Introduction_to_Statistical_Thought

R在统计里应用的中级书籍。推荐有一定概率、R基础的读者参考。CONTENTSLIST OF FIGURESIST OF TABLESPREfaCEPROBABILITY1. 1 BASIC PROBABILITY1.2 PROBABILITY DENSITIES...............1.3 PARAMETRIC FAMILIES OF DISTRIBUTIONS131.3.1 THE BINOMIAL DISTRIBUTION141.3.2 THE POISSON DISTRIBUTION171.3.3 THE EXPONENTIAL DISTRIBUTION201.3.4 THE NORMAL DISTRIBUTION4 CENTERS, SPREADS, MEANS, AND MOMENTS291.5 JoINT, MARGINAL AND CONDITIONAL PROBABILITY1.6 ASSoCIATION, DEPENDENCE, INDEPENDENCE507 SIMULATiON51.7.1 CALCULATING PROBABILITIES57.2 EVALUATING STATISTICAL PROCEDURES1. 8 RI1.9 SOME RESULTS FOR LARGE SAMPLES1.10 EXERCISES802 MODES OF INFERENCE9412. 1 DATA942.2 DATA DESCRIPTION952.2.1 SUMMARY STATISTICS95CONTENTS2.2.2 DISPLAYING DISTRIBUTIONS1012.2.3 EXPLORING RELATIONSHIPS1142.3 LIKELIHOOD1332.3.1 THE LIKELIHOOD FUNCTION1332.3.2 LIKELIHOODS FROM THE CENTRAL LIMIT THEOREM1392.3.3 LIKELIHOODS FOR SEVERAL PARAMETERS14412. 4 ESTIMATION153243 THE SAMPLING DISTRIBUTION OF AN ESTIMATORA,∵·2. 4. 1 THE MAXIMUM LIKELIHOOD ESTIMATE1532.4.2 ACCURACY OF ESTIMATION1551582.5 BAYESIAN INFERENCE1632.6 PREDiCtiON1732.7 HYPOTHESIS TESTING......17712. 8 EXERCISES1913 REGREssiON阝.ⅠⅠ NTRODUCTION2013.2 NORMAL LINEAR MODELS2093.2.1 INTRODUCTION2093.2.2 INFERENCE FOR LINEAR MODELS2203. 3 GENERALIZED LINEAR MODELS2333.3.1 LOGISTIC REGRESSION2333.3.2 POISSON REGRESSION2433.4 PREDICTIONS FROM REGRESSION2473.5 ExERCISES2514 MORE PROBABILITY2624.1 MORE PROBABILITY DENSITY2624.2 RANDOM VECTORS2634.2.1 DENSITIES OF RANDOM VECTORS2634.2.2 MOMENTS OF RANDOM VECTORSI265耳,2.3 FUNCTIONS OF RANDOMⅤ ECTORS....2654.3 REPRESENTING DISTRIBUTIONS2694.4 EXERCISES274⑤ SPECIAL DISTRIBUTIONS27715.1 BINOMIAL AND NEGATIVE BINOMIALI2775.2 MULTINOMIAL···2873 poissON垂·289CONTENTS5.4 UNIFORM3025.5 GAMMA, EXPONENTIAL, CHI SQUARE3035.6 BETA3105.7 NORMAL3135.7.1 THE UNIVARIATE NORMAL DISTRIBUTION3135.7.2 THE MULTIVARIATE NORMAL DISTRIBUTION3185.7.3 MARGINAL, CONDITIONAL, AND RELATED DISTRIBUTIONS3255. 8 THE DISTRIBUTION3285.9 ExERCISES3336 BAYESIAN STATISTIC34416.1 MULTIDIMENSIONAL BAYESIAN ANALYSIS3446.2 METROPOLIS, METROPOLIS-HASTINGS, AND GIBBS35616.3 ExERCISES3757 MORE MODELS3807.1 RANDOM EFFECTS3807.2 TIME SERIES AND MARKOY CHAINS.....3941. 3 SURVIVAL ANALYSIS17. 4 EXERCISES4148 MATHEMATICAL STATISTICS4178.1 PROPERTIES OF STATISTICS4178.1.1 SUFFICIENCY4178. 1.2 CONSISTENCY. BIAS, AND MEAN-SQUARED ERROR4208.2Ⅰ NFORMATION4258. 3 EXPONENTIAL FAMILIES42818 4 ASYMPToTIcS垂·4308. 4. 1 MODES OF CONVERGENCE4368. 4.2 THE S-METHOD4408.4.3 THE ASYMPTOTIC BEHAVIOR OF ESTIMATORS44318.5 ExERCISES448BIBLIOGRApHy453LIST OF FIGURES1.1 PDF FOR TIME ON HOLD AT HELP LINE1.2 Pr FOR THE OUTCOME OF A SPINNER1.3 (A): OCEAN TEMPERATURES; (B): IMPORTANT DISCOVERIES1. 4 CHANGE OF VARIABLES1.5 BINOMIAL PROBABILITIES1.6 P[X=3 AS A FUNCTION OFA7 EXPONENTIAL DENSITIES211. 8 NORMAL DENSITIES241.9 OCEAN TEMPERATURES AT 45N, 30W, 100OM DEPTH51.10 NORMAL SAMPLES AND NORMAL DENSITIES1. 11 HYDROGRAPHIC STATIONS OFF THE COAST OF EUROPE AND AFRICA301. 12 WATER TEMPERATURES1.13 WATER TEMPERATURES WITH STANDARD DEVIATIONS36I.I4 TWo PDF' S WITH土AND±2SDs381.15 PERMISSIBLE VALUES OF N AND X1. 16 FEATURES OF THE JOINT DISTRIBUTION OF(X, Y)I1. 17 LENGTHS AND WIDTHS OF SEPALS AND PETALS OF 150 IRIS PLANTS51口18 CORRELATIONS541. 19 1000 SIMULATIONS OF FOR N SIM=50, 200, 1000591.20 1000 SIMULATIONS OF O UNDER THREE PROCEDURES1.21 MONTHLY CONCENTRATIONS OF CO, AT MAUNA LOA641.22 1000 SIMULATIONS OF A FACE EXPERIMENT1.23 HISTOGRAMS OF CRAPS SIMULATIONSQUANTILI9812.2 HISTOGRAMS OF TOOTH GROWTH1022.3 HISTOGRAMS OF TOOTH GROWTH103LIST OF FIGURES12.4 HISTOGRAMS OF TOOTII GROWTH2.5 CALORIE CONTENTS OF BEEF HOT DOGS1082.6 STRIP CHART OF TOOTH GROWTH1102.7 QUIZ SCORES FROM STATISTICS 103113QQ PLOTS OF WATER TEMPERATURES (C)AT 1000M DEPTH11512.9 MOSAIC PLOT OF UCBADMISSIONS垂·番1192.10 MOSAIC PLOT OF UCBADMISSIONS1202.11 OLD FAITHFUL DATA.1232. 12 WAITING TIME VERSUS DURATION IN THE OLD FAITHFUL DATASET1242. 13 TIME SERIES OF DURATION AND WAITING TIME AT OLD FAITHFUL.........1252.14 TIME SERIES OF DURATION AND WAITING TIME AT OLD FAITHFUL12612. 15 TEMPERATURE VERSUS LATITUDE FOR DIFFERENT VALUES OF LONGITUDE1282. 16 TEMPERATURE VERSUS LONGITUDE FOR DIFFERENT VALUES OF LATITUDE1292. 17 SPIKE TRAIN FROM A NEURON DURING A TASTE EXPERIMENT. THE DOTS SHOW THETIMES AT WHICH THE NEURON FIRED. THE SOLID LINES SHOW TIMES AT WHICH THERAT RECEIVED A DROP OF A. 3 M SOLUTION OF NACL1312. 18 LIKELIHOOD FUNCTION FOR THE PROPORTION OF RED CARSI1342.19 t(0) AFTER >Yi=40 IN 60 QUADRATS.1372.20 LIKELIHOOD FOR SLATER SCHOOL1382.21 MARGINAL AND EXACT LIKELIHOODS FOR SLATER SCHOOL1412.22 MARGINAL LIKELIHOOD FOR MEAN CEO SALARY1432.23 FACE EXPERIMENT: DATA AND LIKELIHOOD14624 LIKELIHOOD FUNCTION FOR QUIZ ScORES1482.25 LOG OF THE LIKELIHOOD FUNCTION FOR(, er)IN EXAMPLE 2. 131522.27 SAMPLING DISTRIBUTION OF THE SAMPLE MEAN AND MEDIAN PS2.26 LIKEL IHOOD FUNCTION FOR THE PROBABILITY OF WINNING CRAPS1571592.28 HISTOGRAMS OF THE SAMPLE MEAN FOR SAMPLES FROM BIN(n,D)·1612.29 PRIOR, LIKELIHOOD AND POSTERIOR IN THE SEEDLINGS EXAMPLEl682.30 PRIOR, LIKELIHOOD AND POSTERIOR DENSITIES FOR WITH n= 1, 4, 1617031 PRIOR, LIKELIHOOD AND POSTERIOR DENSITIES FOR A WITH n =6017132 PRIOR, LIKELIHOOD AND POSTERIOR DENSITY FOR SLATER SCHOOLI1722.33 PLUG-IN PREDICTIVE DISTRIBUTION FOR SEEDLINGS1742.34 PREDICTIVE DISTRIBUTIONS FOR SEEDLINGS AFTER n=0, 1, 601782.35 PDF OF THE BIN(100, 5) DISTRIBUTION18212.36 PDES OF THE BIN(100, 5)(DOTS)AND N(50, 5)(LINE)DISTRIBUTIONS1832.37 APPROXIMATE DENSITY OF SUMMARY STATISTIC W1852.38 NUMBER OF TIMES BABOON FATHER HELPS OWN CHILD1892.39 HISTOGRAM OF SIMULATED VALUES OF WTOT......LIST OF FIGURES3.1 FOUR REGRESSION EXAMPLES202阝.21970 DRAFT LOTTERY DRAFT NUMBERⅴ 'S DAY OF YEAR2053.3 DRAFT NUMBER VS DAY OF YEAR WITH SMOOTHERS2063.4 TOTAL NUMBER OF NEW SEEDLINGS 1993-1997, BY QUADRAT.3.5 CALORIE CONTENT OF HOT DOG2103.6 DENSITY ESTIMATES OF CALORIE CONTENTS OF HOT DOGS2123.9 LIKelIhoo0 D FUNCTIONS FOR(46M,p) IN THE HOT DOG EXAMPLE.)∵、·3. 7 THE PLANTGROWTH DATA2143. 8 ICE CREAM CONSUMPTION VERSUS MEAN TEMPERATURE212273.10 PAIRS PLOT OF THE MTCARS DATA2293.11 MTCARS-VARIOUS PLOTS2323.12 LIKELIHOOD FUNCTIONS FOR B1, Y1, 0) AND 2 IN THE MTCARS EXAMPLE]343. 13 PINE CONES AND O-RINGS2373.14 PINE CONES AND O-RINGS WITH REGRESSION CURVES2383.15 LIKELIHOOD FUNCTION FOR THE PINE CONE DATA3.16 ACTUAL VS FITTED AND RESIDUALS VS. FITTED FOR THE SEEDLING DATA2463. 17 DIAGNOSTIC PLOTS FOR THE SEEDLING DATA.2483. 18 ACTUAL MPG AND FITTED VALUES FROM THREE MODELS2503.19 HAPPINESS QUOTIENT OF BANKERS AND POETSI2554.1 THE(XI, X2) PLANE AND THE (Y1, Y2)PLANE2684.2 PMF'S, PDF'S, AND CDF's2715.1 THE BINOMIAL PME2835.2 THE NEGATIVE BINOMIAL PME..,,,.2865.3 PoISSON PMF FOR = 1, 4.16, 640925.4 RUTHERFORD AND GEIGER'S FIGURE 12975.5 NUMBERS OF FIRINGS OF A NEURON IN 150 MSEC AFIER FIVE DIFFERENT TASTANISTASTANTS: 1=MSG. IM; 2-MSG 3M; 3-NACL 1M; 4=NACL. 3M: 5=WA.TER. PANELS: AA STRIPCHART. EACH CIRCLE REPRESENTS ONE DELIVERY OF ATASTANT. B: A MOSAIC PLOT. C: EACH LINE REPRESENTS ONE TASTANT. D: LIKELIHOOD FUNCTIONS. EACH LINE REPRESENTS ONE TASTANT.2995.6 THE LINE SHOWS POISSON PROBABILITIES FOR =0.2; THE CIRCLES SHOW THEFRACTION OF TIMES THE NEURON RESPONDED WITH 0.1.. 5 SPIKES FOR EACHOF THE FIYⅤ E TASTANTS5.7 GAMMA DENSITIES30415.8 EXPONENTIAL DENSITIES15.9 BETA DENSITIES3125.10 WATER TEMPERATURES(C)AT 100OM DEPTH314LIST OF FIGURES5.11 BIVARIATE NORMAL DENSITY3215.12 BIVARIATE NORMAL DENSITY3235.13 t DENSITIES FOR FOUR DEGREES OF FREEDOM AND THE N(O, 1)DENSITY33216.1 POSTERIOR DENSITIES OF Bo AND BI IN THE ICE CREAM EXAMPLE USING THE PRIORFROM EQUATION 6. 4l6.2 NUMBERS OF PINE CONES IN 1998 AS A FUNCTION OF DBH3526.3 NUMBERS OF PINE CONES IN 1999 AS A FUNCTION OF DBH35316.4 NUMBERS OF PINE CONES IN 2000 AS A FUNCTION OF DBH3546.5 10,000 MCMC SAMPLES OF THE BE(5, 2)DENSITY. TOP PANEL: HISTOGRAM OFSAMPLES FROM THIE METROPOLIS-HASTINGS ALGORITHIM AND THE BE(5, 2)DEN-SITY.MIDDLE PANEL:6i PLOTTED AGAINST i. BOTTOM PANEL: P(0i)PLOTTEDAGainst i.3596.6 10,000 MCMC SAMPLES OF THE BE(5, 2) DENSITY. LEFT COLUMN: (0*10)U(-100,+100); RIGHT COLUMN:()=U(6-.00001,6+.000TOP: HISTOGRAM OF SAMPLES FROM THE METROPOLIS-HASTINGS ALGORITHM ANDTHE BE(5, 2) DENSITY. MIDDLE: 6; PLOTTED AGAINST i. BOTTOM: P(0i)PLOTTED6.7 TRACE PLOTS OF MCMC OUTPUT FROM THE PINE CONE CODE ON PAGE 6DAGAINST L3613656.8 TRACE PLOTS OF MCMC OUTPUT FROM THE PINE CONE CODE WITH A SMALLERPROPOSAL RADIUS.3666.9 TRACE PLOTS OF MCMC OUTPUT FROM THE PINE CONE CODE WITH A SMALLERL PROPOSAL RADIUS AND 100,000 ITERATIONS. THE PLOTS SHOW EVERY 10TH ITERATION····36716.10 TRACE PLOTS OF MCMC OUTPUT FROM THE PINE CONE CODE WITH PROPOSALFUNCTION G ONE AND 100,000 ITERATIONS. THE PLOTS SHOW EVERY 10'TH ITERatION.3696.11 PAIRS PLOTS OF MCMCOUTPUT FROM THE PINE CONES EXAMPLE3706.12 TRACE PLOTS OF MCMC OUTPUT FROM THE PINE CONE CODE WITH PROPOSALFUNCTION G, GROUP AND 100.000 ITERATIONS. THE PLOTS SHOW EVERY 10THITERATION3736. 13 PAIRS PLOTS OF MCMC OUTPUT FROM THE PINE CONIES EXAMPLE WITH PROPOSA16 14 POSTERIOR DENSITY OF B2 AND Y2 FROM EXAMPLE..G. GROUP3743757.1 PLOTS OF THE ORTHODONT DATA: DISTANCE AS A FUNCTION OF AGE, GROUPED BYSUBIECT SEPARATED BY SEX3827.2 PLOTS OF THE ORTHODONT DATA: DISTANCE AS A FUNCTION OF AGE, SEPARATED BYSUBJECT垂·385LIST OF FIGURES7.3 PERCENT BODY FAT OF MAJOR(BLUE)AND MINOR(PURPLE) Pheidole morrisiANTS AT THREE SITES IN TWO SEASONS.3897.4 RESIDUALS FROM MODEL. 7. 4 EACH POINT REPRESENTS ONE COLONY. THERE ISAN UPWARD TREND. INDICATING THE POSSIBLE PRESENCE OF COLONY EFFECTS3911.5 SOME TIME SERIES3967.6 Y+ VS. Y, FOR THE BEAVER AND PRESIDENTS DATA SETS3977.7 Y+k VS Y, FOR THE BEAVER DATA SET AND LAGS 0-5987. 8 COPLOT OF Y +I Y,-IIY, FOR THE BEAVER DATA SET4007.9 FIT OF CO2 DATA......7.10DAⅩCCLOSING PRICES4057. 11 DAX RETURNS4067. 12 SURVIVAL CURVE FOR BLADDER CANCER. SOLID LINE FOR PLACEBO; DASHED LINEFOR THIOTEPA4107. 13 CUMULATIVE HAZARD AND LOG(HIAZARD) CURVES FOR BLADDER CANCER. SOLIDLINE FOR THIOTEPA: DASHED LINE FOR PLACEBO.41318.1 MEAN SQUARED ERROR FOR ESTIMATING BINOMIAL 0. SAMPLE SIZE=5, 20.100, 1000. a=B=0: SOLID LINE. a=B=0.5: DASHED LINE. a=B=1:DOTTED LINE.C=B=4: DASH-DOTTED LINE.42418.2 THE BE(39, .01)DENSITY4348.3 DENSITIES OF Y4358.4 DENSITIES OF Zin43718.5 THE S-METHOD44118.6 TOP PANEL: ASYMPTOTIC STANDARD DEVIATIONS OF On AND On FOR Pr[X s a]THE SOLID LINE SHOWS THE ACTUAL RELATIONSHIP THE DOTTED LINE IS THE LINEOF EQUALITY. BOTTOM PANEL: THE RATIO OF ASYMPTOTIC STANDARD DEVIATIONS. 445