25-06 Discussion Open problems [Tanya] ->Estimation and interpretation of the parameter (flat space for the parameters) [Xiangping] ->Infill asymptotics vs (fixed domain, denser and denser) and domain-increasing asymptotic, akin to time series [Reinhart] ->Handling nonlinear unknown relationships (for e.g. air pollution, ozone reactions: necessary to have covariate present) [Wendy] -->Can you get around the gaussian assumption for linear prediction of another variable? Think not [David] -->Need monotonicity [Tanya] ->Distance correlation (only available for time series) [Jochen] ->State of the art: how many variables? 2-5 in the analysis ->3d observations (1M voxels) from fMRi, how to deal (not to have 5 observations in a voxel [David] ->Any model beyond the Matérn (Marc Genton's student working on powered exponential) [Tanya] ->SPDE: work with precision matrix, don't get Matérn for the marginal [Xiangping] ->Anyone worked with a model for which the Matérn is clearly the true model? [David] -->Cauchy, Matérn (3 parameters) [Tanya] -->Point with SPDE is that you don't care really if you are really close to the field [David] -->Overparametrizing model with no constraint vs binding model: what is the best? [Johan] - numerical optimization ->Matérn should be used to fit the smoothness, but it is usually not estimated (consistently), but rather fixed [David] ->What are the diagnostic for misspecification of the covariance structure in multivariate? more generally model diagnostic [Wendy] -->Some diagnostics and examples in Stein's book [Tanya] -->No decoupling, Herst effect zero [Martin] - kriging estimation depends on the smoothness of the parameter, different between 0.5 and 2 ->Comparison between the different covariance matrix? [Wendy] -->Version with composite likelihood [Tanya], presented by Bo Li ->CRPS; use predictive comparison if the aim is to predict [Alex] - hard to estimate the smoothness, profile likelihood of smoothness is radically difficult; some sort of penalization is needed ->Prior of the smoothness parameter [Somak] ->Informative prior on the range, hard to get both range and smoothness and put noninformative for the smoothness [Craigmile] ->parametrization in likelihood is extremely important for the frequentist, somewhat better in Bayesian with prior - in univariate, proposal is to have a prior centered at 1 [Paulo] ->Some changes in the numerics with the parametrization ->Discrete prior? [Aaron] P. Craigmile facilitates the sampling ->Negative correlated count data (multivariate models) [Nancy] -->Tuning band operator [Martin] for Gaussian -->Poisson lognormal mixture [Alexandra] -->Winsorisation