When there is no obvious choice for the transition kernel q, a possibility is to generate the proposal transition from a fixed distribution 
, independently of the current state z, i.e.:
The acceptance probability a of equation 16 becomes :
For example, in a Bayesian setting, may be the prior distribution. If the target distribution writes 
, where L(y|z) is the likelihood of the state z given the observation y, the acceptance probability reduces to:
In other words, every transition is accepted if the proposed state is more likely than the current state, and if not is rejected with a probability which depends only upon the likelihood function.
Figure 1: Transition in a bidimensional state space generated by an independent sampler. The target distribution 
is represented as black level lines, the proposal transition kernel 
in blue. The red transition is accepted (because 
), while the green one is likely to be rejected.
Figure 1 represents the transition of a Markov chain generated by an independent sampler.