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I have previousely used PyMC3 and am now looking to use tensorflow probability.

I have built some model in both, but unfortunately, I am not getting the same answer. In fact, the answer is not that close. 

    # definition of the joint_log_prob to evaluate samples
    def joint_log_prob(data, proposal):
      prior = tfd.Normal(mu_0, sigma_0, name='prior')
      likelihood = tfd.Normal(proposal, sigma, name='likelihood')
    return (prior.log_prob(proposal) + tf.reduce_mean(likelihood.log_prob(data)))

    proposal = 0

# define a closure on joint_log_prob
    def unnormalized_log_posterior(proposal):
       return joint_log_prob(data=observed, proposal=proposal)

# define how to propose state
    rwm = tfp.mcmc.NoUTurnSampler(
       target_log_prob_fn=unnormalized_log_posterior,
       max_tree_depth = 100,
       step_size = 0.1
       )

# define initial state
     initial_state = tf.constant(0., name='initial_state')



    @tf.function
    def run_chain(initial_state, num_results=7000, num_burnin_steps=2000,adaptation_steps = 1):
       adaptive_kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(
       rwm, num_adaptation_steps=adaptation_steps,
       step_size_setter_fn=lambda pkr, new_step_size: pkr._replace(step_size=new_step_size),
       step_size_getter_fn=lambda pkr: pkr.step_size,
       log_accept_prob_getter_fn=lambda pkr: pkr.log_accept_ratio,  
    )

    return tfp.mcmc.sample_chain(
        num_results=num_results,
        num_burnin_steps= num_burnin_steps,
        current_state=initial_state,
        kernel=adaptive_kernel,
        trace_fn=lambda cs, kr: kr)


    trace, kernel_results = run_chain(initial_state)

This is the posterior using PyMC3 and TFP

I am using NoUTurns sampler, I have added some stepsize adaptation, without it, the result is pretty much the same.

I dont really know how to move forward?

Maybe be joint log probability is wrong?

usman Farooq
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  • I don't see any PyMC code. What is the plot of? Please make [a reproducible example](https://stackoverflow.com/help/minimal-reproducible-example). – merv Nov 29 '19 at 00:27

1 Answers1

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You should use reduce_sum in your log_prob instead of reduce_mean. Otherwise you are effectively downweighting the likelihood by a factor equal to the size of your data set. This would cause the samples to look a lot more like the prior, which might be what you’re seeing in the plot.

Chris Suter
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    I don't see the relationship between the prior and taking the mean (as opposed to the sum). The mean is usually taken with respect to the number of training examples. – nbro Jan 27 '20 at 01:19
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    The joint prob is `p(theta) * p(X | theta)`, where `p(theta)` is prior, `p(X | theta)` is likelihood; `X = {x_i: i=1..N}` is some data.The log joint is log prior + log likelihood. If the likelihood factorizes, the log joint is `log p(X, theta) = log p(theta) + sum_i log p(x_i | theta)` The OP has computed `log p(theta) + (1 / N) * sum_i log p(x_i | theta)` which is wrong -- it's "down-weighting" the likelihood terms, which will tend to cause the "posterior" to look more like the prior than it should for the amount of data (scare quotes on "posterior" cuz it's not the posterior!) – Chris Suter Jan 29 '20 at 02:12