Description 'onepar' 'oneeach' 'absdif' 'dif' 'free' Author(s) See Also

Different parameter restrictions can be included in estimation processes
to make sure `mrf2d`

can successfully include a wide range of model types in
its inference functions.

For model identifiability, at least one linear restriction is necessary.
`mrf2d`

always assume *θ_{0,0,r} = 0* for all relative positions
*r*.

Additionally, each family of restrictions may introduce other restrictions:

This family assumes the model is defined by a single parameter by adding the restriction

*θ_{a,b,r} = φ * 1(a != b).*

Here *1()* denotes de indicator function. In words, the parameter must
be the same value for any pair with different values and 0 for any
equal-valued pair.

Similar to `'onepar'`

, parameters are 0 for equal-valued pairs and a
constant for pairs with different values, but the constant may differ
between different relative positions *r*:

*θ{a,b,r} = φ_r * 1(a != b).*

All parameters *θ_{a,b,r}* with the same absolute difference
between *a* and *b* must be equal within each relative position
*r*. (Note that `'absdif'`

is equal to `'oneeach'`

for binary images).

*θ_{a,b,r} = ∑_d φ_{d,r} * 1(|a-b| == d)*

The same as `'absdif'`

, but parameters may differ between positive and
negative differences.

*θ_{a,b,r} = ∑_d φ_{d,r} * 1(a-b == d)*

No additional restriction, all parameters other than *θ_{0,0,r}*
vary freely.

Victor Freguglia

`vignette("mrf2d-family", package = "mrf2d")`

A paper with detailed description of the package can be found at https://arxiv.org/abs/2006.00383

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