Spatial covariance structure of tau‐PET changes more than Aβ‐PET across disease stages

Abstract Alzheimer’s disease is characterized by β-amyloid plaques and tau tangles. Plasma levels of phospho-tau217 (P-tau217) accurately differentiate Alzheimer’s disease dementia from other dementias, but it is unclear to what degree this reflects β-amyloid plaque accumulation, tau tangle accumulation, or both. In a cohort with post-mortem neuropathological data (N=88), both plaque and tangle density contributed independently to higher P-tau217. Several findings were replicated in a cohort with PET imaging (“BioFINDER-2”, N=426), where β-amyloid and tau PET were independently associated to P-tau217. P-tau217 correlated with β-amyloid PET (but not tau PET) in early disease stages, and with both β-amyloid and (more strongly) tau PET in late disease stages. Finally, P-tau217 mediated the association between β-amyloid and tau in both cohorts, especially for tau outside of the medial temporal lobe. These findings support the hypothesis that plasma P-tau217 is increased by both β-amyloid plaques and tau tangles and is congruent with the hypothesis that P-tau is involved in β-amyloid-dependent formation of neocortical tau tangles.

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A Bayesian Algorithm for Reconstructing Climate Anomalies in Space and Time. Part I: Development and Applications to Paleoclimate Reconstruction Problems

Journal of Climate ◽

10.1175/2009jcli3015.1 ◽

2010 ◽

Vol 23 (10) ◽

pp. 2759-2781 ◽

Cited By ~ 95

Author(s):

Martin P. Tingley ◽

Peter Huybers

Keyword(s):

Time Series ◽

Covariance Matrix ◽

Expectation Maximization Algorithm ◽

Covariance Structure ◽

Model Parameters ◽

Data Types ◽

Spatial Covariance ◽

Bayesian Algorithm ◽

Climate Anomalies ◽

Instrumental Values

Abstract Reconstructing the spatial pattern of a climate field through time from a dataset of overlapping instrumental and climate proxy time series is a nontrivial statistical problem. The need to transform the proxy observations into estimates of the climate field, and the fact that the observed time series are not uniformly distributed in space, further complicate the analysis. Current leading approaches to this problem are based on estimating the full covariance matrix between the proxy time series and instrumental time series over a “calibration” interval and then using this covariance matrix in the context of a linear regression to predict the missing instrumental values from the proxy observations for years prior to instrumental coverage. A fundamentally different approach to this problem is formulated by specifying parametric forms for the spatial covariance and temporal evolution of the climate field, as well as “observation equations” describing the relationship between the data types and the corresponding true values of the climate field. A hierarchical Bayesian model is used to assimilate both proxy and instrumental datasets and to estimate the probability distribution of all model parameters and the climate field through time on a regular spatial grid. The output from this approach includes an estimate of the full covariance structure of the climate field and model parameters as well as diagnostics that estimate the utility of the different proxy time series. This methodology is demonstrated using an instrumental surface temperature dataset after corrupting a number of the time series to mimic proxy observations. The results are compared to those achieved using the regularized expectation–maximization algorithm, and in these experiments the Bayesian algorithm produces reconstructions with greater skill. The assumptions underlying these two methodologies and the results of applying each to simple surrogate datasets are explored in greater detail in Part II.

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Characterization of a contaminated wellfield using 3D electrical resistivity tomography implemented with geostatistical, discontinuous boundary, and known conductivity constraints

Geophysics ◽

10.1190/geo2012-0121.1 ◽

2012 ◽

Vol 77 (6) ◽

pp. EN85-EN96 ◽

Cited By ~ 27

Author(s):

Timothy C. Johnson ◽

Roelof J. Versteeg ◽

Mark Rockhold ◽

Lee D. Slater ◽

Dimitrios Ntarlagiannis ◽

...

Keyword(s):

Electrical Resistivity ◽

Electrical Resistivity Tomography ◽

Covariance Structure ◽

Imaging Data ◽

Spatial Covariance ◽

Hanford Site ◽

Resistivity Tomography ◽

Shallow Subsurface ◽

Subsurface Structures ◽

Regularized Inversion

Continuing advancements in subsurface electrical resistivity tomography (ERT) are increasing its capabilities for understanding shallow subsurface properties and processes. The inability of ERT imaging data to resolve unique subsurface structures and the corresponding need to include constraining information remains one of the greatest limitations, yet provides one of the greatest opportunities for further advancing the utility of the method. We propose a new method of incorporating constraining information into an ERT imaging algorithm in the form of discontinuous boundaries, known values, and spatial covariance information. We demonstrated the approach by imaging a uranium-contaminated wellfield at the Hanford Site in southeastern Washington State, USA. We incorporate into the algorithm known boundary information and spatial covariance structures derived from the highly resolved near-borehole regions of a regularized ERT inversion. The resulting inversion provides a solution which fits the ERT data (given the estimated noise level), honors the spatial covariance structure throughout the model, and is consistent with known bulk-conductivity discontinuities. The results are validated with core-scale measurements, indicating a significant improvement in accuracy over the standard regularized inversion and revealing important subsurface structure known to influence flow and transport at the site.

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Multiplicative cascade models for fine spatial downscaling of rainfall: parameterization with rain gauge data

Hydrology and Earth System Sciences ◽

10.5194/hess-16-671-2012 ◽

2012 ◽

Vol 16 (3) ◽

pp. 671-684 ◽

Cited By ~ 12

Author(s):

D. E. Rupp ◽

P. Licznar ◽

W. Adamowski ◽

M. Leśniewski

Keyword(s):

Rain Rate ◽

Covariance Structure ◽

Rain Gauge ◽

Model Parameters ◽

Spatial Covariance ◽

Simple Method ◽

Frequency Distributions ◽

Rain Gauges ◽

Cascade Generator ◽

Radar Imagery

Abstract. Capturing the spatial distribution of high-intensity rainfall over short-time intervals is critical for accurately assessing the efficacy of urban stormwater drainage systems. In a stochastic simulation framework, one method of generating realistic rainfall fields is by multiplicative random cascade (MRC) models. Estimation of MRC model parameters has typically relied on radar imagery or, less frequently, rainfall fields interpolated from dense rain gauge networks. However, such data are not always available. Furthermore, the literature is lacking estimation procedures for spatially incomplete datasets. Therefore, we proposed a simple method of calibrating an MRC model when only data from a moderately dense network of rain gauges is available, rather than from the full rainfall field. The number of gauges needs only be sufficient to adequately estimate the variance in the ratio of the rain rate at the rain gauges to the areal average rain rate across the entire spatial domain. In our example for Warsaw, Poland, we used 25 gauges over an area of approximately 1600 km2. MRC models calibrated using the proposed method were used to downscale 15-min rainfall rates from a 20 by 20 km area to the scale of the rain gauge capture area. Frequency distributions of observed and simulated 15-min rainfall at the gauge scale were very similar. Moreover, the spatial covariance structure of rainfall rates, as characterized by the semivariogram, was reproduced after allowing the probability density function of the random cascade generator to vary with spatial scale.

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A Matérn model of the spatial covariance structure of point rain rates

Stochastic Environmental Research and Risk Assessment ◽

10.1007/s00477-014-0923-2 ◽

2014 ◽

Vol 29 (2) ◽

pp. 411-416 ◽

Cited By ~ 9

Author(s):

Ying Sun ◽

Kenneth P. Bowman ◽

Marc G. Genton ◽

Ali Tokay

Keyword(s):

Covariance Structure ◽

Spatial Covariance ◽

Rain Rates

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Mapping malaria in the Amazon rain forest: A spatio-temporal mixture model

10.1093/oxfordhb/9780198703174.013.5 ◽

2018 ◽

Author(s):

Alexandra Schmidt ◽

Jennifer Hoeting ◽

João Batista M. Pereira ◽

Pedro Paulo Vieira

Keyword(s):

Mixture Model ◽

Rain Forest ◽

Covariance Structure ◽

Temporal Correlation ◽

Free Form ◽

Spatial Covariance ◽

Temporal Prediction ◽

Amazon Rain Forest ◽

Temporal Model ◽

Spatio Temporal

This article focuses on the use of a spatio-temporal mixture model for mapping malaria in the Amazon rain forest. The spatio-temporal model was developed to study malaria outbreaks over a four year period in the state of Amazonas, Brazil. The goal is to predict malaria counts for unobserved municipalities and future time periods with the aid of a free-form spatial covariance structure and a methodology that allows temporal prediction and spatial interpolation for outbreaks of malaria over time. The proposed structure is unique in that it is not a distance- or neighbourhood-based covariance model. Instead, spatial correlation is allowed among all locations to be estimated freely. To model the temporal correlation between observations, a Bayesian dynamic linear model is incorporated into one level of the spatio-temporal mixture model. The model also provides sensible ways of malaria mapping for municipalities which were not observed.

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