 49
Mean, difference between random variables      92 96
Mean, discrete random variable      80
Mean, grouped data      40
Mean, sum of random variables      90 96
Mean, trimmed      42 49
Measures of location      39
Measures of spread      42
Median, data set      41 47 49
Mixture prior      3 17
Monte Carlo study      7 11 23—24 71
Nonsampling errors      16
Normal distribution      131
Normal distribution, area under standard normal density      354 364
Normal distribution, density      131
Normal distribution, mean      131
Normal distribution, ordinates of standard normal density      355 365
Normal distribution, shape      131
Normal distribution, standard normal probabilities      132
Normal distribution, variance      13 1
Nuisance parameter      7 282 297
Nverse chi-squared distribution      298
Observational study      17 22
Ockham's razor      4 170
Odds ratio      69
Order statistics      30 32 47
Outcome      58
Outlier      40
PARAMETER      5—6 14 21 69
Parameter space      69
Plausible reasoning      56 72
Point estimation      163
Poisson distribution      86 183 358
Poisson distribution, characteristics of      87
Poisson distribution, mean      88
Poisson distribution, probability function      87
Poisson distribution, table      367—368
Poisson distribution, variance      88
Population      5 14 21
Posterior distribution      6
Posterior distribution, discrete parameter      103—101 04
Posterior distribution, normal with discrete prior      200
Posterior distribution, regression slope $\beta$       278
Posterior mean as an estimate for $\pi$       152
Posterior mean square of an estimator      152
Posterior mean, beta distribution      150
Posterior mean, gamma distribution      189
Posterior median as an estimate for $\pi$       152
Posterior median, beta distribution      150
Posterior median, gamma distribution      189
Posterior mode, beta distribution      150
Posterior mode, gamma distribution      189
Posterior probability distribution, binomial with discrete prior      110
Posterior probability of an unobservable event      66
Posterior standard deviation      151
Posterior variance, beta distribution      151
Pre-posterior analysis      8 11
Precision, normal, $\bar{y}$       209
Precision, normal, observation      208
Precision, normal, posterior      208
Precision, normal, prior      208
Precision, regression, likelihood      278
Precision, regression, posterior      278
Precision, regression, prior      278
Predictive distribution, normal      2 14
Predictive distribution, regression model      281
Prior distribution      6
Prior distribution, choosing beta prior for $\pi$ , matching location and scale      146 155
Prior distribution, choosing beta prior for $\pi$ , vague prior knowledge      146
Prior distribution, choosing inverse chi-squared prior for $\sigma^2$       303
Prior distribution, choosing normal prior for $\mu$       209
Prior distribution, choosing normal priors for regression      277
Prior distribution, constructing continuous prior for $\mu$       210
Prior distribution, constructing continuous prior for $\pi$       147 155
Prior distribution, discrete parameter      102
Prior distribution, multiplying by constant      67 111
Prior distribution, uniform prior for $\pi$       155
Prior probability for an unobservable event      66
probability      58
Probability distribution, conditional      93
Probability distribution, continuous random variable, probability density function      123
Probability, addition rule      60
Probability, axioms      59 72
Probability, conditional      62
Probability, conditional, independent events      63
Probability, degree of belief      69
Probability, joint      60
Probability, law of total probability      64 73
Probability, long run relative frequency      68
Probability, marginal      61
Probability, multiplication rule      63 73 94
Quartiles, data set      30 48

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