RStan-models

STAN code using R, used to model data following the distributions mentioned below. A part of Unsupervised Machine Learning course.

Bernoulli model

y∼Bern(θ)
θ∼Beta(α,β)

Binomial model

y∼Bin(N,θ)
θ∼Beta(α,β)

Poisson-Gamma model

y∼Poisson(λ)
λ∼Gamma(α0,β0)

Normal distribution with location

y∼N(μ,σ20)
μ∼N(μ0,σ20)

Normal distribution with location and scale

y∼N(μ,σ2)
μ∼N(μ0,σ20)
and, σ2∼InvGam(α0,β0)
or, σ∼logNormal(μ0,σ20)
or, σ∼Cauchy(μ0,σ0)

Multivariate normal distribution with location and scale

y∼N(μ,σ2I)
μ∼N(μ0,σ20I)
σ2∼InvGam(α0,β0)

Bayesian linear regression

τ∼Gam(α0,β0)
σ2∼InvGam(α0,β0)
w∼N(0,τ−1I)
y∼N(w⊤x,σ2)
K=number of dimensions

Bayesian linear regression with ARD prior

αi=1…K∼Gam(α0,β0)
σ2∼InvGam(α0,β0)
w∼N(0,α−1I)
y∼N(w⊤x,σ2)
K=number of dimensions

PCA with ARD prior

xn∼N(Wzn,τ−1ID)
Wk|αk∼N(0,α−1kID)
αk∼Gam(α0,β0)
τ∼Gam(α0,β0)
z∼N(0,IK)
N=number of data points
D=dimension of data point
K=latent dimension

Bayesian CCA

x(m)n∼N(W(m)zn,(τ(m))−1I)
W(m)k|α(m)k∼N(0,(αk)−1I)
α(m)k∼Gamma(α0,β0)
τ(m)∼Gamma(α0,β0)
zn∼N(0,Ik)

Bayesian CP factorization

yn,d,l∼N(K∑k=1(xn,k⋅wd,k⋅ul,k),τ−1)
xn,k∼N(0,1)
ul,k∼N(0,1)
wd,k∼N(0,α−1k)
τ∼Gam(α0,β0)
αk∼Gam(α0,β0)