Class mcmc_stepper_hmc (o2scl)¶
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template<class func_t, class data_t, class vec_t, class grad_t = std::function<int(size_t, vec_t&, func_t&, vec_t&, data_t&)>, class vec_bool_t = std::vector<bool>>
class mcmc_stepper_hmc : public o2scl::mcmc_stepper_base<func_t, data_t, vec_t>¶ Hamiltonian Monte Carlo for MCMC.
The vectors step_fac, inv_mass, mom_step, and auto_grad are provided to give different values for each of the parameters. However, if these vectors have a smaller size, then the vector index is wrapped back around to the beginning (using the modulus operator).
The Hamiltonian is
\[ H(q,p) = \frac{1}{2} p^{T} M^{-1} p - \log {\cal{L}} (q) \]where \( M \) is the mass matrix and \( {\cal{L}} \) is the likelihood. (The mcmc_para_base class presumes flat prior distributions.) This class assumes the mass matrix is diagonal and then the inverse is stored in inv_mass.The step is then accepted with probability
\[ \mathrm{min}\left\{ 1,\frac{\exp \left[-H_{\mathrm{new}}\right]} {\exp \left[-H_{\mathrm{old}} \right]} \right\} \]Because the user-specified function, \( f \), computes \( \log {\cal{L}} (q) \), the step should be accepted with probability\[ \mathrm{min} \left\{ 1,\exp \left[ - \sum_i^{N} p_{i,\mathrm{new}} ^2 \mu_i/2 + f_{\mathrm{new}} + \sum_i^{N} p_{i,\mathrm{old}} ^2 \mu_i/2 -f_{\mathrm{old}} \right] \right\} \]where \( i \) is an index over \( N \) parameters and \( \mu_i \) is the inverse mass for parameter \( i \).Public Functions
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inline virtual const char *step_type()¶
Stepper type, “HMC”.
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inline mcmc_stepper_hmc()¶
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inline virtual ~mcmc_stepper_hmc()¶
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inline virtual void write_params(o2scl_hdf::hdf_file &hf)¶
Write stepper parameters to the HDF5 file.
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inline void set_gradients(std::vector<grad_t> &vg)¶
Set the vector of user-specified gradients.
Note that this function stores a pointer to the vector of gradient objects and thus the user must ensure that this object is in scope when the MCMC is performed.
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inline int grad_pot(size_t n_params, vec_t &x, func_t &f, vec_t &g, data_t &dat)¶
Automatically compute the gradient using finite-differencing.
Note
The potential energy is negative log f, so we return the negative of the gradient of the log-likelihood.
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inline virtual void step(size_t i_thread, size_t n_params, func_t &f, vec_t ¤t, vec_t &next, double w_current, double &w_next, vec_t &low, vec_t &high, int &func_ret, bool &accept, data_t &dat, rng<> &r, int verbose)¶
Construct a step.
This function constructs
nextandw_next, the next point and log weight in parameter space. The objective functionfis then evaluated at the new point, the return value is placed infunc_ret, and the step acceptance or rejection is stored inaccept.
Public Members
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vec_t step_fac¶
The factor controlling the step size for the fallback random walk (default is a 1-element vector containing 2.0)
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size_t traj_length¶
Trajectory length (default 20)
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prob_dens_gaussian pdg¶
Standard Gaussian for kinetic energy.
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vec_bool_t auto_grad¶
Indicate which elements of the gradient need to be computed automatically (default is a one-element vector containing true).
For parameters in which this vector has an entry of
true, it is assumed that the user-specified gradient object (if present) cannot compute the gradient and thus a simple numerical finite-differencing gradient is required.
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double epsrel¶
The relative stepsize for finite-differencing (default \( 10^{-6} \) )
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double epsmin¶
The minimum stepsize (default \( 10^{-15} \))
Public Static Attributes
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static const size_t grad_failed = 30¶
Error if gradient failed.
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inline virtual const char *step_type()¶