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| 內容簡介： |
●國內第一本解說STaTa——多達45種貝葉斯迴歸分析運用的教科書。
●STaTa+AI+Bayesian超強組合，接軌世界趨勢，讓您躋身大數據時代先驅。
●超強統計軟體STaTa，簡單易懂，功能齊全，廣獲肯定。
●結合「理論、方法、統計」，讓讀者能精準使用Bayesian迴歸。
●內文包含大量圖片示意，配合隨書光碟資料檔，實地演練，學習更有效率。
5G時代的來臨，聯手AI人工智慧邁入嶄新紀元，未來可預見日常將出現更密集的AI科技，更可能改變產業型態、生活體驗，甚至是人類的思考模式。
AI又稱機器智能，迄今已是一門顯學，屬於自然科學和社會科學的交集。其中機器學習演算法及Bayesian後驗機率等貝氏推論，不僅適合傳統科學研究法，更適合於當今大數據bigdata時代的來臨。
本書詳細說明STaTa運用中，45種Bayesian迴歸，以及實務上已非常成熟的AI統計應用技術，可供人工智慧、機器學習等自然科學和社會科研究者使用。內文包含大量圖片示意，搭配隨書附贈光碟，簡潔易懂，學習效果更顯著。
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| 關於作者： |
張紹勳
學歷：國立政治大學資訊管理博士
現職：國立彰化師大專任教授
經歷：致理技術專任副教授
張任坊
學歷：國立海洋大學商船系
現職：長榮海運三副
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| 目錄：
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自序
Chapter01人工智慧的基礎：機器學習理論及貝氏定理Bayes＂theorem1
1-1人工智慧ArtificialIntelligence,AI.........................................................................9
1-1-1AI研究的議題.............................................................................................10
1-1-2強人工智慧vs.弱人工智慧.......................................................................14
1-1-3AI研究方法.................................................................................................15
1-2機器學習machinelearning...................................................................................19
1-2-1監督vs.非監督機器學習...........................................................................24
1-2-2機器學習的演算法algorithm...................................................................26
1-2-3何謂Features≈自變數、Training、Label≈類別依變數？...............40
1-2-4監督機器學習 多變數線性迴歸machinelearning:linearregressionwith
multiplevariables........................................................................................42
1-2-5機器學習：梯度下降演算法gradientdescentalgorithm........................67
1-2-6機器學習：特徵縮放featurescaling.......................................................81
1-3參數估計：最大概似估計、最大後驗Maxposterior、貝葉斯估計................81
1-3-1何謂參數估計？..........................................................................................83
1-3-2a估計法一：最大概似估計MLE≠概似比LR....................................87
1-3-2b最大概似估計法MLE做分類.................................................................97
1-3-3估計法二：最大後驗Maxposterior估計............................................101
1-3-4估計法三：貝葉斯估計...........................................................................105
1-4期望最大化EM演算法.....................................................................................107
Chapter02貝葉斯Bayesian迴歸有45種117
2-1貝氏定理與條件機率重點整理......................................................................118
2-1-1貝氏機率Bayesianprobability..............................................................121
2-1-2貝氏Bayes定理、條件機率.................................................................123
2-2貝葉斯推論Bayesianinference.........................................................................136
2-2-1貝葉斯法則Bayesianrule.....................................................................138
2-2-2推論「排他性和窮舉命題」的可能性inferenceoverexclusiveand
exhaustivepossibilities............................................................................143
2-2-3a貝葉斯推論之數學性質mathematicalproperties.................................145
2-2-3b貝葉斯決策理論.......................................................................................153
2-2-4貝葉斯推論之案例...................................................................................160
2-2-5頻率統計和決策理論之貝葉斯模型，誰優？BayesianInformation
CriterionBIC..........................................................................................165
2-2-6貝葉斯認識論Bayesianepistemology..................................................167
2-2-7貝葉斯推理的影響因素...........................................................................170
2-3常見的分布有15種..............................................................................................175
2-4STaTalikelihood-basedBayesian迴歸有45種...................................................204
2-4-1STaTa共12類：45種Bayesian迴歸....................................................205
2-4-2Metropolis-Hastings演算法bayesmh指令和MonteCarlo...............215
2-4-3貝葉斯線性迴歸的基本原理...................................................................225
2-5貝葉斯統計及正規化BayesianstatisticsandRegularization...........................228
2-5-1過度適配vs.不足適配overfittingandunderfitting.............................229
2-5-2Bayesianstatistics及正規化regularization...........................................231
2-5-3最佳成本函數之正規化optimizecostfunctionbyregularization.......232
Chapter03最大概似ML各家族family：機器學習技術237
3-1最大概似ML之Regression家族family.......................................................238
3-1-1迴歸分析介紹...........................................................................................239
3-1-2線性迴歸linearregression.....................................................................241
3-2多元迴歸的自變數選擇法有三：子集合選取法、正規化、資訊準則法
bayesstatsic指令...............................................................................................246
3-2-1迴歸模型與正規項regulation：Ridge迴歸、Lasso迴歸原理..........253
3-2-2脊迴歸／嶺迴歸ridge的原理：多重共線性ridgeregress外掛指令
...................................................................................................................262
3-2-3a迴歸正規項regulation：lasso迴歸、Ridg迴歸、elastic-net迴歸
lassoregress、ridgeregress、elasticregress外掛指令..........................266
3-2-3b機器學習演算法：套索迴歸LassoRegrissionlassoregress、lasso2、
elasticregress指令..................................................................................283
3-2-4a機器學習演算法：脊迴歸RidgeRegressionrxridge、rxrcrlq、rxrmaxl
等14個指令...........................................................................................288
3-2-4bRidge迴歸分析：解決共線性rxridg外掛指令.................................293
3-2-5機器學習演算法：彈性網路多工Lasso迴歸multitaskLasso
elasticregress指令.................................................................................299
3-2-6邏輯斯迴歸logisticregression..............................................................301
3-3機器學習法：隨機森林外掛指令randomforest、支援向量機外掛指令
svmachines............................................................................................................314
3-3-1機器學習法：隨機森林外掛指令：randomforest.............................314
3-3-2機器學習法：支援向量機SVM外掛指令：svmachines...................326
3-4最大概似的Kernel-Based家族：小樣本、非線性及高維模型識別................349
3-4-1非線性分類之核函數...............................................................................353
3-4-2支援向量機SVM分類器：原型、對偶型、核技巧、現代方法......354
3-4-3a支援向量機SVM原理：小樣本、非線性及高維模型識別..............361
3-4-3b支援向量機做分類svmachines外掛指令...........................................368
3-4-4核迴歸／分段加權迴歸kernelregression：非單調函數lpoly、
npregress、teffects指令.........................................................................377
3-5最大概似ML之Bayes-Based家族前導字「bayes:某迴歸」指令.........399
3-5-1判別模型discriminativemodel與生成模型generativemodel.........404
3-5-2高斯判別分析Gaussiandiscriminantanalysis......................................407
3-5-3樸素貝葉斯naivebayes演算法............................................................412
Chapter04貝葉斯Bayesian線性迴歸之原理421
4-1貝葉斯Bayesian分析........................................................................................425
4-2參數估計：最大概似估計、最大後驗估計、貝葉斯估計................................430
4-3貝葉斯Bayesian線性迴歸................................................................................433
4-3-1a線性迴歸之參數估計最小平方法OLS................................................433
4-3-1b貝葉斯Bayesian迴歸之原理................................................................436
4-3-2貝葉斯線性迴歸：參數分布、預測分布、等價核...............................440
4-3-3貝葉斯線性迴歸：學習過程、優缺點、貝葉斯脊迴歸.......................447
4-4貝葉斯多元線性迴歸之原理Bayesianmultivariatelinearregression.............451
Chapter05Bayes線性迴歸「bayes:regress」、「bayesgraphdiagnostics」、「bayesstatsic」指令457
5-1線性Bayesian迴歸先rsquare、再「bayes:regression」指令.....................459
5-1-1OLS先挑所有自變數的最佳組合再Bayes線性迴歸.....................460
5-1-2OLS先挑所有自變數的最佳組合，再Bayes線性迴歸
bayes:regressyx1x2x3.......................................................................477
5-2方法一Bayes線性迴歸bayes:regress 指令...............................................483
5-2-1Bayes線性迴歸及預測值：使用內定概似及先驗uninformativedata
bayes:regress 指令...........................................................................483
5-2-2Bayes線性迴歸：自定概似及先驗informativedatabayes:regress
指令.....................................................................................................491
5-3方法二Bayes線性迴歸bayesmh:regress 指令.........................................501
5-4線性Bayesian迴歸模型改用bayesmh指令.................................................512
5-4-1Bayesian估計之原理及實作「bayes:regress」指令.........................516
5-4-2MCMC收斂性convergence及假設檢定hypothesestesting............525
5-4-3先驗Priors：Gibbs採樣sampling.....................................................529
5-4-4自定先驗Custompriors.........................................................................533
5-5Bayes迴歸：縮減模型vs.完全模型，誰優？bayesmh、bayesstatsic指令...535
Chapter06Metropolis-Hastings演算法之Bayesian模型bayesmh指令545
6-1bayesmh指令：「線性vs.非線性」、「單變量vs.多變量」、「連續vs.間斷」
模型有8大類........................................................................................................552
6-2bayesmh指令之範例............................................................................................573
6-2-1範例1：OLS線性迴歸regressvs.Bayesian線性迴歸bayes:regress
...................................................................................................................574
6-2-2範例2：Bayesiannormallinearregressionwithnoninformativeprior
未自定參數的分布..............................................................................583
6-2-3範例3：Bayesianlinearregressionwithinformativeprior自定參數
的分布.....................................................................................................588
6-2-4範例4：Bayesiannormallinearregressionwithmultivariateprior........591
6-2-5範例5：檢查收斂性Checkingconvergence........................................594
6-2-6範例6：貝氏事後估計值摘要Postestimationsummaries..................599
6-2-7範例7：敵對模型的比較Modelcomparison......................................601
6-2-8範例8：假設檢定Hypothesistestingbayestestmodel、interval
interval.....................................................................................................603
Chapter07Bayesian邏輯斯模型、多項邏輯斯模型bayes:logistic、bayes:mlogit指令607
7-1邏輯斯迴歸原理....................................................................................................608
7-2Bayesianlogit迴歸分析bayes:logit、bayes:logistic指令...........................612
7-2-1範例1：貝氏Logistic迴歸bayes:logit指令.....................................614
7-2-2範例2：自定之資訊先驗informativeprior：貝氏Logistic迴歸
bayes:logit指令....................................................................................618
7-3對照組：multinomiallogistic迴歸分析bayes:mlogit指令...........................621
7-3-1多項multinomial邏輯斯迴歸之原理...................................................622
7-3-2MultinomialLogit迴歸分析：職業選擇種類mlogit指令................628
7-3-3多項邏輯斯迴歸分析：乳房攝影mammograph選擇的因素
mlogit指令............................................................................................637
7-4實驗組：Bayesianmultinomiallogistic迴歸分析：健康保險bayes:mlogit
指令.....................................................................................................................650
Chapter08聯立方程式：Bayesianmultivariate迴歸bayes:mvreg指令659
8-1多變量Bayesian迴歸分析bayes:mvreg指令................................................660
Chapter09非線性迴歸：廣義線性模型GLMBaye:glm指令667
9-1廣義線性模型之原理............................................................................................668
9-2當依變數是比例proportion時，如何做迴歸glm指令？..........................671
9-3廣義線性迴歸glm、baye:glm指令................................................................684
Chapter10Survival模型baye:streg指令693
10-1存活分析的原理....................................................................................................694
10-1-1存活分析之定義.......................................................................................695
10-1-2為何存活分析是臨床研究最重要的統計法？.......................................698
10-1-3存活分析之三種研究目標.......................................................................703
10-2存活分析Bayesian迴歸baye:streg指令........................................................704
Chapter11多層次multilevel模型bayes:mixed指令717
11-1多層次模型的原理................................................................................................720
11-2Bayesian多層次模型：重複測量bayes:mixed指令.....................................726
Chapter12計數count模型、Zero-Inflated模型bayes:tpoisson、baye:zinb指令743
12-1傳統原理：Count依變數：Zero-InflatedPoisson迴歸vs.negativebinomial
迴歸........................................................................................................................744
12-1-1Poisson分配.............................................................................................745
12-1-2負二項分配NegativeBinomialDistribution.........................................751
12-1-3零膨脹Zero-InflatedPoisson分配.........................................................753
12-2單層次：Zero-InflatedPoisson迴歸vs.負二項迴歸zip、zinb指令............755
12-2-1傳統：Zero-InflatedPoisson迴歸vs.負二項迴歸zip、zinb指令...755
12-2-2BayesianPoisson迴歸bayes:poisson、Bayesian零膨脹Poisson
迴歸bayes:zip指令.............................................................................776
12-2-3Zero-Inflatednegativebinomial模型bayes:zinb指令.......................792
12-3Zero-Inflatedorderedprobitregression練習：釣魚zip指令..........................804
12-4零膨脹Orderedprobit迴歸分析：抽菸嚴重度zioprobit指令......................805
12-5截斷truncatedPoisson迴歸分析bayes:tpoisson指令................................813
12-5-1截斷迴歸truncatedregressiontruncreg指令.....................................813
12-5-2Bayesian截斷Poisson迴歸truncatedregressionbayes:tpoisson指令
...................................................................................................................832
Chapter13Bayesian自我迴歸模型bayes:regressyL1.y指令841
13-1時間列序之統計：自我迴歸autoregressivemodels........................................842
13-1-2ARIMA建構模型之步驟.........................................................................844
13-2穩定數列之自我迴歸模型AR..........................................................................846
13-2-1AR1模型................................................................................................848
13-2-2AR2模型................................................................................................854
13-2-3何謂穩定性定態？.............................................................................858
13-3Bayesian自我迴歸之建模過程bayes:regressyL.y指令.............................859
參考文獻875
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