The ValueError: Encountered 'None' gradient error indicates that TensorFlow was unable to compute the gradient for one of its variables. This can happen for several reasons, such as:

• Some part of your logpdf function is non-differentiable or has an ill-defined gradient.
• One of your initial or intermediate parameters is outside the domain of your logpdf function or Hamiltonian Monte Carlo (HMC) kernel.
• You are using an inappropriate learning rate, step number, or mass vector for your Hamiltonian dynamics.
• You are using an execution mode or custom function that does not support automatic gradient computation.

To resolve this issue, you can try some of the following solutions:

• Verify that your logpdf function and HMC kernel are well-defined and correctly implemented. You can use TensorFlow's debugging tools to check if the gradient is being computed correctly.
• Check if your initial and intermediate parameters are within the valid domain of your logpdf function and HMC kernel. You can use regularization or constraints techniques to ensure that your parameters stay within the valid domain.
• Adjust your learning rate, step number, and mass vector to ensure that your Hamiltonian dynamics are functioning correctly. You can use automatic adaptation techniques to find the best values for these parameters.
• Verify if you are using an execution mode and custom functions that support automatic gradient computation. You can refer to the TensorFlow documentation to check which modes and functions are compatible with automatic gradient computation.

I hope these suggestions help you resolve your problem. If you continue to experience difficulties, please provide more information about your code.

• https://arxiv.org/pdf/2104.14421.pdf
• https://arxiv.org/abs/2010.06772
• https://link.springer.com/article/10.1007/s42952-019-00001-3
• https://doi.org/10.48550/arXiv.2010.06772