The extremal behaviour of a Markov chain is typically characterised by its tail chain. For asymptotically dependent Markov chains, existing formulations fail to capture the full evolution of the extreme event when the chain moves out of the extreme tail region, and, for asymptotically independent chains, recent results fail to cover well-known asymptotically independent processes, such as Markov processes with a Gaussian copula between consecutive values. We use more sophisticated limiting mechanisms that cover a broader class of asymptotically independent processes than current methods, including an extension of the canonical Heffernan‒Tawn normalisation scheme, and reveal features which existing methods reduce to a degenerate form associated with nonextreme states.

The use of automated sensors has grown rapidly in recent years, with sensor data now routinely used for monitoring in a wide range of situations, including human health and behaviour, the environment, wildlife, and agriculture. Livestock farming is a key area of application, and our primary focus here, but the issues discussed are widely applicable. There is the potential to massively increase the use of empirical data for decision-making in real time, and a range of quantitative methods, including machine learning and statistical methods, have been proposed for this purpose within the literature. In many areas, however, development and validation of quantitative approaches are still needed in order for these methods to effectively inform decision-making. Within the context of livestock farming, for example, it must be practically feasible to repeatedly apply the method dynamically in real time on farms in order to optimise decision-making, and we discuss the challenges in using quantitative approaches for this purpose. It is also crucial to evaluate and compare the applied performance of methods in a fair and robust way—such comparisons are currently lacking within the literature on livestock farming, and we outline approaches to addressing this key gap.

The use of automated sensors has grown rapidly in recent years, with sensor data now routinely used for monitoring in a wide range of situations, including human health and behaviour, the environment, wildlife, and agriculture. There is the potential to massively increase use of empirical data for decision making in real time, but in many areas, development and validation of quantitative approaches is still needed in order to move from the developmental stage to this intended practical application. Whilst there is wide-ranging literature in this area, in livestock farming there is a paucity that provides fair robust statistical comparisons of alternative quantitative methods and evidence that resulting decision making performs adequately in practice on farms. That is, it must be practically feasible to repeatedly apply the method dynamically in real time on farms, and optimise decisions made. We discuss alternative quantitative approaches that could be used for real time decision making from automatic monitoring, which we refer to as prediction, as well as approaches to rigorous statistical evaluation of the resulting decision-making process, which we refer to as prediction validation. Associated research challenges are discussed in detail with reference made to livestock farming, but many issues discussed are widely applicable.

The extremal behaviour of a Markov chain is typically characterized by its tail chain. For asymptotically dependent Markov chains existing formulations fail to capture the full evolution of the extreme event when the chain moves out of the extreme tail region and for asymptotically independent chains recent results fail to cover well-known asymptotically independent processes such as Markov processes with a Gaussian copula between consecutive values. We use more sophisticated limiting mechanisms that cover a broader class of asymptotically independent processes than current methods, including an extension of the canonical Heffernan-Tawn normalization scheme, and reveal features which existing methods reduce to a degenerate form associated with non-extreme states.