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Deep Distribution Regression
[article]

2019
*
arXiv
*
pre-print

For a given cut-point c

arXiv:1903.06023v1
fatcat:pnh3q2jeereobat5qlkjbd27l4
*j*, the binary cross entropy (BCE) loss is: BCE(c*j*) = − N n=1 {I(Y n ≤ c*j*) log[F (c*j*; X n , θ)] + [1 − I(Y n ≤ c*j*)] log[1 − F (c*j*; X n , θ)]}. (4) Combining the BCEs across ... Thus the bias for π k (X) is: E[σ(X Tβ k ) − σ(X T β k )] = E dσ(X T β k ) dβ β=β * (β − β) = − K−1*j*=1,*j*=k E[σ(X T β **j*)σ(X T β * k )X T (β*j*− β*j*)] + E[σ(X T β * k ){1 − σ(X T β * k )}X T (β k − ...##
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Nearest-Neighbor Neural Networks for Geostatistics
[article]

2019
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arXiv
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pre-print

We use the exponential correlation function cov(W i , W

arXiv:1903.12125v1
fatcat:mt4itrszabbxfokrmysz3pnvxu
*j*) = σ 2 exp(−||s i − s*j*||/ρ), where σ 2 is the variance, ρ is the range parameter controlling spatial dependence and || · || is the Euclidean ... Flexible methods have been developed to overcome these limitations (*Reich*and Fuentes, 2015, provide a review). ...##
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A nonparametric Bayesian test of dependence
[article]

2015
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arXiv
*
pre-print

The prior of S

arXiv:1501.07198v1
fatcat:ywwdaopwqbe6hfkk5zzcqb7z5a
*j*is S*j*∼ IW D*j*(ρ*j*, W*j*). ... ] S*j*| rest ∼ IW[N + K + ρ*j*, A] P (r = r m | rest) = N i=1 φ*j*(X ij | µ g ij*j*, r m S*j*) K l=1 φ*j*(µ lj | 0, (1 − r m )S*j*) 1 nr nr q=1 N i=1 φ*j*(X ij | µ g ij*j*, r q S*j*) K l=1 φ*j*(µ lj | ...##
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A spatial capture-recapture model for territorial species
[article]

2014
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arXiv
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pre-print

Following Royle and Gardner (2011) , the responses for individual i are modeled as Prob(Y ik =

arXiv:1405.1976v1
fatcat:6uz7wxor6vgx3ganje4pi5r664
*j*) = δ i λwρ(||s−t*j*||) 1+*J*l=1 δ i λwρ(||s−t l ||) k ∈ {1, ...,*J*} 1 1+*J*l=1 δ i λwρ(||s−t l || ... +*J*l=1 γ i δ i λwρ(||s−t l ||) k ∈ {1, ...,*J*} 1 1+*J*l=1 γ i δ i λwρ(||s−t l ||) k =*J*+ 1 (6) P(γ i = 1) = exp[X(s i ) T β] 1 + exp[X(s i ) T β] . ...##
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A Spatial Analysis of Basketball Shot Chart Data

2006
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American Statistician
*

Such charts are used in coaching teams as early as middle school, and are becoming even more

doi:10.1198/000313006x90305
fatcat:4deqkgeiw5fezldyehhl5c2lim
*Brian**J*. ... Deviance is defined as D (b) = −2 log(f (y|b)) = −2 N i=1 p*j*=1 I(y i =*j*) log(θ*j*(η i )) = −2 N i=1 log(θ yi (η i )), where I(y i =*j*) = 1 if y i =*j*, and 0 otherwise. ...##
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A spatiotemporal recommendation engine for malaria control
[article]

2020
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arXiv
*
pre-print

(1 + c 1 ) + b 1 A it if

arXiv:2003.05084v1
fatcat:assz6nnk5jdmdjhm7eyf5ctleq
*j*= i; (c 2 + b 2 A it )/m i if*j*∈ I i , i.e., zone*j*is the neighbor of zone i; 0 otherwise. ... (a it − a jt ) 2 , where α 0 ≥ 0, α = (α 0 , . . . , α q ), and i ∼*j*indicates that zone i and zone*j*are neighbors. ...##
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Modeling Multivariate Mixed-Response Functional Data
[article]

2016
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arXiv
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pre-print

London,

arXiv:1601.02461v1
fatcat:mtq43ijo3jgchaie4ituf5cw34
*J*. Fernandes, C. Salinas, W. Zhao, Ms. L. Summerlin and Ms. P. Hudson. W of the Center for Oral Health Research (COHR) at ... Define M = min{k : p 1k ≥ P 1 , p 2k < P 2 } where p 1k = k i=1 λ i / n*j*=1 λ*j*, p 2k = λ k / n*j*=1 λ*j*and the positive eigenvalues are the first n ≥ k eigenvalues. ...*Reich*and Bandyopadhyay (2010) and*Reich*et al. (2013) offer ways to incorporate informative missingness and apply their methods to the same periodontal data. ...##
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Instrumental variables, spatial confounding and interference
[article]

2021
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arXiv
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pre-print

However, incorporating spatial error to a model does not necessarily address the bias due to unmeasured confounding (Hodges and

arXiv:2103.00304v1
fatcat:byls4doxfze2zpks4bvbedorcq
*Reich*, 2010;*Reich*et al., 2020) . ... Y is set to √ f · A + √ g · U + √*j*· , where f = 0.063, g = 0.023,*j*= 0.914, and has a standard normal distribution. The simulation includes 1,000 repetitions. ...##
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Multivariate spectral downscaling for PM2.5 species
[article]

2019
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arXiv
*
pre-print

., 2010;

arXiv:1909.03816v1
fatcat:dbrpdnqqn5c37cwom7ndimfciq
*Reich*et al., 2013; Bechler et al., 2015) , and to account for forecast errors (Berrocal et al., 2012) . ... The spatial dependence within the i-th pollutant is Cov {w i (s), w i (s )} = K*j*=1 L 2 ij ρ*j*(||s − s ||, φ*j*) , and between the i-th and*j*-th pollutants is Cov {w i (s), w*j*(s )} = K k=1 L ik L jk ...##
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Confounder selection via penalized credible regions

2014
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Biometrics
*

For the empirical Bayes approach β

doi:10.1111/biom.12203
pmid:25123966
fatcat:xypjb4rwfrdwbf4sccgxzv63ee
*j*= η*j*α*j*, η*j*∼ Bern(0.5), and α*j*∼ N(0, 10 2 ); Bayesian adjustment for confounding (BAC; Wang et al., 2012) with ω = ∞ using the R package BEAU; and adaptive ... LASSO with γ = 2. we let τ y = σ 2 y /{(p + 1) −1 p*j*=0 β 2*j*} and τ x = σ 2 x /(p −1 p*j*=1 γ 2*j*) where σ, β, [ We computed the AUC for the credible region approach and adaptive LASSO by calculating ...##
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The R2D2 Prior for Generalized Linear Mixed Models
[article]

2021
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arXiv
*
pre-print

terms gives Var(η i ) = W p

arXiv:2111.10718v1
fatcat:ctcuzkmxq5aqzo2bus255w3rmy
*j*=1 φ*j*+ W q k=1 φ p+k = W . ... We also compute the difference between the true β and estimated β, || β − β|| 2 = p*j*=1 ( β*j*− β*j*) 2 /p. ... 1 φ*j*. ...##
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Distributed Inference for Spatial Extremes Modeling in High Dimensions
[article]

2022
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arXiv
*
pre-print

Let u ij = {1 + ξ i (s

arXiv:2204.14165v1
fatcat:vbji7q5trrd35dzr7fiutnbfb4
*j*)(u*j*− µ i (s*j*)/σ i (s*j*)} 1/ξ i (s*j*) ,*j*= 1, 2. ... Finally, we approximate b 1 (s) ≈ 13*j*=1 z i1,*j*(s)η 1,*j*,k , b 2 (s) ≈ 13*j*=1 z i2,*j*(s)η 2,*j*,k , s ∈ D k , for some unknown parameters {η 1,*j*,k , η 2,*j*,k } 13*j*=1 . ...##
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A semiparametric Bayesian model for spatiotemporal extremes
[article]

2018
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arXiv
*
pre-print

Let the matrix of zone-specific indicators be A with dimension n × 3 with its (i,

arXiv:1812.11699v1
fatcat:ububbntpijbnpjcv2qdbxg6bri
*j*)-th element a ij = 1 if i-th station lies within Zone*j*and 0 otherwise. ... ., 2013; Genest and Nešlehová, 2012) and max-stable processes (*Reich*and Shaby, 2012; Mathieu, 2013; Davison and Huser, 2015) . ...##
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Constrained Bayesian Nonparametric Regression for Grain Boundary Energy Predictions
[article]

2020
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arXiv
*
pre-print

The main effect ap- proximation is then g i (b

arXiv:2002.00938v1
fatcat:zdbfcqubzvchno7gtt7ybsmqxm
*j*) ≈ m r=1 B r (b*j*)β ijr . ... We then randomly generate error ij ∼ N (0, γ 2 ),*j*= 1, 2, 3 as the measurement error associated with l ij ,*j*= 1, 2, 3. ...##
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Bayesian Quantile Regression for Censored Data

2013
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Biometrics
*

*Brian*

*Reich*, NCSU Bayesian Quantile Regression for Censored Data

*Brian*

*Reich*, NCSU Bayesian Quantile Regression for Censored Data Climate change versus global warming Global warming refers to an increase ...

*Brian*

*Reich*, NCSU Bayesian Quantile Regression for Censored Data ...

*Brian*

*Reich*, NCSU Bayesian Quantile Regression for Censored Data

*Brian*

*Reich*, NCSU Bayesian Quantile Regression for Censored Data . Our model with logistic q 0 with L = 4 and L = 8 4. ...

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