Technology analysis is one of the important tasks in technology and industrial management. Much information about technology is contained in the patent documents. So, patent data analysis is required for technology analysis. The existing patent analyses relied on the quantitative analysis of the collected patent documents. However, in the technology analysis, expert prior knowledge should also be considered. In this paper, we study the patent analysis method using Bayesian inference which considers prior experience of experts and likelihood function of patent data at the same time. For keyword data analysis, we use Bayesian predictive interval estimation with count data distributions such as Poisson. Using the proposed models, we forecast the future trends of technological keywords of artificial intelligence (AI) in order to know the future technology of AI. We perform a case study to provide how the proposed method can be applied to real areas. In this paper, we retrieve the patent documents related to AI technology, and analyze them to find the technological trend of AI. From the results of AI technology case study, we can find which technological keywords are more important or critical in the entire structure of AI industry. The existing methods for patent keyword analysis were depended on the collected patent documents at present. But, in technology analysis, the prior knowledge by domain experts is as important as the collected patent documents. So, we propose a method based on Bayesian inference for technology analysis using the patent documents. Our method considers the patent data analysis with the prior knowledge from domain experts.