Электронная библиотека Попечительского советамеханико-математического факультета Московского государственного университета
 Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум Авторизация Поиск по указателям     Bolstad W.M. — Introduction to Bayesian Statistics Обсудите книгу на научном форуме Нашли опечатку?Выделите ее мышкой и нажмите Ctrl+Enter 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 302 Bayes' theorem, normal observations known mean, Jeffreys' prior for 302 Bayes' theorem, normal observations known mean, positive uniform prior for 301 Bayes' theorem, normal observations with known variance, continuous prior for 205 Bayes' theorem, normal observations with known variance, discrete prior for 199 Bayes' theorem, normal observations with known variance, flat prior for 206 Bayes' theorem, normal observations with known variance, mixture prior      324 Bayes' theorem, normal observations with known variance, normal prior for 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 153 Bayesian credible interval, difference between normal means , equal variances      240 Bayesian credible interval, difference between normal means , unequal variances      246 Bayesian credible interval, difference between proportions 248 Bayesian credible interval, normal mean 21 1 Bayesian credible interval, normal standard deviation 309 Bayesian credible interval, Poisson parameter 192 Bayesian credible interval, regression slope 280 Bayesian credible interval, used for Bayesian two-sided hypothesis test      176 Bayesian estimator, binomial proportion 152 Bayesian estimator, normal 308 Bayesian estimator, normal mean 224 Bayesian hypothesis test, one-sided, binomial proportion 173 Bayesian hypothesis test, one-sided, difference between normal means 242 Bayesian hypothesis test, one-sided, normal mean 230 Bayesian hypothesis test, one-sided, normal standard deviation 310 Bayesian hypothesis test, one-sided, Poisson parameter 193 Bayesian hypothesis test, one-sided, regression slope 280 Bayesian hypothesis test, two-sided, binomial proportion 176 Bayesian hypothesis test, two-sided, difference between normal means 243 245 Bayesian hypothesis test, two-sided, normal mean 234 Bayesian hypothesis test, two-sided, Poisson parameter 194 Bayesian hypothesis test, two-sided, regression slope 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 226 Frequentist confidence interval regression slope 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 171 Frequentist hypothesis test, one-sided, normal mean 229 Frequentist hypothesis test, p-value      172 Frequentist hypothesis test, rejection region      172 Frequentist hypothesis test, two-sided, binomial proportion 173 Frequentist hypothesis test, two-sided, normal mean 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 203 Likelihood, normal variance      299 Likelihood, Poisson      184 Likelihood, regression, intercept 277 Likelihood, regression, slope 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 278 Posterior mean as an estimate for 152 Posterior mean square of an estimator      152 Posterior mean, beta distribution      150 Posterior mean, gamma distribution      189 Posterior median as an estimate for 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, 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 , matching location and scale      146 155 Prior distribution, choosing beta prior for , vague prior knowledge      146 Prior distribution, choosing inverse chi-squared prior for 303 Prior distribution, choosing normal prior for 209 Prior distribution, choosing normal priors for regression      277 Prior distribution, constructing continuous prior for 210 Prior distribution, constructing continuous prior for 147 155 Prior distribution, discrete parameter      102 Prior distribution, multiplying by constant      67 111 Prior distribution, uniform prior for 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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