study.usecases.md

In MikeXL/bayes: Fun with Bayes and Monte Carlo Simulation

Use Cases

As I have been working on the case of call centre a lot, like to use that as cases of demo.

1. call reduction program

A program introduced in call centre aiming to reduce calls. The experiment carries on ten customers, heck, don't say it is too small of sample size, just hypothetical demo.

here is the data on customer call counts, 5 weeks before and after the program for the ten customers.

before <- c(20, 17, 21, 18, 29, 7, 17, 9, 17, 0)
after  <- c(18, 18, 19, 20, 10, 9, 16, 10, 8, 0)

now we need to know if the program effective.

we can simply do this.

  t.test(before, after, paired=T)

but that won't be fun at all, let's simulate

  diff <- after - before
  out  <- bayes.t.test(diff)
  require(coda)
  mcmc.out <- as.mcmc(out)
  plot(mcmc.out)
  summary(mcmc.out)

2. yet another call reduction program

Now we are running another more realistic call reduction program, rather we have the two experiments groups call them A (control) and B (treatment), and we monitor the two groups for 10 weeks.

a <- c(12, 14, 16, 6, 13, 11, 10, 18, 10,  9)
b <- c(8,  5,  9,  9,  8,  7,  6, 10, 18,  7)

As the data follow poisson distribution, again, we can do the boring thing

  poisson.test(c(sum(a), sum(b)), c(10, 10))

again, let's do the fun thing

  out <- bayes.poisson.test(a, b)
  require(coda)
  out <- cbind(out, NA)
  colnames(out) <- c("lambda_a", "lambda_b", "lambda_a/lambda_b")
  out[, 3] <- out[, 1] / out[, 2]
  mcmc.out <- as.mcmc(out)
  plot(mcmc.out)
  summary(mcmc.out)

3. repeat reduction program

This is another interesting one, if you are in the call centre business, you don't like customer to call you repeated for the same problem. And sometime it is called First Call Resolution (FCR) or first order success (FOS), depends on which part of the department you are in.

Again, we have an lovely program aiming improve the FCR, that has run 10 weeks for the two groups naming A and B, in both case n=1000.

a <- c(803, 784, 802, 782, 760, 781, 772, 767, 795, 792)
b <- c(811, 827, 827, 817, 828, 824, 847, 832, 839, 829)
n <- 1000

as the success of a call or repeats sorta follow Bernoulli trial, we can use binomial test in the boring way

  binom.test(sum(a), n*length(a), p=sum(b)/(n*length(b)))

or do it in the exciting way

  require(coda)
  x <- cbind(a, rep(n, length(a)))
  y <- cbind(b, rep(n, length(b)))
  out.x <- bayes.binomial.test(x)     # estimate probability (theta) for x
  out.y <- bayes.binomial.test(y)     # estimate probability (theta) for y
  mcmc.out.x <- as.mcmc(out.x)
  mcmc.out.y <- as.mcmc(out.y)
  plot(mcmc.out.x)
  plot(mcmc.out.y)
  summary(mcmc.out.x)
  summary(mcmc.out.y)

the simplest solution here

    prior <- rbeta(10000, a, b)
    posterior <- rbeta(10000, a+y, b+n-y)

one more thing

I found SAS amazed me with ocean of procedures for doing the similar things, here we can just talk on PROC GENMOD

data callcentre; input n calls city$ treatment; ln = log(n); datalines; 278 10 calgary 0 148 25 calgary 1 543 66 edmonton 0 148 7 edmonton 1 523 61 van 0 150 10 van 1 ; run;

assume we have collected the call data from number of customers above (n). Good habit to start with negative binomial then poisson if desired and when dispersion parameter is 0.

PROC GENMOD DATA = callcentre;
  CLASS city treatment;
  MODEL calls = treatment * city / d=nb offset=ln;
  BAYES cprior=normal dprior=gamma;
  LSMEANS treatment * city / diff cl;
  /*LSMESTIMATES works too but with designate positional*/
RUN;

MikeXL/bayes documentation built on Aug. 1, 2020, 1:36 a.m.