  The tendency of Large Language Models (LLMs) to generate hallucinations and
exhibit overconfidence in predictions raises concerns regarding their
reliability. Confidence or uncertainty estimations indicating the extent of
trustworthiness of a model's response are essential to developing reliable AI
systems. Current research primarily focuses on LLM confidence estimations in
English, remaining a void for other widely used languages and impeding the
global development of reliable AI applications. This paper introduces a
comprehensive investigation of \textbf Multi\textbf{ling}ual
\textbf{Conf}idence estimation (\textsc{MlingConf}) on LLMs. First, we
introduce an elaborated and expert-checked multilingual QA dataset.
Subsequently, we delve into the performance of several confidence estimation
methods across diverse languages and examine how these confidence scores can
enhance LLM performance through self-refinement. Extensive experiments
conducted on the multilingual QA dataset demonstrate that confidence estimation
results vary in different languages, and the verbalized numerical confidence
estimation method exhibits the best performance among most languages over other
methods. Finally, the obtained confidence scores can consistently improve
performance as self-refinement feedback across various languages.
