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