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
diff[A](xs: Seq[A])(implicit A: Numeric[A]): Seq[A]
Calculate the lagged difference between items in a Seq
Calculate the lagged difference between items in a Seq
- xs
a sequence of numeric values
- returns
a sequence of numeric values containing the once lagged difference
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def
dinvGammaStep(mod: Model, priorV: InverseGamma, priorW: InverseGamma, observations: Vector[Data]): Kleisli[Rand, State, 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 ffbs(mod: Model, observations: Vector[Data])(s: State): Rand[State]
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def
gibbsMetropStep(proposal: (Parameters) ⇒ Rand[Parameters], mod: Model, priorV: InverseGamma, priorW: InverseGamma, observations: Vector[Data]): Kleisli[Rand, State, 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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isInstanceOf[T0]: Boolean
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def
likelihood(g: (Double) ⇒ DenseMatrix[Double])(s: State): Double
Calculate the marginal likelihood for metropolis hastings
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def
main(args: Array[String]): Unit
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- App
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- @deprecatedOverriding( "main should not be overridden" , "2.11.0" )
- 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, proposal: (Parameters) ⇒ Rand[Parameters]): (State) ⇒ Rand[State]
A metropolis step for a DLM
A metropolis step for a DLM
- mod
a DLM model
- proposal
a symmetric proposal distribution for the parameters of a DLM
- returns
a function from State => Rand[State] which performs a metropolis step to be used in a Markov Chain
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def
observationSquaredDifference(f: (Double) ⇒ DenseMatrix[Double], state: Vector[(Double, DenseVector[Double])], observations: Vector[Data]): DenseVector[Double]
Calculate the sum of squared differences between the one step forecast and the actual observation for each time sum((y_t - f_t)^2)
Calculate the sum of squared differences between the one step forecast and the actual observation for each time sum((y_t - f_t)^2)
- f
the observation matrix, a function from time => DenseMatrix[Double]
- state
an array containing the state sampled from the backward sampling algorithm
- observations
an array containing the actual observations of the data
- returns
the sum of squared differences between the one step forecast and the actual observation for each time
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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], observations: Vector[Data])(s: State): Rand[State]
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
- observations
the observed values of the time series
- 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, g: (Double) ⇒ DenseMatrix[Double])(s: State): Rand[State]
Sample the diagonal system matrix for an irregularly observed DLM
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def
toString(): String
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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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(Since version 2.11.0) the delayedInit mechanism will disappear