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1 SimFlock: An object oriented model Sampling from the hyper - PDF document

Nov 08, 2022 •116 likes •193 views

State of nature concept The hyper distribution : Monte Carlo Simulation II An infinite population of flocks each having its own state of nature defining Advanced Herd Management average growth, mortality, Anders Ringgaard Kristensen laying

  1. State of nature concept The hyper distribution : Monte Carlo Simulation II An infinite population of flocks each having its own state of nature defining Advanced Herd Management average growth, mortality, Anders Ringgaard Kristensen 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 1 Slide 2 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. For a systematic description of the approach used in the SimFlock model, reference is made to Kristensen & Mortality is represented as survival rates p . Pedersen (2003) – link at the homepage. We need to model the “fact” that the survival rate for chicks Basic principle: is correlated to the survival rate for growers etc. • Each parameter of the state of nature is specified through a If we observe N birds over a given period and count the distribution instead of a value. Such a distribution is called a number n that survive, then n is binomially distributed hyper distribution. The parameters of a hyper distribution with parameters p and N . are called hyper parameters. If other factors influence p we can express the effect in a • Estimated from production data from 30 flocks in logistic model, which is more or less the standard tool Zimbabwe. when dealing with binomially distributed data. • Easy, if parameters are independent • Difficult if they interact Slide 3 Slide 4 The Logit-transformation The SimFlock survival rate model Logit logit( p ij ) = µ + α j + F i + ( α F ) ij 4 3 2 Where 1 µ is the intercept Logit(p) 0 • α 1 , α 2 , α 3 , α 4 are the systematic effects of bird groups 0 0,2 0,4 0,6 0,8 1 -1 • -2 • F i ∼ N(0, σ F ) is the random effect of flock (i.e. chicks, growers, pullets and cockerels) -3 • ( α F ) ij ∼ N(0, σ α F ) is the random interaction between -4 p flock and bird group. The Logit-transformation converts a probability p ∈ [0;1] to a State of nature parameters: p i 1 , p i 2 , p i 3 , p i 4 , i.e. a value y ∈ ]- ∞ ; ∞ [. The transformed variable, y , may be used survival rate for each bird group. Hyper parameters: µ , α 1 , α 2 , α 3 , α 4 , σ F , σ α F – as response variable in “usual” regression analysis etc. estimated from field data from 30 flocks in Zimbabwe. Slide 5 Slide 6 1

  2. SimFlock: An object oriented model Sampling from the hyper distribution Breeding animals Draw a random value F i from N(0, σ F 2 ) Hens & Cocks 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 ) Eggs Infertile Household Calculate the 4 logit values ( j = 1, 2, 3, 4) y ij = logit( p ij ) = µ + α j + F i + ( α F ) ij consumption Chicks Dead 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) Growers Pullets Cockerels Market Slide 7 Slide 8 User interface – visible objects SimFlock: Elements – where are they? Decision rule Θ State of nature Φ 0 All birds and eggs present in the flock shown. States of the birds can be Hyper distribution p ( Φ 0 = φ 0 ) investigated Demo State variables Φ s 1 … Φ sT Output variables Ω Slide 9 Slide 10 SimFlock: Decision variables SimFlock: State of nature parameters In SimFlock, a state of nature is described Built-in decisions (farmer icon): by 42 parameters: • Intended flock size: • Daily gains of birds, general linear model • Hens • Survival rates, logistic model • Cocks • Full grown weights, normal distribution • Egg removing policy • Age at puberty, normal distribution • Days from start laying • Egg fertilization probability, beta distribution • Season • Egg hatching probability, logistic model • Policy for buying breeding birds: • Number of eggs before incubation, normal dist. • Hens • Cocks Each time a parameter is defined, a hyper distribution is specified. Other decisions modeled through expected effects (e.g. on mortality). Slide 11 Slide 12 2

  3. SimFlock: State variables SimFlock: Hyper distribution(s) The state variables of day i are the states of the individual birds and eggs on that day: • Eggs: The hyper distribution of the state of nature is specified • Fertilized/not fertilized through 64 hyper parameters. • Birds: • Age Most of them estimated from the field data collected in 30 • Weight flocks. • Growth potential The hyper distribution represents the whole population of • Full grown weight flocks under the conditions in question. • Laying capacity • Gender A state of nature drawn from the hyper distribution represents • … one (hypothetical) flock. • Farmer: • By drawing e.g. many states of nature we can generate many • Needs meat? realistic hypothetical flocks. There are millions of state variables in a simulation run. • Decision rules may have different effects in different flocks. Slide 13 Slide 14 States of a bird States of a pullet All birds: In addition to the general states: • Unique ID (given at hatching – next integer) • Pullet: • Age (updated daily) • Age at first egg, “puberty” (drawn at • Weight (updated daily) transition) • Gender (drawn at random at hatching) • Growth state (drawn at transition) • Full grown weight (drawn at random at • Cockerel: hatching) • Age at “puberty” (drawn at transition) • Growth potential (permanent, drawn at • Growth state (drawn at transition) hatching) Cocks: No further states. For chicks and growers furthermore: • Growth state (drawn at hatching/transition) Slide 15 Slide 16 SimFlock: Output variables States of a hen A total of 40 are defined: • Realised gain In addition to the general states: • Realised mortality • Behavior, not used? (drawn at transition) • Eggs removed • Chickens produced • Laying capacity (drawn at transition) • … • State in cycle (laying, incubating, brooding, Usual technical and economical key barren) – updated daily. figures. • 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 Slide 18 3

  4. SimFlock: Simulation Use of the simulation model The farmer, birds and eggs are System comprehension represented as objects in the model. • Answering “what if” questions Each (simulated) day, the states of all General decision support (at population objects are updated: level) • Age • Weight • The main purpose of SimFlock • Survival Decision support at flock level • Transition (e.g. egg → chick, chick → grower, • Not yet possible etc) • Eggs in nest • … Slide 19 Slide 20 System comprehension General decision support Usually carried out under one state of nature Population level Answer questions like: Carried out under multiple states of nature • If we assume the state of nature parameters are Φ 0 = φ 0 what are then the consequences? Questions like: • Under what circumstances does it pay to change the decision rule from Θ 1 to Θ 2 ? • What if we could improve the survival rate of chicks? • Generate multiple states of nature (random • Vary the survival rate systematically – run flocks) • Run a simulation job under Θ 1 simulations and explore the results • Run a simulation job under Θ 2 • etc. Weakness: State of nature parameters are • Identify the states of nature where it pays mutually correlated! Slide 21 Slide 22 Decision support at flock level A BN for state of nature in a flock Hyper distribution. Should “Jens Hansen” change his management from decision rule Θ 1 to Θ 2 ? Initially set to the Problems: distribution in the • We don’t know the state of nature for Jens Hansen’s flock. population • 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) State of nature. 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. Observed in Jens • If anybody wants to solve this problem within the framework of a Hansen’s flock. Master’s thesis it would be very much appreciated! When observed, we can update the rest! Slide 23 Slide 24 4

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