README.Rmd

---
title: "Introduction to propro"
author: "Gert Janssenswillen"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Introduction to propro}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
warning = FALSE
)
```

```{r warning = F, message = F}
library(propro)
library(bupaR)
library(petrinetR)
```


This document introduces propro, an R-package for constructing probabilistic process models using Bayesian inference and MCMC. In this illustration, we will use the following event log.

```{r, fig.width = 7}
log <- log_2_paper_ICPM
log %>%
    trace_explorer(coverage = 1)
```

Furthermore, we will use the following model.

```{r, fig.width = 7}
net <- model_2_paper_ICPM
net$final_marking <- "p8"
render_PN(net)
```

Constructing a process model strats with the create_propro function
```{r}
create_propro(log, net) -> propro
```
Which we can view by printing it

```{r}
print_propro(propro)
```

In order to see what the different beta's refer to, we can plot the underlying automaton

```{r, fig.width = 7}
plot_automaton(propro)
```

We now have to specify the priors. Let's start by automatically setting to complements of all splits which have two options.
```{r}
propro %>%
    set_prior_complements(n = 2) %>%
    list_priors()
```


Furthermore, we can see that the some probabilities should be the same if we interpret the petri net strictly. We therefor implement the following constraints.

beta 3 = beta 12
beta 5 = beta 10 = beta 14 = beta 19
beta 8 = beta 17
beta 7 = beta 16
beta 9 = beta 18

```{r}
propro %>%
    set_prior_complements(n = 2) %>%
    set_prior("beta[12]", "<- beta[3]")%>%
    set_prior("beta[10]", "<- beta[5]")%>%
    set_prior("beta[14]", "<- beta[5]")%>%
    set_prior("beta[19]", "<- beta[5]")%>%
    set_prior("beta[17]", "<- beta[8]")%>%
    set_prior("beta[16]", "<- beta[7]")%>%
    set_prior("beta[18]", "<- beta[9]") %>%
    list_priors


```

Now we can define the remain priors. For beta 7,8 and 9, we will use a Dirichlet distributions. Therefore, we first combine these into one prior specification. Then we define the distribution and add alpha to the data.

```{r}
propro %>%
    set_prior_complements(n = 2) %>%
    set_prior("beta[12]", "<- beta[3]")%>%
    set_prior("beta[10]", "<- beta[5]")%>%
    set_prior("beta[14]", "<- beta[5]")%>%
    set_prior("beta[19]", "<- beta[5]")%>%
    set_prior("beta[17]", "<- beta[8]")%>%
    set_prior("beta[16]", "<- beta[7]")%>%
    set_prior("beta[18]", "<- beta[9]") %>%
    combine_consecutive_priors(start = 7, end = 9) %>%
    set_prior("beta[7:9]", "<- ddirich(alpha[1:3])") %>%
    add_data("alpha", c(1,1,1)) %>%
    list_priors
```
All remaining priors we will set to beta distribution with paramters a = 1 and b = 1.

```{r}
propro %>%
    set_prior_complements(n = 2) %>%
    set_prior("beta[12]", "<- beta[3]")%>%
    set_prior("beta[10]", "<- beta[5]")%>%
    set_prior("beta[14]", "<- beta[5]")%>%
    set_prior("beta[19]", "<- beta[5]")%>%
    set_prior("beta[17]", "<- beta[8]")%>%
    set_prior("beta[16]", "<- beta[7]")%>%
    set_prior("beta[18]", "<- beta[9]") %>%
    combine_consecutive_priors(start = 7, end = 9) %>%
    set_prior("beta[7:9]", "~ddirich(alpha[1:3])") %>%
    add_data("alpha", c(1,1,1)) %>%
    set_prior("beta[1]", "~dbeta(1,1)")%>%
    set_prior("beta[3]", "~dbeta(1,1)")%>%
    set_prior("beta[5]", "~dbeta(1,1)")%>%
    set_prior("beta_f", "~dbeta(1,1)") %>%
    list_priors()
```

Finally, let's add additional variable. For example, a delta which compares beta[5] with beta[8]. Then we save the propro model.

```{r}
propro %>%
    set_prior_complements(n = 2) %>%
    set_prior("beta[12]", "<- beta[3]")%>%
    set_prior("beta[10]", "<- beta[5]")%>%
    set_prior("beta[14]", "<- beta[5]")%>%
    set_prior("beta[19]", "<- beta[5]")%>%
    set_prior("beta[17]", "<- beta[8]")%>%
    set_prior("beta[16]", "<- beta[7]")%>%
    set_prior("beta[18]", "<- beta[9]") %>%
    combine_consecutive_priors(start = 7, end = 9) %>%
    set_prior("beta[7:9]", "~ddirich(alpha[1:3])") %>%
    add_data("alpha", c(1,1,1)) %>%
    set_prior("beta[1]", "~dbeta(1,1)")%>%
    set_prior("beta[3]", "~dbeta(1,1)")%>%
    set_prior("beta[5]", "~dbeta(1,1)")%>%
    set_prior("beta_f", "~dbeta(1,1)") %>%
    add_variable("delta[1]", "<- beta[5] - beta[9]") -> propro 
```

The final models looks as follows.
```{r}
propro %>%
    print_propro()
```

We can now run the model, after writing it to a file.

```{r message = F}
propro %>%
    write_propro("propro_model2.txt") %>%
    run_propro(n.chains = 2, n.iter = 40000, n.burnin = 1000)
```