We present 16-GHz Sunyaev-Zeldovich observations using the Arcminute Microkelvin Imager (AMI) and subsequent Bayesian analysis of six galaxy clusters at redshift ($z approx 1$) chosen from an X-ray and Infrared selected sample from Culverhouse et al. (2010). In the subsequent analysis we use two cluster models, an isothermal beta-model and a Dark Matter GNFW (DM-GNFW) model in order to derive a formal detection probability and the cluster parameters. We detect two clusters (CLJ1415+3612 & XMJ0830+5241) and measure their total masses out to a radius of 200 $times$ the critical density at the respective clusters redshift. For CLJ1415+3612 and XMJ0830+5241, we find M_{mathrm{T},200} for each model, which agree with each other for each cluster. We also present maps before and after source subtraction of the entire sample and provide 1D and 2D posterior marginalised probability distributions for each fitted cluster profile parameter of the detected clusters. Using simulations which take into account the measured source environment from the AMI Large Array (LA), source confusion noise, CMB primordials, instrument noise, we estimate from low-radius X-ray data from Culverhouse et al. (2010), the detectability of each cluster in the sample and compare it with the result from the Small Array (SA) data. Furthermore, we discuss the validity of the assumptions of isothermality and constant gas mass fraction. We comment on the bias that these small-radius estimates introduce to large-radius SZ predictions. In addition, we follow-up the two detections with deep, single-pointed LA observations. We find a 3 sigma tentative decrement toward CLJ1415+3612 at high-resolution and a 5 sigma high-resolution decrement towards XMJ0830+5241.
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