object StudentT
Fit a state space model with a latent Gaussian state and a Student's t observation distribution using the fact that the student's t-distribution is an Inverse Gamma mixture of normals
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- case class PmmhState(ll: Double, p: DlmParameters, nu: Int, accepted: Int) extends Product with Serializable
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case class
State(p: DlmParameters, variances: Vector[Double], nu: Int, state: Vector[SamplingState], accepted: Int) extends Product with Serializable
The state of the Markov chain for the Student's t-distribution gibbs sampler
The state of the Markov chain for the Student's t-distribution gibbs sampler
- p
the DLM parameters
- variances
the variances for each of the observations V_t
- nu
the degrees of freedom of the Student's t-distribution
- state
the currently sampled state using FFBS
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- def filter(mod: Dlm, variances: Vector[Double], observations: Vector[Data], params: DlmParameters): Vector[KfState]
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- def interpolate(data: Vector[Data], mod: Dglm, nu: Int, p: DlmParameters): Process[State]
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def
interpolateStep(data: Vector[Data], mod: Dglm, p: DlmParameters): (State) ⇒ Rand[State]
Sample the latent state for the student's t model
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def
ll(ys: Vector[Data], xs: Vector[SamplingState], mod: Dglm, p: DlmParameters)(nu: Int): Double
Calculate the log-likelihood of the student's t-distributed model
Calculate the log-likelihood of the student's t-distributed model
- ys
a vector of observations
- xs
a sample from the latent-state of the student's t model
- mod
the Student t DGLM
- p
the
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def
sample(data: Vector[Data], priorW: InverseGamma, priorNu: DiscreteDistr[Int], propNu: (Int) ⇒ Rand[Int], propNuP: (Int, Int) ⇒ Double, mod: Dglm, params: DlmParameters): Process[State]
Perform Gibbs Sampling for the Student t-distributed model
Perform Gibbs Sampling for the Student t-distributed model
- priorW
the prior distribution of the system noise matrix
- mod
the DGLM representing the Student's t model
- params
the initial parameters
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def
sampleNu(prop: (Int) ⇒ Rand[Int], propP: (Int, Int) ⇒ Double, prior: (Int) ⇒ Double, likelihood: (Int) ⇒ Double): (Int) ⇒ Rand[(Int, Boolean)]
Sample the degrees of freedom for the observation distribution
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def
samplePmmh(data: Vector[Data], priorW: ContinuousDistr[Double], priorV: ContinuousDistr[Double], priorNu: DiscreteDistr[Int], prop: (DlmParameters) ⇒ Rand[DlmParameters], propNu: (Int) ⇒ Rand[Int], propNuP: (Int, Int) ⇒ Double, model: Dlm, n: Int, initP: DlmParameters, initNu: Int): Process[PmmhState]
Particle Marginal Metropolis Hastings for the Student's t-distributed state space model
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def
sampleScaleT(dof: Int, variances: Vector[Double]): Gamma
Sample the (square of the) scale of the Student's t distribution
Sample the (square of the) scale of the Student's t distribution
- dof
the degrees of freedom of the Student's t observation distribution
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def
sampleState(variances: Vector[Double], mod: Dlm, observations: Vector[Data], params: DlmParameters): Rand[Vector[SamplingState]]
Sample the state, incorporating the drawn variances for each observation
Sample the state, incorporating the drawn variances for each observation
- variances
the sampled auxiliary parameters
- mod
the DLM
- params
the parameters of the DLM model
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def
sampleVariances(ys: Vector[Data], f: (Double) ⇒ DenseMatrix[Double], dof: Int, theta: Vector[SamplingState], p: DlmParameters): Vector[Double]
Sample the variances of the Normal distribution These are auxilliary variables required when calculating the one-step prediction in the Kalman Filter
Sample the variances of the Normal distribution These are auxilliary variables required when calculating the one-step prediction in the Kalman Filter
- ys
an array of observations of length N
- f
the observation matrix
- dof
the degrees of freedom of the Student's t-distribution
- returns
a Rand distribution over the list of N variances
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def
step(data: Vector[Data], priorW: InverseGamma, priorNu: DiscreteDistr[Int], propNu: (Int) ⇒ Rand[Int], propNuP: (Int, Int) ⇒ Double, mod: Dglm, p: DlmParameters): (State) ⇒ Rand[State]
A single step of the Student t-distribution Gibbs Sampler
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def
stepPmmh(priorW: ContinuousDistr[Double], priorV: ContinuousDistr[Double], priorNu: DiscreteDistr[Int], prop: (DlmParameters) ⇒ Rand[DlmParameters], propNu: (Int) ⇒ Rand[Int], propNuP: (Int, Int) ⇒ Double, ll: (DlmParameters, Int) ⇒ Double): (PmmhState) ⇒ Rand[PmmhState]
Perform a single step of the PMMH algorithm for the Student's t distributed state space model
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