Monte Carlo Simulation II Advanced Herd Management Anders Ringgaard - PowerPoint PPT Presentation

Monte Carlo Simulation II Advanced Herd Management Anders Ringgaard Kristensen Slide 1

State of nature concept The hyper distribution : The hyper distribution : An infinite population of An infinite population of flocks each having its own flocks each having its own state of nature defining state of nature defining average growth, mortality, average growth, mortality, laying performance etc. laying performance etc. Flock 1 Flock 2 Flock 3 Flock 4 Flock 5 We can draw as many random (but realistic!) flocks from the hyper distribution as we wish. Slide 2

Distribution of state of nature: Main problem It is difficult to specify the distribution of the state of nature. For a systematic description of the approach used in the SimFlock model, reference is made to Kristensen & Pedersen (2003) – link at the homepage. Basic principle: • Each parameter of the state of nature 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. • Estimated from production data from 30 flocks in Zimbabwe. • Easy, if parameters are independent • Difficult if they interact Slide 3

Example: Mortality in SimFlock It is expected that the mortalities of different bird groups in the same flock are correlated. Mortality is represented as survival rates p . We need to model the “fact” that the survival rate for chicks is correlated to the survival rate for growers etc. If we observe N birds over a given period and count the number n that survive, then n is binomially distributed with parameters p and N . If other factors influence p we can express the effect in a logistic model, which is more or less the standard tool when dealing with binomially distributed data. Slide 4

The Logit-transformation Logit 4 3 2 1 Logit(p) 0 0 0,2 0,4 0,6 0,8 1 -1 -2 -3 -4 p The Logit-transformation converts a probability p ∈ [ 0; 1] to a value y ∈ ] - ∞ ; ∞ [ . The transformed variable, y , may be used as response variable in “usual” regression analysis etc. Slide 5

The SimFlock survival rate model logit( p ij ) = µ + α j + F i + ( α F ) ij Where µ is the intercept • α 1 , α 2 , α 3 , α 4 are the systematic effects of bird groups • (i.e. chicks, growers, pullets and cockerels) • F i ∼ N(0, σ F ) is the random effect of flock • ( α F ) ij ∼ N(0, σ α F ) is the random interaction between flock and bird group. State of nature parameters: p i 1 , p i 2 , p i 3 , p i 4 , i.e. a survival rate for each bird group. 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. Slide 6

Sampling from the hyper distribution Draw a random value F i from N(0, σ F 2 ) Draw 4 random values ( α F ) i 1 , ( α F ) i 2 , ( α F ) i 3 and ( α F ) i 4 from N(0, σ α F 2 ) Calculate the 4 logit values ( j = 1, 2, 3, 4) 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) Slide 7

SimFlock: An object oriented model Breeding animals Hens & Cocks Eggs Infertile Household consumption Chicks Dead Growers Pullets Cockerels Market Slide 8

User interface – visible objects All birds and eggs present in the flock shown. States of the birds can be investigated Demo Slide 9

SimFlock: Elements – where are they? Decision rule Θ State of nature Φ 0 Hyper distribution p ( Φ 0 = φ 0 ) State variables Φ s 1 … Φ sT Output variables Ω Slide 10

SimFlock: Decision variables 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). Slide 11

SimFlock: State of nature parameters In SimFlock, a state of nature is described by 42 parameters: • Daily gains of birds, general linear model • Survival rates, logistic model • Full grown weights, normal distribution • Age at puberty, normal distribution • Egg fertilization probability, beta distribution • Egg hatching probability, logistic model • Number of eggs before incubation, normal dist. Each time a parameter is defined, a hyper distribution is specified. Slide 12

SimFlock: Hyper distribution(s) The hyper distribution of the state of nature is specified through 64 hyper parameters. Most of them estimated from the field data collected in 30 flocks. The hyper distribution represents the whole population of flocks under the conditions in question. 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 realistic hypothetical flocks. • Decision rules may have different effects in different flocks. Slide 13

SimFlock: State variables The state variables of day i are the states of the individual birds and eggs on that day: • Eggs: • Fertilized/ not fertilized • Birds: • Age • Weight • Growth potential • Full grown weight • Laying capacity • Gender • … • Farmer: • Needs meat? There are millions of state variables in a simulation run. Slide 14

States of a bird All birds: • Unique ID (given at hatching – next integer) • Age (updated daily) • Weight (updated daily) • Gender (drawn at random at hatching) • Full grown weight (drawn at random at hatching) • Growth potential (permanent, drawn at hatching) Cocks: No further states. For chicks and growers furthermore: • Growth state (drawn at hatching/ transition) Slide 15

States of a pullet In addition to the general states: • Pullet: • Age at first egg, “puberty” (drawn at transition) • Growth state (drawn at transition) • Cockerel: • Age at “puberty” (drawn at transition) • Growth state (drawn at transition) Slide 16

States of a hen In addition to the general states: • Behavior, not used? (drawn at transition) • Laying capacity (drawn at transition) • State in cycle (laying, incubating, brooding, barren) – updated daily. • Days since transition in cycle – updated daily • Eggs at incubating (drawn at transition in cycle) • Eggs in nest – updated daily. • Fertile eggs in nest – updated daily. Slide 17

SimFlock: Output variables A total of 40 are defined: • Realised gain • Realised mortality • Eggs removed • Chickens produced • … Usual technical and economical key figures. Slide 18

SimFlock: Simulation The farmer, birds and eggs are represented as objects in the model. Each (simulated) day, the states of all objects are updated: • Age • Weight • Survival • Transition (e.g. egg → chick, chick → grower, etc) • Eggs in nest • … Slide 19

Use of the simulation model System comprehension • Answering “what if” questions General decision support (at population level) • The main purpose of SimFlock Decision support at flock level • Not yet possible Slide 20

System comprehension Usually carried out under one state of nature Answer questions like: • If we assume the state of nature parameters are Φ 0 = φ 0 what are then the consequences? • What if we could improve the survival rate of chicks? • Vary the survival rate systematically – run simulations and explore the results • etc. Weakness: State of nature parameters are mutually correlated! Slide 21

General decision support Population level Carried out under multiple states of nature Questions like: • Under what circumstances does it pay to change the decision rule from Θ 1 to Θ 2 ? • Generate multiple states of nature (random flocks) • Run a simulation job under Θ 1 • Run a simulation job under Θ 2 • Identify the states of nature where it pays Slide 22

Decision support at flock level Should “Jens Hansen” change his management from decision rule Θ 1 to Θ 2 ? Problems: • We don’t know the state of nature for Jens Hansen’s flock. • We need to put Jens Hansen’s flock into the model: • Not so difficult in SimFlock but very difficult in SimHerd or the Dina Pig simulation model Not yet possible in any(?) simulation model. • Nevertheless, it has often been done with SimHerd (by ignoring the problems) Solution: • Combine the simulation model with a Bayesian network • Distinguish between true underlying levels and observed consequences • Observe the consequences, enter evidence and propagate to obtain a distribution for the state of nature in this particular flock. • If anybody wants to solve this problem within the framework of a Master’s thesis it would be very much appreciated! Slide 23

A BN for state of nature in a flock Hyper distribution. Initially set to the distribution in the population State of nature. Observed in Jens Hansen’s flock. When observed, we can update the rest! Slide 24