Real Estate Valuation in Areas with Few Transactions Using a Robust Bayesian Hedonic Model

经典的真实的房地产估价方法在有足够的局部市场信息时尤其有效。在这里，统计程序（享乐程序，如回归分析）通常用于销售比较方法的框架内，以预测准确的市场价值。在交易很少的地区，传统的统计评价方法只能提供不可靠的结果，甚至失败，因为这些方法需要适当的样本量;通常在回归分析中每个自变量需要15次购买。因此，交易量少的地区的情况对适当预测市场价值的方法和办法构成特殊挑战。该研究项目的目标是开发一种创新模式，在交易很少的情况下进行可靠的评估。为此，提出了一个强大的贝叶斯方法应该开发。在这种方法中，可以将专家知识集成到数据支持的模型中，如多元回归分析，它可以处理小样本量。研究项目所涉及的特殊挑战既涉及数据特征，也涉及先验知识。随机样本（数据和事务）显示出非常小的数据范围;它们被离群值污染，并显示出方差的异质性。先验知识将从几个质量不同的来源生成或收集，因此这些信息应该在它们之间进行加权，并与数据进行加权。为了解决这个提交的项目中的不同任务，将开发一个强大的贝叶斯模型，该模型使用很少的数据，可以联合收割机定性地结合不同的先验知识。除了估值实践之外，数据并不假设服从正态分布;因此，将开发一种确定正确分布函数的方法。加权将通过方差分量估计进行。将开发蒙特卡罗方法，以实现稳健贝叶斯特征模型的数值解。在第一种情况下，使用来自具有大量交易的子市场的数据。通过闭环模拟，将模拟交易较少的区域，其中数据被系统地减少，然后将模拟不同的离群值类型。为了验证的结果，所开发的方法的应用将进行在真实的子市场的交易很少。因此，所开发的模型能够在小样本范围的数据中有效地工作（即使所选样本包含一些离群值），并结合先验知识（通过专家访谈，批准证书和提供数据收集），从而可以预测可靠且更准确的市场价值和质量声明。

The classical procedures of real estate evaluation works especially well if sufficient informations from different partial markets are available. Right there, statistic procedures (hedonic procedures e.g. regression analysis) are usually used within the framework of the sale comparison approach in order to predict an accurate market value. In areas with few transactions classical statistic evaluation approaches provide only unreliable results or even fail, since these approaches require suitable sample sizes; normally 15 purchases per independent variable in the regression analysis are needed. Therefore, the situation in areas with few transactions represents a special challenge for the methodology and the approach to predict the market value adequately. The goal of the research project is it to develop an innovative model, which enables reliable evaluation in situations with few transactions. For this propose a robust Bayesian approach should be developed. In this approach, it is possible to integrate expert knowledge into data supported models, like the multiple regression analysis, which can deals with small sample size. Special challenges, with which the research project deals, concern on both the data characteristic and on the prior knowledge. The random samples (data and transactions) exhibit a very small data extent; they are contaminated with outliers and show heterogeneity in the variances. The prior knowledge will be generated or collected from several qualitatively different sources, so that these informations should be weighted among themselves and with the data additionally. In order to solve the different tasks in this submitted project a robust Bayesian model will be developed which works with few data and can combine qualitatively different prior knowledge. Other than the valuation practice, the data are not assumed to obey the normal distribution; a method will be, therefore, developed which determines the correct distribution function. The weighting will be carried out by means of variance component estimation. Monte Carlo methods will be developed to enable the numerical solution of the robust Bayesian hedonic model. In the first instance, data from submarkets with numerous transactions are used. By means of closed loop simulation, areas with few transactions will be simulated, in which the data are systematically reduced, and afterwards different outlier types will be simulated. In order to validate the results, the application of the developed approach will be carried out in real submarkets with few transactions. As a result, the developed model is able to work efficiently in data with small sample range (even if the selected sample contains some outliers) in combination of prior knowledge (collected by expert interviews, approval certificate and offering data), so that a reliable and i.e. more accurate market value with quality statements can be predicted.