# Conditional MH() proposals fail to accept (simplified question)

**URL:** <https://discourse.julialang.org/t/conditional-mh-proposals-fail-to-accept-simplified-question/119531>\
**Category:** Probabilistic Programming\
**Tags:** turing\
**Created:** [September 17, 2024, 10:12pm UTC](https://discourse.julialang.org/t/conditional-mh-proposals-fail-to-accept-simplified-question/119531 "2024-09-17T22:12:48Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![aws](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/aws/32/209472_2.png) [@aws](https://discourse.julialang.org/u/aws)\
**Post date:** [September 17, 2024, 10:12pm UTC](https://discourse.julialang.org/t/conditional-mh-proposals-fail-to-accept-simplified-question/119531/1 "2024-09-17T22:12:48Z")

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Hello,

I am attempting to perform Gibbs sampling using a mixture of close formed conditional posteriors and other samplers. Ultimately, I will use this to estimate parameters in a nonlinear model where I can write out the posterior distribution for some components but not all.

In the simple working example below, I simulate data from a normal distribution with known mean = 0 and variance parameter varphi. I know the closed form for conditional posteriors for varphi ([https://en.wikipedia.org/wiki/Conjugate\_prior](https://en.wikipedia.org/wiki/Conjugate_prior) - Normal with known mean). Since I can write out the conditional posterior distributions for varphi, I can sample from the conditional posteriors directly using MH() with a static proposal, or so I thought. When I run the code below, I notice that the updates for varphi are never accepted - and they should be accepted every time in theory.

My question is, why isn’t MH() behaving as I would expect? This is pretty odd.

Replicable code is pasted below. Thank you for any insight. This seems like a use case that would be generally relevant.

```julia
using Turing
using Distributions
using MCMCChains
using StatsPlots
using PDMats

# Simulation setup
n = 1000 # number of subjects

# Linear regression model
@model function J_samp(y, n)
    
    varphi ~ Gamma(1, 1)
    y ~ MvNormal(zeros(n), PDiagMat(fill(1, n) ./ varphi))

    # Gamma parameter for MH() proposals
    v = (1 + 0.5 * sum((y) .^ 2))

    return y
    
end

# Generate y
model = J_samp(missing, n)
chain = sample(model, Prior(), 1)
y = generated_quantities(model, chain)[1]

# Perform Gibbs sampling
n_samples = 20000
model2 = J_samp(y, n)
samp_meth = Gibbs(
    MH(:varphi => v -> Gamma(1 + 1000/2, (1 / v))),
    )

chain2 = sample(model2, samp_meth, n_samples)
plot(group(chain2, :varphi))

```

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**Author:** ![Red-Portal](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/red-portal/32/9102_2.png) [@Red-Portal](https://discourse.julialang.org/u/Red-Portal)\
**Post date:** [September 22, 2024, 9:48pm UTC](https://discourse.julialang.org/t/conditional-mh-proposals-fail-to-accept-simplified-question/119531/2 "2024-09-22T21:48:48Z")

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In your example, I am not sure if there is a way to tell Turing to plug in `v` as you intended. Instead, it most likely thought that you intended a _random walk_ proposal, therefore plugging the previous value of `varphi` in place of `v`. As of now, I don’t think `MH` has an interface that lets you use the complete conditional information to form a static proposal.