Testing the assumptions behind importance sampling

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Pareto Smoothed Importance Sampling (2015, methodology): “Previous research has focused on identifying whether the variance is finite or infinite (Peruggia, 1997; Epifani et al., 2008; Koopman et al., 2009), but we demonstrate in Section 4that it can often be more useful to look at the continuous k̂ values than the discrete number of moments.”
Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC (2015, methodology): “By examining the shape parameter k of the ﬁtted Pareto distribution, we are able to obtain sample based estimates of the existence of the moments (Koopman et al, 2009).”
Efficient high-dimensional importance sampling (2007, background): “See also Koopman and Shephard (2004) for a test based upon extreme values theory.”
A dynamic bivariate Poisson model for analysing and forecasting match results in the English Premier League (2015, methodology): “The basis of our modelling approach is proposed by Maher (1982). In this study, the double Poisson distribution, with the means expressed as team-specific attack and defense strengths, is adopted as the underlying distribution for goal scoring.”