以貝氏方法來處理部分區分(partially-classified)或是失去部分訊息資料的類別抽樣(categorical sampling with censored data)，大部分建立在「誠實回答」(truthful reporting)以及「無價值性失去部分訊息」(non-informative censoring)的前提下。Dr.Jiang(1995)取消以上兩個限制，提出quasi-Bayes method來近似這類問題的貝氏解。另外我們也嘗試利用Gelfand and Smith(1990)針對Gibbs sampler所提出的收斂方法來估計。本文重點在比較此兩種方法的估計值準確性，並考慮先驗參數(prior)對估計精準的影響。

以貝式方法處理部分區分(partially-classified)失去部分訊息資料的類別抽樣(categorical sampling with censored data)大部分皆建立在“無價值性失去部分訊息的類別資料”(non-informative censored categorical data)與“誠實回答”(truthful reporting)的前提下。Jiang (1995)取消這兩個假設，提出類似Makov & Smith(1977)和Smith & Makov(1978)對混合分配(mixture distribution)所用之準貝式法(quasi-Bayes method)來得到近似解。而本文將討Jiang提出之準貝式法的收斂性，及考慮先驗分配對估計精準度的影響。

The polytopic model (PM) structure is often used in the areas of automatic control and fault detection and isolation (FDI). It is an alternative to the multiple model approach which explicitly allows for interpolation among local models. This thesis proposes a novel approach to PM estimation by modeling the set of PM weights as a random vector with Dirichlet Distribution (DD). A new approximate (adaptive) PM estimator, referred to as a Quasi-Bayesian Adaptive Kalman Filter (QBAKF) is derived and implemented. The model weights and state estimation in the QBAKF is performed adaptively by a simple QB weights' estimator and a single KF on the PM with the estimated weights. Since PM estimation problem is nonlinear and non-Gaussian, a DD marginalized particle filter (DDMPF) is also developed and implemented similar to MPF. The simulation results show that the newly proposed algorithms have better estimation accuracy, design simplicity, and computational requirements for PM estimation.

對於使用貝氏法來處理部份區分(partially-classified)或是失去部分訊息資料的類別抽樣(categorical sampling with censored data)，大多建立在「誠實回答」(truthful reporting)以及「無價值性失去部分訊息」(non-informative censoring)的前提下。Jiang(1995)及Jiang and Dickey(2006)取消以上兩個限制，提出貝氏解並利用準貝氏法(quasi-Bayes)來求近似解，而Jiang and Ko(2004)也利用吉氏取樣器(Gibbs sampler)來近似這類問題的貝氏解。本文首先嘗試利用Kuroda, Geng and Niki(2001)所提的“平均變異數和(average variance sum)”估計法 來應用到我們問題的貝氏解。在小樣本時，數值上我們可求得貝氏解，因此本文另一個重點為在小樣本時比較以上三種方法估計值的準確性，並考慮先驗參數(prior)的選取對估計的影響。 本文更進一步證明若選取到某種特殊的先驗參數時，利用“平均變異數和”的方法所計算出來的結果會和 準貝氏法的估計結果相同，而且皆等於用貝氏法計算出的結果。