Bayesian Methods for Completing Data in Space-Time Panel Models

Completing data sets that are collected in heterogeneous units is a quite frequent problem. Chow and Lin (1971) were the first to develop a unified framework for the three problems (interpolation, extrapolation and distribution) of predicting times series by related series (the `indicators'). This paper develops a spatial Chow-Lin procedure for cross-sectional and panel data and compares the classical and Bayesian estimation methods. We outline the error covariance structure in a spatial context and derive the BLUE for the ML and Bayesian MCMC estimation. Finally, we apply the procedure to Spanish regional GDP data between 2000-2004. We assume that only NUTS-2 GDP is known and predict GDP at NUTS-3 level by using socio-economic and spatial information available at NUTS-3. The spatial neighborhood is defined by either km distance, travel time, contiguity and trade relationships. After running some sensitivity analysis, we present the forecast accuracy criteria comparing the predicted values with the observed ones.Interpolation, Spatial panel econometrics, MCMC, Spatial

Bayesian Methods for Completing Data in Space-time Panel Models

Completing data sets that are collected in heterogeneous units is a quite frequent problem. Chow and Lin (1971) were the first to develop a united framework for the three problems (interpolation, extrapolation and distribution) of predicting times series by related series (the 'indicators'). This paper develops a spatial Chow-Lin procedure for cross-sectional and panel data and compares the classical and Bayesian estimation methods. We outline the error covariance structure in a spatial context and derive the BLUE for the ML and Bayesian MCMC estimation. Finally, we apply the procedure to Spanish regional GDP data between 2000-2004. We assume that only NUTS-2 GDP is known and predict GDPat NUTS-3 level by using socio-economic and spatial information available at NUTS-3. The spatial neighborhood is defined by either km distance, travel-time, contiguity and trade relationships. After running some sensitivity analysis, we present the forecast accuracy criteria comparing the predicted with the observed values.Interpolation, Spatial panel econometrics, MCMC, Spatial Chow-Lin, Missing regional data, Spanish provinces, 'Polycentric-periphery' relationship

Gaussian processes with linear operator inequality constraints

This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence engineering systems, where this kind of information is often made available from phenomenological knowledge. We consider a GP $f$ over functions on $\mathcal{X} \subset \mathbb{R}^{n}$ taking values in $\mathbb{R}$, where the process $\mathcal{L}f$ is still Gaussian when $\mathcal{L}$ is a linear operator. Our goal is to model $f$ under the constraint that realizations of $\mathcal{L}f$ are confined to a convex set of functions. In particular, we require that $a \leq \mathcal{L}f \leq b$, given two functions $a$ and $b$ where $a < b$ pointwise. This formulation provides a consistent way of encoding multiple linear constraints, such as shape-constraints based on e.g. boundedness, monotonicity or convexity. We adopt the approach of using a sufficiently dense set of virtual observation locations where the constraint is required to hold, and derive the exact posterior for a conjugate likelihood. The results needed for stable numerical implementation are derived, together with an efficient sampling scheme for estimating the posterior process.Comment: Published in JMLR: http://jmlr.org/papers/volume20/19-065/19-065.pd

Bayesian Methods for Completing Data in Spatial Models

Chow and Lin (1971) were the first to develop a unified framework for the three problems(interpolation, extrapolation and distribution) of predicting times series by related series(the ‘indicators’). This paper develops a spatial Chow-Lin procedure for cross-sectional data and compares the classical and Bayesian estimation methods. We outline the error covariance structure in a spatial context and derive the BLUE for ML and Bayesian MCMC estimation. In an example, we apply the procedure to Spanish regional GDP data between2000 and 2004. We assume that only NUTS-2 GDP is known and predict GDP at NUTS-3level by using socio-economic and spatial information available at NUTS-3. The spatial neighbourhood is defined by either km distance, travel time, contiguity or trade relationships. After running some sensitivity analysis, we present the forecast accuracy criteria comparing the predicted values with the observed ones

Spatial reallocation of areal data - a review

The analysis of socio-economic data often implies the combination of data bases originating from different administrative sources so that data have been collected on several separate partitions of the zone of interest into administrative units. It is therefore necessary to reallocate the data from the source spatial units to the target spatial units. We propose a review of the literature on statistical methods of spatial reallocation rules (spatial interpolation). Indeed one can distinguish several types of reallocation depending on whether the initial data and the final output are areal data or point data. We concentrate here on the areal-to-areal change of support case when initial and final data have an areal support with a particular attention to disaggregation for continuous data. There are three main types of such techniques: proportional weighting schemes also called dasymetric methods, smoothing techniques and regression based interpolation

Principles and methods of scaling geospatial Earth science data

The properties of geographical phenomena vary with changes in the scale of measurement. The information observed at one scale often cannot be directly used as information at another scale. Scaling addresses these changes in properties in relation to the scale of measurement, and plays an important role in Earth sciences by providing information at the scale of interest, which may be required for a range of applications, and may be useful for inferring geographical patterns and processes. This paper presents a review of geospatial scaling methods for Earth science data. Based on spatial properties, we propose a methodological framework for scaling addressing upscaling, downscaling and side-scaling. This framework combines scale-independent and scale-dependent properties of geographical variables. It allows treatment of the varying spatial heterogeneity of geographical phenomena, combines spatial autocorrelation and heterogeneity, addresses scale-independent and scale-dependent factors, explores changes in information, incorporates geospatial Earth surface processes and uncertainties, and identifies the optimal scale(s) of models. This study shows that the classification of scaling methods according to various heterogeneities has great potential utility as an underpinning conceptual basis for advances in many Earth science research domains. © 2019 Elsevier B.V

Change of support problemへの新たな空間統計モデルの開発

筑波大学 (University of Tsukuba)201