Implementing Monte Carlo integration requires significant domain expertise. While simple samplers, such as unidirectional path tracing, are relatively forgiving, more complex algorithms, such as bidirectional path tracing or Metropolis methods, are notoriously difficult to implement correctly. We propose Aether, an embedded domain specific language for Monte Carlo integration, which offers primitives for writing concise and correct-by-construction sampling and probability code. The user is tasked with writing sampling code, while our compiler automatically generates the code necessary for evaluating PDFs as well as the book keeping and combination of multiple sampling strategies. Our language focuses on ease of implementation for rapid exploration, at the cost of run time performance. We demonstrate the effectiveness of the language by implementing several challenging rendering algorithms as well as a new algorithm, which would otherwise be prohibitively difficult.