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The olive (Olea europaea L.) is an economically important species for countries that have Mediterranean climate and has been an appropriate, useful alternative for intensive farming systems in the arid zones of Chile. For this reason, the objective of this study was to determine the components of variance, broad-sense heritability, and prediction of genetic values using the Bayesian techniques on twenty-eight olive clones in the southern part of the Atacama Desert. The algorithm of independent chains was used to estimate parameter distributions a posteriori. The field experiment was set up in 2000, and during six years six quantitative traits were monitored in different periods. Estimations of heritability and associated credibility intervals (parentheses) were H-2 = 0.50 (0.38-0.61), 0.50 (0.38-0.61), 0.81 (0.74-0.86), 0.53 (0.42-0.64), 0.26 (0.14-0.40), and 0.44 (0.17-0.65) for fruit production (2006), total fruit production (20032006), area of trunk cross section (2006), tree productivity (2006), alternation of production (2003-2006), and precocity (2003). Genetic advance by direct selection varied from 16 to 55% with a selection intensity of 28.6%. Pearson correlations, calculated between genetic values of alternation of production and production traits, were negative and significant. Selection of olive clones for precocity would not generate any significant effect on production traits. Moderate heritability for fruit production, alternation of production, and precocity suggest a positive response to the selection of olive clones under the environmental conditions of the southern part of the Atacama desert.