HamiltonianMC

Hamiltonian Monte Carlo (HMC) sampler

Uses gradient information for efficient exploration of the posterior. HMC simulates Hamiltonian dynamics to propose distant states with high acceptance probability.

Hamiltonian: $$ H(\theta, p) = -\log p(\theta|y) + \frac{1}{2}p^T p $$ where $\theta$ is position (parameters), $p$ is momentum.

Leapfrog integrator preserves volume and is reversible:

Half-step momentum: $p_{i+1/2} = p_i + \frac{\epsilon}{2}\nabla_\theta \log p(\theta_i|y)$
Full-step position: $\theta_{i+1} = \theta_i + \epsilon p_{i+1/2}$
Half-step momentum: $p_{i+1} = p_{i+1/2} + \frac{\epsilon}{2}\nabla_\theta \log p(\theta_{i+1}|y)$

See

Conceptual Introduction to HMC

Constructors

Constructor

new HamiltonianMC(stepSize?, nSteps?): HamiltonianMC

Defined in: mc/src/samplers/hmc.js:37

Accepts either positional arguments or a single options object.

Parameters

stepSize?

any = 0.01

Leapfrog step size (epsilon), or an options object { stepSize, nSteps }

nSteps?

number = 10

Number of leapfrog steps (L)

Returns

HamiltonianMC

Examples

new HamiltonianMC(0.01, 10)

new HamiltonianMC({ stepSize: 0.01, nSteps: 10 })

Properties

nSteps

nSteps: number

Defined in: mc/src/samplers/hmc.js:44

stepSize

stepSize: any

Defined in: mc/src/samplers/hmc.js:43

Methods

getParams()

getParams(): object

Defined in: mc/src/samplers/hmc.js:51

Get the sampler’s configuration.

Returns

object

nSteps

nSteps: number

stepSize

stepSize: number

hamiltonian()

hamiltonian(position, momentum, model): number

Defined in: mc/src/samplers/hmc.js:106

Compute Hamiltonian (total energy)

Parameters

position

any

Current position

momentum

any

Current momentum

model

Model

The probabilistic model

Returns

number

Hamiltonian value

leapfrog()

leapfrog(position, momentum, model): any

Defined in: mc/src/samplers/hmc.js:62

Leapfrog integrator for Hamiltonian dynamics

Parameters

position

any

Current position (parameters)

momentum

any

Current momentum

model

Model

The probabilistic model

Returns

any

New position and momentum

sample()

sample(model, initialValues, nSamples?, burnIn?, thin?): any

Defined in: mc/src/samplers/hmc.js:133

Run HMC sampling.

The sampling controls may be passed positionally or as a single options object. When an options object is supplied as the third argument, the burnIn and thin positional arguments are ignored in favour of the object’s fields.

Parameters

model

Model

The probabilistic model

initialValues

any

Initial parameter values

nSamples?

any = 1000

Number of samples, or an options object

burnIn?

number = 500

Number of burn-in samples to discard (positional form)

thin?

number = 1

Thinning interval (positional form)

Returns

any

Trace object with samples and diagnostics

Examples

hmc.sample(model, { mu: 0 }, 1000, 500, 1)

hmc.sample(model, { mu: 0 }, { nSamples: 1000, burnIn: 500, thin: 1 })