Combining functional data with hierarchical Gaussian process models

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.     

Agricultural land use efficiency and food crop production in Ghana

Despite the low productivity of the extensive agriculture system, Ghana recorded the largest reduction of undernourishment in the past two decades. We used biophysical analysis to determine the efficiency and potentials of the extensive system and its future sustainability. The results indicate that food production in Ghana has increased steadily over the past two decades and correlated highly with cropped area and population (R ² < 0.85 and 0.82), but not with fertilizer (R ² = 0.06). Sufficient food production could be sustained in the short term. In the longer term, however, the food situation in Ghana appears precarious if population growth continues while land remains the same.