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Metodiev Martin

2026-09-14

Preparing the data

Load the galaxy dataset:

![plot of chunk load data](figure/load data-1.png)

Computing the sample from MCMC output using bayesmix

Define the logposterior as a function of G and y:

Calculating the MCMC output for 2 components:

## 
## Attaching package: 'bayesmix'

## The following object is masked from 'package:Rfast':
## 
##     Sort

## Compiling model graph
##    Declaring variables
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 82
##    Unobserved stochastic nodes: 88
##    Total graph size: 345
## 
## Initializing model

![plot of chunk mcmc output for 2 components](figure/mcmc output for 2 components-1.png)![plot of chunk mcmc output for 2 components](figure/mcmc output for 2 components-2.png)![plot of chunk mcmc output for 2 components](figure/mcmc output for 2 components-3.png)

Same for 3 components:

## Compiling model graph
##    Declaring variables
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 82
##    Unobserved stochastic nodes: 90
##    Total graph size: 348
## 
## Initializing model

![plot of chunk mcmc output for 3 components](figure/mcmc output for 3 components-1.png)![plot of chunk mcmc output for 3 components](figure/mcmc output for 3 components-2.png)![plot of chunk mcmc output for 3 components](figure/mcmc output for 3 components-3.png)

Computing the THAMES

Estimates of the logarithm of the marginal likelihood:

## radius is too large, decreasing radius ...
## radius is too large, decreasing radius ...

##      G = 2     G = 3
## 1 -235.254 -226.6771

The marginal likelihood is maximised at G=3, which indicates evidence for the Gaussian mixture model with G=3 components. It is also possible to plot the overlap graphs and compute the criterion of overlap (co):

![plot of chunk plot overlap g2 and g3](figure/plot overlap g2 and g3-1.png)![plot of chunk plot overlap g2 and g3](figure/plot overlap g2 and g3-2.png)

##   G = 2 G = 3
## 1     2     3

The CO is largest for G=3, which indicates that the mixture components are most distringuishable when G=3. The CO can also be computed directly, without computing the THAMES:

![plot of chunk plot overlap g2 and g3 using overlapgraph function](figure/plot overlap g2 and g3 using overlapgraph function-1.png)![plot of chunk plot overlap g2 and g3 using overlapgraph function](figure/plot overlap g2 and g3 using overlapgraph function-2.png)

##   G = 2 G = 3
## 1     2     3

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.