diff --git a/previews/PR16/index.html b/previews/PR16/index.html index 720ba27..c717439 100644 --- a/previews/PR16/index.html +++ b/previews/PR16/index.html @@ -1,6 +1,8 @@ -Home · SSMProblems
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SSMProblems

Installation

In the julia REPL:

]add SSMProblems

Documentation

SSMProblems defines a generic interface for State Space Problems (SSM). The main objective is to provide a consistent interface to work with SSMs and their logdensities.

Consider a markovian model from[Murray]: state space model

The model is fully specified by the following densities:

  • Initialisation: $f_0(x)$
  • Transition: $f(x)$
  • Emission: $g(x)$

And the dynamics of the model reduces to:

\[x_t | x_{t-1} \sim f(x_t | x_{t-1})\]

\[y_t | x_t \sim g(y_t | x_{t})\]

assuming $x_0 \sim f_0(x)$.

The joint law follows:

\[p(x_{0:T}, y_{0:T}) = f_0(x_0) \prod_t g(y_t | x_t) f(x_t | x_{t-1})\]

Model users can define their SSM using the following interface:


-struct Model <: AbstractStateSpaceModel end
+Home · SSMProblems
Edit on GitHub
SSMProblems
Installation
In the julia REPL:
]add SSMProblems
Documentation
SSMProblems defines a generic interface for State Space Problems (SSM). The main objective is to provide a consistent interface to work with SSMs and their logdensities.
Consider a markovian model from[Murray]: state space model
The model is fully specified by the following densities:
  • Initialisation: $f_0(x)$
  • Transition: $f(x)$
  • Emission: $g(x)$
And the dynamics of the model reduces to:
\[\begin{aligned}
+x_t | x_{t-1} &\sim f(x_t | x_{t-1}) \\
+y_t | x_t &\sim g(y_t | x_{t})
+\end{aligned}\]
assuming $x_0 \sim f_0(x)$. 
The joint law follows:
\[p(x_{0:T}, y_{0:T}) = f_0(x_0) \prod_t g(y_t | x_t) f(x_t | x_{t-1})\]
Users can define their SSM with SSMProblems in the following way:
struct Model <: AbstractStateSpaceModel end
 
 # Define the structure of the latent space
 particleof(::Model) = Float64
@@ -36,4 +38,4 @@
         particles[i] = transition!!(rng, t, model, particles[i])
         logweights[i] += emission_logdensity(t, model, particles[i])
     end
-end
Interface
SSMProblems.emission_logdensity — Function
emission_logdensity(model, timestep, state, observation[, cache])
Compute the log potential of the current particle. This effectively "reweight" each particle.
source
SSMProblems.transition!! — Function
transition!!(rng, model[, timestep, state, cache])
Simulate the particle for the next time step from the forward dynamics.
source
SSMProblems.transition_logdensity — Function
transition_logdensity(model, timestep, prev_state, next_state[, cache])
(Optional) Computes the log-density of the forward transition if the density is available.
source
  • Murray
    Murray, Lawrence & Lee, Anthony & Jacob, Pierre. (2013). Rethinking resampling in the particle filter on graphics processing units. 

+end

Interface

SSMProblems.emission_logdensity — Function
emission_logdensity(model, state, observation[, timestep, cache])

Compute the log potential of the current particle. This effectively "reweight" each particle.

source
SSMProblems.linearize — Method
linearize(particle)

Return the trace of a particle, i.e. the sequence of states from the root to the particle.

source
SSMProblems.transition!! — Function
transition!!(rng, model[, timestep, state, cache])

Simulate the particle for the next time step from the forward dynamics.

source
SSMProblems.transition_logdensity — Function
transition_logdensity(model, prev_state, current_state[, timestep, cache])

(Optional) Computes the log-density of the forward transition if the density is available.

source
  • Murray

    Murray, Lawrence & Lee, Anthony & Jacob, Pierre. (2013). Rethinking resampling in the particle filter on graphics processing units.

diff --git a/previews/PR16/search/index.html b/previews/PR16/search/index.html index 3b6895c..b9f9547 100644 --- a/previews/PR16/search/index.html +++ b/previews/PR16/search/index.html @@ -1,2 +1,2 @@ -Search · SSMProblems

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    +Search · SSMProblems

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      diff --git a/previews/PR16/search_index.js b/previews/PR16/search_index.js index 28c8b96..d460a72 100644 --- a/previews/PR16/search_index.js +++ b/previews/PR16/search_index.js @@ -1,3 +1,3 @@ var documenterSearchIndex = {"docs": -[{"location":"#SSMProblems","page":"Home","title":"SSMProblems","text":"","category":"section"},{"location":"#Installation","page":"Home","title":"Installation","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"In the julia REPL:","category":"page"},{"location":"","page":"Home","title":"Home","text":"]add SSMProblems","category":"page"},{"location":"#Documentation","page":"Home","title":"Documentation","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"SSMProblems defines a generic interface for State Space Problems (SSM). 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