Exercise Interval arithmetic and 1D Monte Carlo Simulation

MVEN10 Risk Assessment in Environment and Public Health

Author

Ullrika Sahlin

Exercise overview

Do individually

Background

All estimates (derived from data, modelling or from experts) have associated uncertainty. This uncertainty can be described in different ways and propagated through the assessment model.

Purpose

  • To apply interval arithmetic

  • To explore the principle of 1 dimensional Monte Carlo simulation

Content

The daily dose equation with values taken from the course book by Burgman.

Duration

30 minutes

Reporting

Be prepared to report back at the end of the exercise.

References

The course book chapter 9 and 10 (specifically 9.3.2 and 10.8.1.)

The daily dose equation

\[Dose = \frac{C \cdot IR \cdot EF}{bw}\]

The following estimates are provided:

Concentration mg/l (C): 0.00063

Intake rate l/day (IR): 5

Exposure frequency unitless (EF): 0.15

Body weight mg (bw): 25.11

  1. Calculate the daily intake dose!

Interval artithmetic

To consider uncertainty in estimates, we express uncertainty by intervals defined by a lower and upper bounds.

Concentration mg/l (C): [0.000007, 0.0033]

Intake rate l/day (IR): [4,6]

Exposure frequency unitless (EF): [0.12,0.18]

Body weight mg (bw): [8.43,45.14]

  1. Calculate intervals for daily intake dose using interval arithmetic.

1D Monte Carlo simulation

To consider uncertainty in estimates, we express uncertainty by probability distributions defined by a distribution type and associated parameters.

The aim is that you should be able to do this in Excel and R.

Concentration mg/l (C): \(C\sim N(0.00063,0.000063)\)

Intake rate l/day (IR): \(IR \sim N(5,0.5)\)

Exposure frequency unitless (EF): \(EF \sim U(0.12,0.18)\)

Body weight mg (bw): \(bw \sim N(25.11,2.51)\)

Use 1D Monte Carlo simulation to

  1. approximate the expected value of the daily intake
  2. approximate the standard deviation of the daily intake
  3. derive an approximate 90% probability interval for daily intake
  4. the probability that the daily intake is above the thresholds for the tolerably level

Solution for Monte Carlo simulation done in Excel

Download the file, open it and go to sheet 1.

Solution for Monte Carlo simulation done in R

I let you work on this