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

如果能从不同的局部市场获得足够的信息，传统的房地产评估程序尤其有效。在这里，统计程序（享乐程序，如回归分析）通常在销售比较方法的框架内使用，以预测准确的市场价值。在交易很少的领域，经典的统计评估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，每个自变量需要购买15次。因此，交易较少的地区的情况对充分预测市场价值的方法和方法提出了特殊的挑战。该研究项目的目标是开发一种创新模型，使在交易较少的情况下能够进行可靠的评估。为此，建议开发一种健壮的贝叶斯方法。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，可以处理小样本量。该研究项目所面临的特殊挑战涉及数据特征和先验知识两方面。随机样本（数据和事务）显示非常小的数据范围；它们受到异常值的污染，并且在方差上表现出异质性。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以及与数据一起进行加权。为了解决本项目中的不同任务，将开发一个鲁棒贝叶斯模型，该模型可以在少量数据下工作，并且可以将定性不同的先验知识结合起来。除估值实践外，不假设数据服从正态分布；因此，将开发一种方法来确定正确的分布函数。加权将通过方差分量估计的方法进行。蒙特卡罗方法将发展，使数值解决鲁棒贝叶斯享乐模型。在第一个实例中，使用来自具有大量交易的子市场的数据。通过闭环模拟，模拟交易较少的区域，系统地减少数据，然后模拟不同的离群类型。为了验证结果，将在交易较少的实际子市场中应用所开发的方法。因此，所开发的模型能够结合先验知识（通过专家访谈，批准证书和提供数据收集）在小样本范围（即使所选样本包含一些异常值）的数据中有效地工作，从而可以预测可靠的，即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.