Vector Differential Calculus in Statistics

By Matt P. Wand. 2002

48 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/805c66a3bf8d1e53c7d3d986c11087fa21d53053

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Citations in the corpus

Regression Density Estimation With Variational Methods and Stochastic Approximation (2012, methodology): “The updates that are available in closed form are easy to derive using vector differential calculus (e.g., see Wand 2002).”
Likelihood-Based Inference for Max-Stable Processes (2009, unknown): “Vector differential calculus (e.g., Wand 2002) leads to Dσ ij(ψ) ≡ [ −vϕ(w) azi − wϕ(v) azj + { C ( (w2 − 1)ϕ(v) a2z2j + (1 + wv)ϕ(w) a2zizj ) + B ( (v2 − 1)ϕ(w) a2z2i + (1 + wv)ϕ(v) a2zizj ) + (w − 2v − wv 2)ϕ(w) a3z2i zj + (v − 2w − vw 2)ϕ(v) a3z2j zi }/ (BC + D) ] Dσ a , where we have used the…”
Variational inference for count response semiparametric regression (2013, unknown): “Here we use Algorithm 1 to fit a version of the Bayesian penalized model that Marley & Wand (2010) fitted via MCMC. Thurston, Wand & Weincke (2000) and Marley & Wand (2010) considered Negative Binomial additive models of the form: adductsi|β,u1,u2,u3,u4, κ ind.∼ Negative-Binomial(exp{β0 + f1(ageInit”
Fully simplified multivariate normal updates in non-conjugate variational message passing (2014, unknown): “2 of Wand (2002), dvec(Σq(β,u)) S = −1 diag[exp{Cμq(β,u) + 12diagonal(CΣq(β,u)C T )}]12Q(C) dvec(Σq(β,u)) −12vec ([ σ−2 β Ip 0 0 μq(1/σ2)IK ])T d vec(Σq(β,u))”
Semiparametric Mean Field Variational Bayes: General Principles and Numerical Issues (2016, methodology): “From Theorem 2(b) of Wand (2014), vec[C diag{dμω(μ,Σ)}C] = Q(C) dμω(μ,Σ).”