object GibbsSampling extends App
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- case class State(p: Parameters, state: Vector[(Double, DenseVector[Double])]) extends Product with Serializable
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def
arlikelihood(state: Vector[(Double, DenseVector[Double])], p: Parameters, phi: DenseVector[Double]): Double
Calculate the marginal likelihood of phi given the values of the latent-state and other static parameters
Calculate the marginal likelihood of phi given the values of the latent-state and other static parameters
- state
a sample of the latent state of an AR(1) DLM
- p
the static parameters of a DLM
- phi
autoregressive
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def
dinvGammaStep(mod: Model, priorV: InverseGamma, priorW: InverseGamma, observations: Vector[Data]): (State) ⇒ Rand[State]
A single step of a Gibbs Sampler
A single step of a Gibbs Sampler
- mod
the model containing the definition of the observation matrix F_t and system evolution matrix G_t
- priorV
the prior distribution on the observation noise matrix, V
- priorW
the prior distribution on the system noise matrix, W
- observations
an array of Data containing the observed time series
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def
gibbsMetropStep(proposal: (Parameters) ⇒ Rand[Parameters], mod: Model, priorV: InverseGamma, priorW: InverseGamma, observations: Vector[Data]): (State) ⇒ Rand[State]
Use metropolis hastings to determine the initial state distribution x0 ~ N(m0, C0)
Use metropolis hastings to determine the initial state distribution x0 ~ N(m0, C0)
- proposal
a proposal distribution for the parameters of the initial state
- mod
a DLM model specification
- priorV
the prior distribution of the observation noise matrix
- priorW
the prior distribution of the system noise matrix
- observations
a vector of observations
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def
likelihood(theta: Vector[(Double, DenseVector[Double])], g: (Double) ⇒ DenseMatrix[Double])(p: Parameters): Double
Calculate the marginal likelihood for metropolis hastings
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def
main(args: Array[String]): Unit
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- def metropSamples(proposal: (Parameters) ⇒ Rand[Parameters], mod: Model, priorV: InverseGamma, priorW: InverseGamma, initParams: Parameters, observations: Vector[Data]): Process[State]
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def
metropStep(mod: Model, theta: Vector[(Double, DenseVector[Double])], proposal: (Parameters) ⇒ Rand[Parameters]): (Parameters) ⇒ Rand[Parameters]
A metropolis step for a DLM
A metropolis step for a DLM
- mod
a DLM model
- theta
the currently sampled state of the DLM
- proposal
a symmetric proposal distribution for the parameters of a DLM
- returns
a function from Parameters => Rand[Parameters] which performs a metropolis step to be used in a Markov Chain
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def
sample(mod: Model, priorV: InverseGamma, priorW: InverseGamma, initParams: Parameters, observations: Vector[Data]): Process[State]
Return a Markov chain using Gibbs Sampling to determine the values of the system and observation noise covariance matrices, W and V
Return a Markov chain using Gibbs Sampling to determine the values of the system and observation noise covariance matrices, W and V
- mod
the model containing the definition of the observation matrix F_t and system evolution matrix G_t
- priorV
the prior distribution on the observation noise matrix, V
- priorW
the prior distribution on the system noise matrix, W
- initParams
the initial parameters of the Markov Chain
- observations
an array of Data containing the observed time series
- returns
a Process
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def
sampleObservationMatrix(prior: InverseGamma, f: (Double) ⇒ DenseMatrix[Double], ys: Vector[Data], theta: Vector[(Double, DenseVector[Double])]): Rand[DenseMatrix[Double]]
Sample the (diagonal) observation noise covariance matrix from an Inverse Gamma distribution
Sample the (diagonal) observation noise covariance matrix from an Inverse Gamma distribution
- prior
an Inverse Gamma prior distribution for each variance element of the observation matrix
- ys
the observed values of the time series
- theta
a sample of the DLM state
- returns
the posterior distribution over the diagonal observation matrix
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def
samplePhi(prior: Beta, lambda: Double, tau: Double, s: State): (Double) ⇒ Rand[Double]
Sample the autoregressive parameter with a Beta Prior and proposal distribution
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def
sampleSystemMatrix(prior: InverseGamma, theta: Vector[(Double, DenseVector[Double])], g: (Double) ⇒ DenseMatrix[Double]): Rand[DenseMatrix[Double]]
Sample the diagonal system matrix for an irregularly observed DLM
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def
updateModel(mod: Model, phi: Double*): Model
Update an autoregressive model with a new value of the autoregressive parameter
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