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### Deep Distribution Regression [article]

Rui Li, Howard D. Bondell, Brian J. Reich
2019 arXiv   pre-print
For a given cut-point c 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 −  ...

### Nearest-Neighbor Neural Networks for Geostatistics [article]

Haoyu Wang, Yawen Guan, Brian J Reich
2019 arXiv   pre-print
We use the exponential correlation function cov(W i , W 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).  ...

### A nonparametric Bayesian test of dependence [article]

Yimin Kao, Brian J Reich, Howard D Bondell
2015 arXiv   pre-print
The prior of S j is S j ∼ IW D jj , 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 |  ...

### A spatial capture-recapture model for territorial species [article]

Brian J. Reich, Beth Gardner
2014 arXiv   pre-print
Following Royle and Gardner (2011) , the responses for individual i are modeled as Prob(Y ik = 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] .  ...

### A Spatial Analysis of Basketball Shot Chart Data

Brian J Reich, James S Hodges, Bradley P Carlin, Adam M Reich
2006 American Statistician
Such charts are used in coaching teams as early as middle school, and are becoming even more 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.  ...

### A spatiotemporal recommendation engine for malaria control [article]

Qian Guan, Brian J. Reich, Eric B. Laber
2020 arXiv   pre-print
          (1 + c 1 ) + b 1 A it if 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.  ...

### Modeling Multivariate Mixed-Response Functional Data [article]

Beth A. Tidemann-Miller, Brian J. Reich, Ana-Maria Staicu
2016 arXiv   pre-print
London, 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.  ...

### Instrumental variables, spatial confounding and interference [article]

Andrew Giffin, Brian J. Reich, Shu Yang, Ana G. Rappold
2021 arXiv   pre-print
However, incorporating spatial error to a model does not necessarily address the bias due to unmeasured confounding (Hodges and 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.  ...

### Multivariate spectral downscaling for PM2.5 species [article]

Yawen Guan, Brian J Reich, James A Mulholland, Howard H Chang
2019 arXiv   pre-print
., 2010; 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  ...

### Confounder selection via penalized credible regions

Ander Wilson, Brian J. Reich
2014 Biometrics
For the empirical Bayes approach β 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  ...

### The R2D2 Prior for Generalized Linear Mixed Models [article]

Eric Yanchenko, Howard D. Bondell, Brian J. Reich
2021 arXiv   pre-print
terms gives Var(η i ) = W p 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 ( βj − β j ) 2 /p.  ...  1 φ j .  ...

### Distributed Inference for Spatial Extremes Modeling in High Dimensions [article]

Emily C. Hector, Brian J. Reich
2022 arXiv   pre-print
Let u ij = {1 + ξ i (s 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 .  ...

### A semiparametric Bayesian model for spatiotemporal extremes [article]

Arnab Hazra, Brian J. Reich, Benjamin A. Shaby, Ana-Maria Staicu
2018 arXiv   pre-print
Let the matrix of zone-specific indicators be A with dimension n × 3 with its (i, 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) .  ...

### Constrained Bayesian Nonparametric Regression for Grain Boundary Energy Predictions [article]

Haoyu Wang, Srikanth Patala, Brian J. Reich
2020 arXiv   pre-print
The main effect ap- proximation is then g i (b 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.  ...

### Bayesian Quantile Regression for Censored Data

Brian J. Reich, Luke B. Smith
2013 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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