# Block Sampling Particle Filter (Linear Gaussian Model; Optimal Proposal)

### Description

The `blockpfGaussianOpt`

function provides a simple example for
RcppSMC. It is based on a block sampling particle filter for a linear
Gaussian model. This is intended only to illustrate the potential of block
sampling; one would not ordinarily use a particle filter for a model in
which analytic solutions are available. The 'optimal' block sampler in the
sense of Doucet, Briers and Senecal (2006) can be implemented in this case.

The `simGaussian`

function simulates data from the associated linear
Gaussian state space model.

### Usage

1 2 | ```
blockpfGaussianOpt(data, particles=1000, lag=5, plot=FALSE)
simGaussian(len)
``` |

### Arguments

`data` |
A vector variable containing the sequence of observations. |

`particles` |
An integer specifying the number of particles. |

`lag` |
An integer specifying the length of block to use. |

`plot` |
A boolean variable describing whether plot should illustrate the estimated path along with the uncertainty. |

`len` |
The length of the data sequence to simulate. |

### Details

The `blockpfGaussianOpt`

function provides a simple example for
RcppSMC. It is based on a simple linear Gaussian state space model in
which the state evolution and observation equations are:
x(n) = x(n-1) + e(n) and
y(n) = x(n) + f(n)
where e(n) and f(n) are mutually-independent standard normal random
variables. The 'optimal' block-sampling proposal described by Doucet
et al (2006) is employed.

The `simGaussian`

function simulates from the same model returning both
the state and observation vectors.

### Value

The `blockpfGaussianOpt`

function returns a matrix containing the final
sample paths and a vector containing their weights.

The `simGaussian`

function returns a list containing the state and data
sequences.

### Author(s)

Adam M. Johansen and Dirk Eddelbuettel

### References

A. Doucet, M. Briers, and S. Senecal. Efficient Block Sampling Strategies for sequential Monte Carlo methods. Journal of Computational and Graphical Statistics, 15(3):693-711, 2006.

### Examples

1 2 | ```
sim <- simGaussian(len=250)
res <- blockpfGaussianOpt(sim$data,lag=5,plot=TRUE)
``` |

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