---
title: "batchmix workflow"
author: "Stephen Coleman"
output: pdf_document
%\VignetteEngine{knitr::knitr}
%\VignetteIndexEntry{Using BatchMixtureModel}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)

set.seed(1)
```

## Introduction

This document shows the basics of applying our Bayesian model-based 
clustering/classification with joint batch correction in ``R``. It shows how to
generate some toy data, apply the model, assess convergence and process outputs.

## Data generation

We simulate some data using the ``generateBatchData`` function.

```{r dataGen}
library(ggplot2)
library(batchmix)

# Data dimensions
N <- 600
P <- 4
K <- 5
B <- 7

# Generating model parameters
mean_dist <- 2.25
batch_dist <- 0.3
group_means <- seq(1, K) * mean_dist
batch_shift <- rnorm(B, mean = batch_dist, sd = batch_dist)
std_dev <- rep(2, K)
batch_var <- rep(1.2, B)
group_weights <- rep(1 / K, K)
batch_weights <- rep(1 / B, B)
dfs <- c(4, 7, 15, 60, 120)

my_data <- generateBatchDataMVT(
  N,
  P,
  group_means,
  std_dev,
  batch_shift,
  batch_var,
  group_weights,
  batch_weights,
  dfs
)
```

This gives us a named list with two related datasets, the ``observed_data`` 
which includes batch effects and the ``corrected_data`` which is batch-free. It
also includes ``group_IDs``, a vector indicating class membership for each item,
``batch_IDs``, which indicates batch of origin for each item, and ``fixed``,
which indicates which labels are observed and fixed in the model. We pull these 
out of the names list in the format that the modelling functions desire them.

```{r dataClean}
X <- my_data$observed_data

true_labels <- my_data$group_IDs
fixed <- my_data$fixed
batch_vec <- my_data$batch_IDs

alpha <- 1
initial_labels <- generateInitialLabels(alpha, K, fixed, true_labels)
```

## Modelling

Given some data, we are interested in modelling it. We assume here that the set
of observed labels includes at least one example of each class in the data. 

```{r runMCMCChains}
# Sampling parameters
R <- 1000
thin <- 50
n_chains <- 4

# Density choice
type <- "MVT"

# MCMC samples and BIC vector
mcmc_output <- runMCMCChains(
  X,
  n_chains,
  R,
  thin,
  batch_vec,
  type,
  initial_labels = initial_labels,
  fixed = fixed
)
```

We want to assess two things. First, how frequently the proposed parameters in the Metropolis-Hastings step are accepted:

```{r plotAcceptanceRatesEarly}
plotAcceptanceRates(mcmc_output)
```

Secondly, we want to asses how well our chains have converged. To do this we plot the ``complete_likelihood`` of each chain. This is the quantity most relevant to a clustering/classification, being dependent on the labels. The ``observed_likelihood`` is independent of labels and more relevant for density estimation.

```{r likelihood}
plotLikelihoods(mcmc_output)
```

We see that our chains disagree. We have to run them for more iterations. We use the ``continueChains`` function for this.

```{r continueChains}
R_new <- 9000

# Given an initial value for the parameters
new_output <- continueChains(
  mcmc_output,
  X,
  fixed,
  batch_vec,
  R_new,
  keep_old_samples = TRUE
)
```

To see if the chains better agree we re-plot the likelihood.

```{r continuedLikelihood}
plotLikelihoods(new_output)
```

We also re-check the acceptance rates.

```{r plotAcceptanceRates}
plotAcceptanceRates(new_output)
```

This looks like several of the chains agree by the 5,000th iteration.

## Process chains

We process the chains, acquiring point estimates of different quantities.

```{r processChains}
# Burn in
burn <- 5000

# Process the MCMC samples
processed_samples <- processMCMCChains(new_output, burn)
```

## Visualisation

For multidimensional data we use a PCA plot.

```{r pca}

chain_used <- processed_samples[[1]]

pc <- prcomp(X, scale = T)
pc_batch_corrected <- prcomp(chain_used$inferred_dataset)

plot_df <- data.frame(
  PC1 = pc$x[, 1],
  PC2 = pc$x[, 2],
  PC1_bf = pc_batch_corrected$x[, 1],
  PC2_bf = pc_batch_corrected$x[, 2],
  pred_labels = factor(chain_used$pred),
  true_labels = factor(true_labels),
  prob = chain_used$prob,
  batch = factor(batch_vec)
)

plot_df |> 
  ggplot(aes(
    x = PC1,
    y = PC2,
    colour = true_labels,
    alpha = prob
  )) +
  geom_point()

plot_df |> 
  ggplot(aes(
    x = PC1_bf,
    y = PC2_bf,
    colour = pred_labels,
    alpha = prob
  )) +
  geom_point()

test_inds <- which(fixed == 0)

sum(true_labels[test_inds] == chain_used$pred[test_inds])/length(test_inds)

```
