Statistical challenges in modern astronomy

Despite centuries of close association, statistics and astronomy are surprisingly distant today. Most observational astronomical research relies on an inadequate toolbox of methodological tools. Yet the needs are substantial: astronomy encounters sophisticated problems involving sampling theory, survival analysis, multivariate classification and analysis, time series analysis, wavelet analysis, spatial point processes, nonlinear regression, bootstrap resampling and model selection. We review the recent resurgence of astrostatistical research, and outline new challenges raised by the emerging Virtual Observatory. Our essay ends with a list of research challenges and infrastructure for astrostatistics in the coming decade.