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Freshwater ecosystems can experience harmful algal blooms, which negatively impact recreational uses, aesthetics, taste, and odor in drinking water. Cyanobacterial toxins can have dire repercussions on aquatic wildlife and human health, and the most ubiquitous worldwide are the hepatotoxic compounds known as microcystins. The factors that influence the occurrence and magnitude of cyanobacteria blooms and toxin production vary in space and time and remain poorly understood. It is within this context that we present a suite of statistical models, parameterized with Bayesian inference techniques, to link the retrospective analysis of important environmental factors with the probability of exceedance of threshold microcystin levels. Our modelling framework is applied to the Bay of Quinte, Lake Ontario, Canada; a system with a long history of eutrophication problems. Collectively, 16.1% of the samples of the system collected during the study period (2003-2016) exceeded the drinking water guideline of 1.5 mu gL(-1), while approximately 3% of recorded values exceeded the recommended recreational threshold of 20 mu gL(-1). Using a segmented regression model with a stochastic breakpoint of microcystin concentrations estimated at 0.54 mu g L-1, we demonstrate that the environmental conditions associated with increased probability of exceedance of the drinking water standard are chlorophyll a concentration (3)(7) mu g L-1, water temperature (3)20 degrees C, ammonium concentration <= 40 mu gL(-1), total phosphorus concentration (3)25 mu g L-1, and wind speed <= 37 km h(-1). Considering the multitude of factors that can influence the ambient levels of toxins, our study argues that the adoption of probabilistic water quality criteria offers a pragmatic approach to accommodate the associated uncertainty by permitting a realistic frequency of violations. In this context, we present a framework to evaluate the confidence of compliance with probabilistic standards that stipulate less than 10% violations of microcystin threshold ambient levels. (C) 2019 Elsevier Ltd. All rights reserved.