The Anglo-Australian Planet Search has now accumulated 12 years of radial-velocity data with long-term instrumental precision better than 3 m/s. In this paper, we expand on earlier simulation work, to probe the frequency of near-circular, long-period gas-giant planets residing at orbital distances of 3-6 AU -- the so-called Jupiter analogs. We present the first comprehensive analysis of the frequency of these objects based on radial-velocity data. We find that 3.3% of stars in our sample host Jupiter analogs; detailed, star-by-star simulations show that no more than 37% of stars host a giant planet between 3-6 AU.
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