The Teaching of the Two Truths in the Nirvān4 a School of Chinese Buddhism

departmental bulletin pape

A Mixture-Modeling Approach to Estimating the Effect of Genes Affecting a Quantitative Trait from a Biparent Cross of Inbred Lines

本研究之結果顯示：在雜交試驗中，控制一數量性狀在兩親本間之差異的基因效應，可藉由取自兩親本(P1及P2)、雜交第二代(F2)，及/或雜交第一代(F1)的數據，利用混合分布模式之求配來估算。此外，由混合分布模式之求配也可以估計有關基因座間的重組率。 我們以一項大麥雜交試驗所獲得之株高數據(Leonard et al., 1957)為例，說明利用混合分布模式之求配估計這些參數的過程。首先，利用SAS/STAT所提供的集群分析程序(FASTCLUS)，將取自F2族群的觀測值分為幾個子群，再以各子群的參數估值做為求配混合分布模式的起始值，藉由限制的EM演算法尋找模式中各項參數的最大概度估值。其次，以McLachlan and Basford (1988)提出的方法計算近似訊識矩陣(approximate information matrix)的反矩陣，藉之估計各參數估值的變方變積矩陣，或藉由參數靴環自助法(parametric bootstrap method)獲得的99個由自助重抽樣品估得的估值，直接估算這些參數估值的變方變積矩陣。由此數例的結果顯示：這種估計程序比Powers之析出法(Powers, 1963)可以由數據中獲得更多的訊息。 我們也藉由模擬試驗探討各參數之點估值及信賴區間的統計特性。結果顯示，藉由混合分布模式之求配估計遺傳參數確實是一個可行的方法。當缺乏F1族群的試驗數據時，對估計的精密度影響不大。而在估算參數估值之變方變積矩陣時，則是以參數靴環自助法所求得的變方變積矩陣較佳。In this study we show that the effects of the genes contributing to the difference in a quantitative trait between the two parents (P1 and P2)in a cross experiment can be estimated by fitting a mixture model by the data sampled from P1, P2, F2, and/or F1 populations. Additionally, this approach also gives estimates for recombination rates among the loci involved. As an example, we applied this estimation procedure to analyze the data of plant height in a biparent cross of barley (Leonard et al., 1957). The F2 data was firstly split into groups by a clustering procedure (FASTCLUS) provided in SAS/STAT. Taking the estimates given by the clustering analysis as starting values, a constrained EM algorithm was employed to find the maximum likelihood estimates for the parameters of the mixture model. The covariance matrix of the estimates was then obtained either by inverting the approximate information matrix (using the method developed by McLachlan and Basford, 1988), or by using a parametric bootstrap procedure with 99 replications. The numerical example seems to indicate that the present approach extracts more information than by using Powers' partitioning methods (Powers, 1963). A simulation was performed to investigate the statistical behavior of the point estimates and confidence interval for the parameters obtained by this approach. The result indicates that this procedure is feasible and useful. It also shows that no great loss in precision will occur if data of F1 are not available, and the covariance matrix obtained by bootstrap resampling is far better than that obtained from inverting the approximate information matrix.中 文 摘 要-----------------------------------------------------------II 英 文 摘 要----------------------------------------------------------III 第一章 前言-----------------------------------------------------------1 第二章 文獻回顧-----------------------------------------------------3 2-1節 傳統上估計基因效應的方法-------------------3 2-2節 常態混合分布的參數估計----------------------5 第三章 基因效應等遺傳參數的估計----------------------------12 3-1節 混合分布模式------------------------------------12 3-2節 點估計---------------------------------------------14 3-3節 區間估計------------------------------------------17 3-4節 數例------------------------------------------------22 第四章 模擬試驗----------------------------------------------------28 4-1節 假設模式------------------------------------------28 4-2節 模擬數據的產生與混合分布模式的求配---29 第五章 討論與結論-------------------------------------------------36 參考文獻--------------------------------------------------------------3

The Extension of Hedonic Price Theory in Housing Mass appraisal Models— The Application of Quantile Regression

特徵價格模型是傳統常被使用於不動產大量估價的模型，由於模型將造成所有價位的不動產其特徵都具有同樣的邊際價格而無法解釋現實不動產特徵的各種可能狀況，故引發本研究利用分量迴歸建立大量估價模型之動機。研究利用台灣不動產成交行情公報的資料進行台北市大廈的實證分析，針對特徵價格法的延伸與估價準確度做檢視。嘗試應用分量迴歸建立大量估價模型，討論住宅特徵對於價格的邊際影響力於不同價位的住宅是否存在差異，並討論分量迴歸模型的估價精確度。研究採用交互驗證法與重複實驗30次討論模型的估計效果，並利用平均絕對百分比誤差（MAPE）以及命中率（Hit Rate）做為模型預測優劣程度的衡量標準，以討論分量迴歸模型是否可以較最小平方特徵價格模型有更為準確的估計表現。實證首先探討價格分量之下各住宅屬性對於價格的影響狀況，得到大部分住宅特徵對於價格的邊際影響力的確會因住宅價位的不同而有所差異。在估價準確度的部份，經測試得到利用分量迴歸建立大量估價模型的估價效果達研究的預期目標，且其估計表現優於最小平方特徵價格模型。藉由分量迴歸模型，得到隨著住宅價位的增加，坪數與屋齡對於價格的影響力並非呈現一致的趨勢；坪數輪廓與屋齡輪廓出現轉折也為變數增加二次項變數的原因得到實證依據。重複實驗30次的整體表現，分量迴歸模型的MAPE較最小平方迴歸模型低了1.687％；誤差落在正負10％的Hit Rate較最小平方迴歸模型高了3.81％；誤差落在正負20％的Hit Rate較最小平方迴歸模型高了5.14％。30次的實證為分量迴歸模型的估價表現更優於最小平方迴歸模型得到較具說服力的結果。Hedonic pricing models are traditionally used for real estate automated valuation models. Because the conditional mean calculated by OLS does not give a complete description of the relationship between dependent variable and independent variables, which leads to the motive of this study. This study inspects the extension of hedonic pricing models and appraisal accuracy, and we attempt to apply quantile regression to real estate automated valuation models and discuss the difference of the marginal contribution in each individual characteristic under different price level. Our study adopts cross validation and repeats empirical process for 30 times, and we use MAPE and hit rate to evaluate accuracy and argue if quantile regression models have better estimation. The empirical results show that the marginal contribution of housing area and age changes with price level; the turning points of area curve and age curve show empirical evidence for including square variables. The entirety performance of repeated experiments points out that the MAPE of quantile regression model is 1.687% lower than OLS model; as error ranged between 10% to -10%, the hit rate of quantile regression model is 3.81% higher than OLS model; as error ranged between 20% to -20%, the hit rate of quantile regression model is 5.14% higher than OLS model. The 30 times experiment of quantile regression models shows a much more persuasive result than OLS models

運用財務及非財務指標建構企業財務預警模式之研究

出版單位:真理大

人工智慧風潮下公共服務制度設計策略與法規調適作為之研究

TW