https://github.com/freguglia/mrf2dbayes

An extension of mrf2d for Bayesian analysis.
https://github.com/freguglia/mrf2dbayes

Last synced: 18 days ago
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An extension of mrf2d for Bayesian analysis.

• Host: GitHub
• URL: https://github.com/freguglia/mrf2dbayes
• Owner: Freguglia
• Created: 2020-12-19T23:34:43.000Z (about 4 years ago)
• Default Branch: main
• Last Pushed: 2024-01-19T18:10:03.000Z (11 months ago)
• Last Synced: 2024-01-19T19:27:58.172Z (11 months ago)
• Language: R
• Homepage:
• Size: 289 KB
• Stars: 0
• Watchers: 3
• Forks: 0
• Open Issues: 5
• Metadata Files:
  • Readme: README.Rmd

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README

        
---

output: github_document

---

```{r, include = FALSE}

knitr::opts_chunk$set(

  collapse = TRUE,

  comment = "#>",

  fig.path = "man/figures/README-",

  out.width = "100%"

)

set.seed(1)

```

# mrf2dbayes

[![R build status](https://github.com/Freguglia/mrf2dbayes/workflows/R-CMD-check/badge.svg)](https://github.com/Freguglia/mrf2dbayes/actions)

[![Lifecycle: experimental](https://img.shields.io/badge/lifecycle-experimental-orange.svg)](https://www.tidyverse.org/lifecycle/#experimental)

The goal of `mrf2dbayes` is to provide out-of-the-box implementations of Bayesian inference algorithms for Markov Random Fields on 2-dimensional lattices with pairwise interactions. It can be viewed as a Bayesian extension of the [`mrf2d`](https://github.com/Freguglia/mrf2k) package.

## Installation

The development version from [GitHub](https://github.com/) can be installed with:

``` r

# install.packages("devtools")

devtools::install_github("Freguglia/mrf2dbayes")

```

## Functionalities

### Likelihood approximations

Because the likelihood function for Markov Random Fields is unavailable due to an intractable normalizing constant, `mrf2dbayes` uses an approximate-posterior distribution approach, which substitutes the likelihood function for an approximation in the acceptance ratio of the Metropolis-Hastings algorithm steps.

log-Likelihood approximations are represented by `llapprox` object. These can be created with the homonym function `llapprox()` and passing a reference field, an interaction structure (`mrfi` object from `mrf2d`), an interaction family (also introduced in `mrf2d`), a method and its related additional arguments.

Approximation methods currently implemented are:

  * `"pseudo"`: Pseudolikelihood approximation.

  * `"gt"`: Monte-Carlo Likelihood approximation from Geyer \& Thompson (1992).

  * TODO: `"wl"`: Wang-Landau algorithm.

  * TODO: `"cpseudo"`: Corrected Pseudolikelihood approach from ...

```{r}

library(mrf2dbayes)

# Example MRF from mrf2d

z <- mrf2d::Z_potts

lla <- llapprox(z, mrfi(1), "oneeach", method = "pseudo")

```

### MRF parameters posterior sampling

`mrfbayes()` runs a Metropolis-Hastings algorithm to sample from the posterior distribution of the MRF parameters considering centered Gaussian priors and Gaussian transition kernels. It takes an observed (discrete) random field, `llapprox` object and the size of the chain (`nsamples`) as arguments, as well as other arguments to control parameters such as the prior distribution variance and the transition kernel variance.

```{r, cache = TRUE}

metrop <- mrfbayes(z, lla, nsamples = 10000)

```

A `mrfbayes_out` object is returned. `plot()` and `summary()` methods are available.

```{r, out.width = "70%", fig.align = 'center'}

plot(metrop)

summary(metrop)

```

### Hidden MRF Bayesian analysis

Considering a Gaussian mixture driven by a Hidden MRF, a Metropolis-Within-Gibbs approach is used to sample the hidden (latent) field, the parameters of the hidden MRF and the parameters of the emission distribution simultaneously. 

A Gaussian prior is used for the means of the emission distribution and an Inverse-Gamma for the variances.

```{r, cache = TRUE}

bold5000 <- mrf2d::bold5000

# Dummy discrete field as reference

dummy <- matrix(sample(0:4, 

                       prod(dim(bold5000)), replace = TRUE),

                nrow = nrow(bold5000), ncol = ncol(bold5000))

lla_bold <- llapprox(dummy, mrfi(1), "onepar", method = "pseudo")

```

```{r, cache = TRUE}

hmrf_metrop <- hmrfbayes(bold5000, lla_bold, nsamples = 20000)

```

```{r}

mrf2d::cplot(bold5000)

```

```{r}

plot(hmrf_metrop, "pars")

plot(hmrf_metrop, "theta")

plot(hmrf_metrop, "zprobs")

```