Combining functional data with hierarchical Gaussian process models

Abstract

Gaussian process models have been used in applications ranging from machine learning to fisheries management. In the Bayesian framework, the Gaussian process is used as a prior for unknown functions, allowing the data to drive the relationship between inputs and outputs. In our research, we consider a scenario in which response and input data are available from several similar, but not necessarily identical, sources. When little information is known about one or more of the populations it may be advantageous to model all populations together. We present a hierarchical Gaussian process model with a structure that allows distinct features for each source as well as shared underlying characteristics. Key features and properties of the model are discussed and demonstrated in a number of simulation examples. The model is then applied to a data set consisting of three populations of Rotifer Brachionus calyciflorus Pallas. Specifically, we model the log growth rate of the populations using a combination of lagged population sizes. The various lag combinations are formally compared to obtain the best model inputs. We then formally compare the leading hierarchical Gaussian process model with the inferential results obtained under the independent Gaussian process model.

Hidden similarities in the dynamics of a weakly synchronous marine metapopulation

“…Under this specification, the correlation between 2 site-specific maps evaluated at the same input, f i ðxÞ and f j ðxÞ, reduces to ρ D . Moreover, simulations indicate that ρ D provides a good approximation of AEf i , f j ae=½AEf i , f i aeAEf j , f j ae 1=2 where AEf i , f j ae = R f i ðxÞf j ðxÞdx and the integral covers domain of the data (51). Thus ρ D (the "dynamic correlation") indicates the similarity of the reconstructed maps between sites.…”

Age structure augments the predictive power of time series for fisheries and conservation

“…There are several ways to approximate this function from available data including the piecewise constant "Simplex" (Sugihara and May 1990), local weighted linear regression "S-Map" (Sugihara 1994), and splines (Ellner and Turchin 1995). In this study, we used Gaussian Process regression (Poynor and Munch 2017)…”