solution

We print out the inference table and then provide a helper function to let you quickly see the conditional inferences.

You can also see the solutions in Chapter 12 or by using the shiny.

1 Set up and helper function

library(CausalQueries)
library(knitr)
library(tidyverse)

data_consistent <- function(my_table, seen = c("S1", "Y0")) {
  for(j in seen){
    my_table <- 
    my_table[c(names(my_table)[grepl(j,  names(my_table))], "in_query",   "priors")]
  }

  my_table <- my_table |> filter(
    my_table |> select(-in_query, -priors) |> apply(1, sum) > 0)

  my_table |> select(-in_query, -priors)
  
  pDQ <- my_table |> filter(in_query) |> pull(priors) |> sum()
  pD  <- my_table |> pull(priors) |> sum()
  print(c("prob of Data and Query:", pDQ))
  print(c("prob of Data:", pD))
  print(c("prob Query | Data:", pDQ/pD))
  
  print(my_table)

}  

2 Model parameters

Check that the model has the parameters we want!

model <- 
  make_model("S -> C -> Y <- R <- X; X -> C -> R") |>
  set_restrictions(labels = list(C = c('1110', '1111'), 
                                 R = c('0000', '0001'), 
                                 Y = '0001'),
                 keep = TRUE)

query <- "Y[X=1] > Y[X=0]"

model$parameters_df |> kable()

	param_names	node	gen	param_set	nodal_type	given	param_value	priors
1	S.0	S	1	S	0		0.5	1
2	S.1	S	1	S	1		0.5	1
3	X.0	X	2	X	0		0.5	1
4	X.1	X	2	X	1		0.5	1
12	C.1110	C	3	C	1110		0.5	1
20	C.1111	C	3	C	1111		0.5	1
21	R.0000	R	4	R	0000		0.5	1
29	R.0001	R	4	R	0001		0.5	1
45	Y.0001	Y	5	Y	0001		1.0	1

my_table <-
  model  |>
  grab(what = "ambiguities_matrix") |>
  data.frame() |>
  mutate(
    in_query = get_query_types(model, query)$types,
    priors   = CausalQueries:::get_type_prob(model)) 

3 Look up table for conditional inferences

my_table |> kable()

	S1X1C0R0Y0	S0X0C1R0Y0	S1X0C1R0Y0	S0X1C1R0Y0	S1X1C1R0Y0	S0X1C1R1Y1	S1X1C1R1Y1	in_query	priors
S0X0C1110R0000Y0001	0	1	0	0	0	0	0	FALSE	0.0625
S1X0C1110R0000Y0001	0	0	1	0	0	0	0	FALSE	0.0625
S0X1C1110R0000Y0001	0	0	0	1	0	0	0	FALSE	0.0625
S1X1C1110R0000Y0001	1	0	0	0	0	0	0	FALSE	0.0625
S0X0C1111R0000Y0001	0	1	0	0	0	0	0	FALSE	0.0625
S1X0C1111R0000Y0001	0	0	1	0	0	0	0	FALSE	0.0625
S0X1C1111R0000Y0001	0	0	0	1	0	0	0	FALSE	0.0625
S1X1C1111R0000Y0001	0	0	0	0	1	0	0	FALSE	0.0625
S0X0C1110R0001Y0001	0	1	0	0	0	0	0	TRUE	0.0625
S1X0C1110R0001Y0001	0	0	1	0	0	0	0	FALSE	0.0625
S0X1C1110R0001Y0001	0	0	0	0	0	1	0	TRUE	0.0625
S1X1C1110R0001Y0001	1	0	0	0	0	0	0	FALSE	0.0625
S0X0C1111R0001Y0001	0	1	0	0	0	0	0	TRUE	0.0625
S1X0C1111R0001Y0001	0	0	1	0	0	0	0	TRUE	0.0625
S0X1C1111R0001Y0001	0	0	0	0	0	1	0	TRUE	0.0625
S1X1C1111R0001Y0001	0	0	0	0	0	0	1	TRUE	0.0625

4 Examples of conditional inferences

(using a helper funciton to display the subset of the data we care about)

An inference:

4.1 I observe \(S=0, Y=0\) only:

  data_consistent(my_table, seen = c("S0", "Y0"))

[1] "prob of Data and Query:" "0.125"                  
[1] "prob of Data:" "0.375"        
[1] "prob Query | Data:" "0.333333333333333" 
                    S0X0C1R0Y0 S0X1C1R0Y0 in_query priors
S0X0C1110R0000Y0001          1          0    FALSE 0.0625
S0X1C1110R0000Y0001          0          1    FALSE 0.0625
S0X0C1111R0000Y0001          1          0    FALSE 0.0625
S0X1C1111R0000Y0001          0          1    FALSE 0.0625
S0X0C1110R0001Y0001          1          0     TRUE 0.0625
S0X0C1111R0001Y0001          1          0     TRUE 0.0625

4.2 I observe \(S = 1, X = 1, C = 0\)

data_consistent(my_table, seen = c("S1", "X1", "C0"))

[1] "prob of Data and Query:" "0"                      
[1] "prob of Data:" "0.125"        
[1] "prob Query | Data:" "0"                 
                    S1X1C0R0Y0 in_query priors
S1X1C1110R0000Y0001          1    FALSE 0.0625
S1X1C1110R0001Y0001          1    FALSE 0.0625