Last time I looked, Edward was all single precision. I don’t know how fundamental this is built into TensorFlow.
Single-precision is AFAIK important for computing on the GPU, regardless of the library you use: GPUs I have worked with (relatively cheap ones, though) have terrible performance in double precision: While in single precision, my computation would run some 20 times faster on the GPU than on the 8 core CPU, the total time became comparable with double precision. Might be different for some of the expensive GPU models, though (the Tesla P100 seems to have decent double precision performance).