The State-of-nature: (Basically) a collection of all the - PDF document

1/15/2020 Department of Veterinary and Animal Sciences Department of Veterinary and Animal Sciences Outline 1. Summary of Monday’s lecture 2. The SimFlock model • User interface Monte Carlo Simulation II • State variables • Decision variables State of nature Anders Ringgaard Kristensen and • Hyper distribution Dan Børge Jensen • Output variables 3. Use of the simulation model • Running simulation jobs • Results and interpretation 4. Simulation as a decision support tool Advanced Quantitative Methods in Herd Management Slide 2 Department of Veterinary and Animal Sciences Summary from Monday Simulation models, two (main) types: 1. Deterministic: no randomness – same input, same output 2. Stochastic: random sampling – same input, different output 1. Random sampling is done using random number generation with an appropriate distribution function The State-of-nature: (Basically) a collection of all the information that describes • the system, you are trying to model SimFlock Model Uncertainty of the state-of-nature: Each parameter of the s.o.n is specified through a • distribution instead of a value. Such a distribution is called a hyper distribution. • The parameters of a hyper distribution are called hyper • parameters. The SimBatch model A simulation model implemented in R • Fairly straight forward – you could make one yourself! • Department of Veterinary and Animal Sciences User interface – visible objects SimFlock: Elements – where are they? Decision rule Θ Small holder State of nature Φ 0 farms in Africa Hyper distribution p ( Φ 0 = φ 0 ) All birds and eggs present in State variables Φ s 1 … Φ sT the flock shown. Output variables Ω States of the birds can be investigated Θ: thetha, upper case Φ: phi, upper case Demo Ω : Omega, upper case Advanced Quantitative Methods in Herd Management Slide 6 1

1/15/2020 Department of Veterinary and Animal Sciences Department of Veterinary and Animal Sciences SimFlock: State variables of the objects SimFlock: An object oriented model The farmer, birds, and eggs are The state variables of day i are the states of the represented as individual birds and eggs on that day: Breeding animals objects in the model! • Eggs: Hens & Cocks • Fertilized/not fertilized Specific state variables: • Birds: • Age Cocks: No further states Eggs Infertile • Weight Household Chicks and growers: Growth state • Growth potential • Full grown weight consumption Pullet: Age at “puberty”, Growth state • Laying capacity Chicks • Gender Cockerel: Age at “puberty”, Growth state Dead • … Hen: Behavior, Laying capacity, • Farmer: State in cycle, Growers • Needs meat? Days since transition in cycle, Eggs at incubating Eggs in nest, Fertile eggs in nest Pullets Cockerels There are millions of state variables in a simulation run. Market Department of Veterinary and Animal Sciences SimFlock: Decision variables 5 Minute Break Built-in decisions (farmer icon): • Intended flock size: • Hens • Cocks • Egg removing policy • Days from start laying • Season • Policy for buying breeding birds: • Hens • Cocks Other decisions modeled through expected effects (e.g. on mortality). Advanced Quantitative Methods in Herd Management Slide 9 Department of Veterinary and Animal Sciences Department of Veterinary and Animal Sciences Distribution of state of nature: Main problem Example: Mortality in SimFlock It is difficult to specify the distribution of the state of nature. It is expected that the mortalities of different bird groups in the same flock are correlated – this should be included in Solution: the model! • We use hyper distributions Mortality is represented as survival rates p . • The hyper parameters are stimated from production data from 30 flocks in Zimbabwe. If we observe N birds over a given period and count the • Easy, if parameters are independent number n that survive, then n is binomially distributed • Difficult if they interact with parameters p and N with p ~ n/N. If other factors influence p (e.g. the bird group) we can express the effect in a logistic model For a systematic description of the approach used in the SimFlock model, reference is made to Kristensen & Pedersen (2003) – link (standard tool for dealing with binomially distributed data) at the homepage. Advanced Quantitative Methods in Herd Management Advanced Quantitative Methods in Herd Management Slide 11 Slide 12 2

1/15/2020 Department of Veterinary and Animal Sciences The Logit-transformation The SimFlock survival rate model logit( p ij ) = µ + α j + F i + ( α F ) ij Logit 4 Where 3 • µ is the intercept 2 1 • α 1 , α 2 , α 3 , α 4 are the systematic effects of bird groups Logit(p) 0 (i.e. chicks, growers, pullets and cockerels) 0 0,2 0,4 0,6 0,8 1 -1 • F i ~ N(0, σ F ) is the random effect of flock -2 • ( α F ) ij ~ N(0, σ α F ) is the random interaction between -3 flock and bird group. -4 p State of nature parameters: p i 1 , p i 2 , p i 3 , p i 4 , i.e. a The Logit-transformation converts a probability p ∈ [0;1] to a survival rate for each bird group. value y ∈ ]- ∞ ; ∞ [. The transformed variable, y , may be used as response variable in “usual” regression analysis etc. Hyper parameters: µ , α 1 , α 2 , α 3 , α 4 , σ F , σ α F – estimated from field data from 30 flocks in Zimbabwe. Department of Veterinary and Animal Sciences Department of Veterinary and Animal Sciences SimFlock: State of nature parameters Defining the Survival state of nature - sampling from the hyper distribution In SimFlock, a state of nature is described by 42 parameters : Draw a random effect of flock • Daily gains of birds, general linear model F i • Survival rates, logistic model • Full grown weights, normal distribution from N(0, σ F 2 ) • Age at puberty, normal distribution • Egg fertilization probability, beta distribution Draw 4 random bird/flock interaction values • Egg hatching probability, logistic model ( α F ) i 1 , ( α F ) i 2 , ( α F ) i 3 , ( α F ) i 4 • Number of eggs before incubation, normal dist. from N(0, σ α F 2 ) Each time a parameter is defined, a hyper Calculate the 4 logit values ( j = 1, 2, 3, 4) distribution is specified. y ij = logit( p ij ) = µ + α j + F i + ( α F ) ij Transform to 4 survival rates ( j = 1, 2, 3, 4) log( p ij /(1- p ij )) = y ij ⇔ p ij = 1/(e - y ij + 1) Advanced Quantitative Methods in Herd Management Slide 16 Department of Veterinary and Animal Sciences Department of Veterinary and Animal Sciences SimFlock: Output variables SimFlock: Hyper distribution(s) A total of 40 are defined: The hyper distribution of the state of nature is specified • Realised gain through 64 hyper parameters . • Realised mortality Most of them estimated from the field data collected in 30 • Eggs removed flocks. • Chickens produced A state of nature drawn from the hyper distribution represents • … one (hypothetical) flock. • By drawing e.g. many states of nature we can generate many Usual technical and economical key realistic hypothetical flocks. figures. • Decision rules may have different effects in different flocks. Advanced Quantitative Methods in Herd Management Advanced Quantitative Methods in Herd Management Slide 17 Slide 18 3

1/15/2020 10 Minute Break Use of the simulation model Department of Veterinary and Animal Sciences Department of Veterinary and Animal Sciences Use of the simulation model System comprehension Usually carried out under one state of nature System comprehension • Answering “what if” questions Answer questions like: • If we assume the state of nature parameters are General decision support (at population level) Φ 0 = φ 0 what are then the consequences? • The main purpose of SimFlock • What if we could improve the survival rate of chicks? Decision support at flock level • Vary the survival rate systematically – run simulations and explore the results • Not yet possible • etc. Weakness: State of nature parameters are mutually correlated! Advanced Quantitative Methods in Herd Management Advanced Quantitative Methods in Herd Management Slide 21 Slide 22 Department of Veterinary and Animal Sciences Department of Veterinary and Animal Sciences General decision support Defining a simulation job in SimFlock Population level Create an initial flock Specify: Carried out under multiple states of nature • Number of states of nature (if more than 1) • A question of obtaining a representative sample of flocks Questions like: from the abstract population. • Under what circumstances does it pay to change • Number of replications per state of nature the decision rule from Θ 1 to Θ 2 ? • How precise do you want the results for each flock to be? • Generate multiple states of nature • Mean values (random flocks) • Distribution • Run a simulation job under Θ 1 • Number of days to simulate • Run a simulation job under Θ 2 • A long simulation period will increase the precision • Burn-in days • Identify the states of nature where it pays • We want to ignore the effect of the initial flock. Advanced Quantitative Methods in Herd Management Advanced Quantitative Methods in Herd Management Slide 23 Slide 24 4