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In this paper, we propose a novel model to analyze serially correlated two-dimensional functional data observed sparsely and irregularly on a domain which may not be a rectangle. Our approach employs a mixed effects model that specifies the principal component functions as bivariate splines on triangles and the principal component scores as random effects which follow an auto-regressive model. We apply the thin-plate penalty for regularizing the bivariate function estimation and develop an effective EM algorithm along with Kalman filter and smoother for calculating the penalized likelihood estimates of the parameters. Our approach was applied on simulated datasets and on Texas monthly average temperature data from January year 1915 to December year 2014. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

We developed an enhanced Kalman‐based approach to quantify abrupt changes and significant non‐linearity in vertical land motion (VLM) along the coast of Chile and the Antarctic Peninsula using a combination of multi‐mission satellite altimetry (ALT), tide gauge (TG), and GPS data starting from the early 1990s. The data reveal the spatial variability of co‐seismic and post‐seismic subsidence at TGs along the Chilean subduction zone in response to the Mw8.8 Maule 2010, Mw8.1 Iquique 2014, and Mw8.3 Illapel 2015 earthquakes that are not retrievable from the interpolation of sparse GPS observations across space and time. In the Antarctic Peninsula, where continuous GPS data do not commence until ∼1998, the approach provides new insight into the ∼2002 change in VLM at the TGs of +5.3 ± 2.2 mm/yr (Palmer) and +3.5 ± 2.8 mm/yr (Vernadsky) due to the onset of ice‐mass loss following the Larsen‐B Ice Shelf breakup. We used these data to constrain viscoelastic Earth model parameters for the northern Antarctic Peninsula, obtaining a preferred lithosphere thickness of 115 km and upper mantle viscosity of 0.9 × 1018 Pa s. Our estimates of regionally‐correlated ALT systematic errors are small, typically between ∼±0.5–2.5 mm/yr over single‐mission time scales. These are consistent with competing orbit differences and the relative errors apparent in ALT crossovers. This study demonstrates that, with careful tuning, the ALT‐TG technique can provide improved temporal and spatial sampling of VLM, yielding new constraints on geodynamic models and assisting sea‐level change studies in otherwise data sparse regions and periods. Plain Language Summary: The difference in sea‐level records from satellite altimeters and coastal tide gauges can reveal the Earth surface's vertical land motion (VLM) and potential errors in either system. Time‐varying changes in the VLM can occur because of phenomena such as earthquakes or glacier melt which changes the mass load on the crust. We developed a flexible data combination framework to use records from multi‐mission altimeters (ALTs), tide gauges (TGs), and GPS sites to allow the estimation of substantial non‐linear VLM that complements the previous estimates which can be sparse in the 1990s especially. We considered the study period since the launch time of TOPEX mission in ∼1992. We used our new approach to investigate the earthquake‐induced deformation at TG locations along the near‐coast subduction zone in Chile that could not be inferred from temporally and spatially sparse GPS records. We also provide insights into the rapid change in VLM at coastal TGs in the Antarctic Peninsula after the Larsen‐B Ice Shelf breakup in ∼2002, where the existing knowledge dates to ∼1998 from only one GPS at Palmer station. These significant insights into present‐day deformation help to fill the knowledge gap from GPS‐inferred records and improve VLM sampling across space and time. More generally, this new approach may assist resolve complex VLM for sea‐level studies globally and could add new constraints to inverse geophysical modeling, especially where GPS data are sparse in space and/or time. Key Points: We developed an advanced Kalman approach to estimate highly non‐linear vertical land motion using altimeter, tide gauge and GPS data, while simultaneously capturing significant mission‐specific systematic errorsWe derived new estimates of pre‐seismic velocity, co‐seismic jumps, and post‐seismic velocity at tide gauges in Chile that add additional constraints on the solid‐Earth response to major earthquakes in the regionWe observed the onset of rapid uplift at tide gauges in the Antarctic Peninsula caused by the 2002 breakup of the Larsen‐B Ice Shelf, filling a historical knowledge gap from GPS records and further constraining modeled viscoelastic deformation [ABSTRACT FROM AUTHOR]

This paper derives the limit of the Kalman filter and smoother as the inverse of the process noise covariance tends to zero (the zero informational limit) in the case that there is direct feedthrough (of full column rank) of the process noise input to the measurements. Two forms of the filter in the limit are derived with the second being a standard Kalman filter without unknown inputs. The latter form is used to derive necessary and sufficient conditions for convergence and stability of the filter. These consist of a controllability condition and a minimum phase condition. The filter and smoother are applied to an automotive example to estimate an unknown road profile. The example illustrates the usefulness of the stability and convergence conditions to inform the choice of a suitable set of sensors. [ABSTRACT FROM AUTHOR]

Healthcare processes comprise multiple stages in practice. Also, few researchers have addressed Phase I monitoring of healthcare outcomes. Hence, the purpose of the proposed method is Phase I monitoring by two risk adjusted control charts in multistage healthcare processes. The proposed control charts are based on the Bernoulli state space model and consider other categorical covariates in addition to patient's risk. To estimate the model parameters, an expectation-maximization algorithm is applied in a Kalman filter and smoother framework. The performance of the proposed monitoring schemes is compared in two and three stages. The simulation results show that the standardized likelihood ratio test method has competitive performance relative to Hotelling's chart under different step shifts and drift. Also, Hotelling's chart is superior to the standardized likelihood ratio test method in for outlier patients. Finally, a real case is utilized to show the applicability of the proposed risk adjusted charts. [ABSTRACT FROM AUTHOR]

Spatial–temporal Gaussian process regression is a popular method for spatial–temporal data modeling. Its state-of-art implementation is based on the state-space model realization of the spatial–temporal Gaussian process and its corresponding Kalman filter and smoother, and has computational complexity O (N M 3) , where N and M are the number of time instants and spatial input locations, respectively, and thus can only be applied to data with large N but relatively small M. In this paper, our primary goal is to show that by exploring the Kronecker structure of the state-space model realization of the spatial–temporal Gaussian process, it is possible to further reduce the computational complexity to O (M 3 + N M 2) and thus the proposed implementation can be applied to data with large N and moderately large M. The proposed implementation is illustrated over applications in weather data prediction and spatially-distributed system identification. Our secondary goal is to design a kernel for both the Colorado precipitation data and the GHCN temperature data, such that while having more efficient implementation, better prediction performance can also be achieved than the state-of-art result. [ABSTRACT FROM AUTHOR]

This article proposes a new framework to estimate and analyse structural fiscal balances of the UK, by combining the state-space modelling with the Bayesian DSGE modelling. In this way, trends and cycles of aggregate variables can be extracted from data consistently with the macroeconomic theory. A setting of an integrated random walk for the underlying stochastic trends fits the data best. An expansion in government spending can increase nominal fiscal revenue to a certain degree, but the effect is not persistent due to two kinds of crowd-out effects: it crowds out domestic investment; and it pushes up the price of domestic goods and simultaneously crowds out the foreign demand. The shocks to the nominal interest rate, foreign output and the government spending are the three major contributors to the variation of the fiscal revenue cycle. [ABSTRACT FROM AUTHOR]