Parameter Estimation in Linear Models

Koch, Karl‐Rudolf

doi:10.1007/978-3-662-03976-2_4

Cited by 38 publications

(54 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Statistical tests of whether the characteristic y varied across factors involved null hypotheses of the form Hβ = 0, where β = [β 0 , β s , β c ] T , and H is the linear contrast (47). We first performed a statistical test of overall differences across all factors with H = [0, 1, 0; 0, 0, 1].…”

Section: Methodsmentioning

confidence: 99%

“…In short, the test involved comparing the likelihood of an appropriately restricted model with the original model (47). We first performed a statistical test of overall differences across factors.…”

Section: Methodsmentioning

confidence: 99%

“…Statistical tests involved null hypotheses of the form Hβ = 0, where β = [β 0 , β m , β d , β s , β c , β ms , β mc , β ds , β dc , β 1 , β 2 , β 3 , β 4 ] T , and H is the linear contrast (47). We tested whether ADNI-Mem deteriorated across disease stages (i.e., from CN to MCI to AD) for each factor.…”

Section: Methodsmentioning

confidence: 99%

See 2 more Smart Citations

Bayesian model reveals latent atrophy factors with dissociable cognitive trajectories in Alzheimer’s disease

Zhang¹,

Mormino

Sun³

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

159

166

View full text Add to dashboard Cite

We used a data-driven Bayesian model to automatically identify distinct latent factors of overlapping atrophy patterns from voxelwise structural MRIs of late-onset Alzheimer's disease (AD) dementia patients. Our approach estimated the extent to which multiple distinct atrophy patterns were expressed within each participant rather than assuming that each participant expressed a single atrophy factor. The model revealed a temporal atrophy factor (medial temporal cortex, hippocampus, and amygdala), a subcortical atrophy factor (striatum, thalamus, and cerebellum), and a cortical atrophy factor (frontal, parietal, lateral temporal, and lateral occipital cortices). To explore the influence of each factor in early AD, atrophy factor compositions were inferred in beta-amyloid-positive (Aβ+) mild cognitively impaired (MCI) and cognitively normal (CN) participants. All three factors were associated with memory decline across the entire clinical spectrum, whereas the cortical factor was associated with executive function decline in Aβ+ MCI participants and AD dementia patients. Direct comparison between factors revealed that the temporal factor showed the strongest association with memory, whereas the cortical factor showed the strongest association with executive function. The subcortical factor was associated with the slowest decline for both memory and executive function compared with temporal and cortical factors. These results suggest that distinct patterns of atrophy influence decline across different cognitive domains. Quantification of this heterogeneity may enable the computation of individual-level predictions relevant for disease monitoring and customized therapies. Factor compositions of participants and code used in this article are publicly available for future research.

show abstract

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Bayesian model reveals latent atrophy factors with dissociable cognitive trajectories in Alzheimer’s disease

Zhang¹,

Mormino

Sun³

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

159

166

View full text Add to dashboard Cite

show abstract

“…To ensure the quality of least-squares solution, we screen the observables for outliers using Baada's data snooping technique (Koch, 1987;Caspary, 1988). First the standardized residual of an observ- able is computed as…”

Section: Levelingmentioning

confidence: 99%

Multiple sensors applied to monitorland subsidence in Central Taiwan

et al. 2015

View full text Add to dashboard Cite

Abstract. During 1992During -2013, pumping of groundwater caused large-scale aquifer-system compaction and land subsidence in the Choshui River Alluvial Fan (CRAF) in Taiwan. The subsidence has already endangered the operation of Taiwan High Speed Rail (THSR). In this paper, we introduce the multiple sensors monitoring system to study the extent of subsidence in CRAF and its mechanism, including GPS (Global Positioning System), PSI (Persistent Scatterer Interferometry), leveling and multi-layer compaction monitoring well. These sensors complement each other in spatial and temporal resolutions.

show abstract

“…Thus, the longitudes of the ionospheric pierce points were shifted by the time difference between the epoch of observation and the map reference epoch, as used for the generation of the IONosphere map EXchange (IONEX) product [Schaer et al, 1998]. Finally the spherical harmonic coefficients were estimated together with the differential code biases by an least squares adjustment, following Koch [1997]. Within the adjustment process a zero mean condition was imposed on the satellite DCBs, and consecutive vTEC maps were slightly constrained to obtain stable estimates for uncovered regions.…”

Section: Global Maps Of Vertical Total Electron Contentmentioning

confidence: 99%

Effect of the Earth's oblateness on the estimation of global vertical total electron content maps

Hobiger¹,

Kondo²,

Koyama³

et al. 2007

Geophysical Research Letters

View full text Add to dashboard Cite

[1] Global Navigation Satellite Systems like the Global Positioning System and the Russian counterpart GLONASS permit the estimation of ionosphere parameters in the form of vertical total electron content (vTEC) values. Although the GNSS reference systems are rotation-symmetric ellipsoids, simple approximations of gravitational equipotential surfaces, the modeling of global vTEC maps is carried out in spherical systems, since this simplifies mathematical expressions. Due to the Earth's oblateness this approximation is in slight disagreement to the geometric situation of the observations. Thus it is expected that estimated vTEC values will change when the WGS84 ellipsoid is taken as a reference for all computations. We will discuss both, the direct effect (i.e due to a shift of the ionospheric pierce point) and the indirect effect, caused by a change of the mapping function, on global vTEC values using a single layer model of the ionosphere. We show that the estimated global TEC maps change slightly by up to ±0.4 TECU when refined mathematical models are considered and we discuss how differential code biases are affected by this change. Citation: Hobiger, T., T. Kondo, Y. Koyama, R. Ichikawa, and R. Weber (2007), Effect of the Earth's oblateness on the estimation of global vertical total electron content maps, Geophys. Res. Lett., 34, L11113,

show abstract

Parameter Estimation in Linear Models

Cited by 38 publications

References 0 publications

Bayesian model reveals latent atrophy factors with dissociable cognitive trajectories in Alzheimer’s disease

Bayesian model reveals latent atrophy factors with dissociable cognitive trajectories in Alzheimer’s disease

Multiple sensors applied to monitorland subsidence in Central Taiwan

Effect of the Earth's oblateness on the estimation of global vertical total electron content maps

Contact Info

Product

Resources

About