Lec21.Nonlin3 - Nonlinear Regression III Return of the Arrowtooth Flounder Y e a r Biom ass(Thousands of mt 1 9 8 2 1 9 8 4 1 9 8 6 1 9 8 8 1 9 9 0

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Unformatted text preview: Nonlinear Regression III Return of the Arrowtooth Flounder Y e a r Biom ass (Thousands of mt) 1 9 8 2 1 9 8 4 1 9 8 6 1 9 8 8 1 9 9 0 1 9 9 2 1 9 9 100200300400500 A r r o w t o t t t t C B B B k B 1 Change in Biomass Future Biomass Related to Current Biomass Levels ) ( 1 t t t B B B B Observation Stochasticity t t t t t t B Bobs B B B B ) ( 1 biomass.obs = function(param,data=arrowtooth) { Binf = param[1] k = param[2] Bobs = data$Bobs Cobs = data$Cobs B = Bobs[1] n = length(Bobs) Time = seq(n) dP = rep(0,n) for(i in Time[-n]) { dP[i] = k*(1-B[i]/Binf)*B[i] B[i+1] = B[i]+dP[i]-Cobs[i] } B.pred <<- B RSS = sum((B-Bobs)^2) return(RSS) Nonlinear Model Fitting Using nlminb biomass.obs.fit = nlminb(c(500,0.5), biomass.obs) biomass.obs.fit$parameters 525.0800158 0.4215014 Y e a r Biom ass (Thousands of mt) 1 9 8 2 1 9 8 4 1 9 8 6 1 9 8 8 1 9 9 0 1 9 9 2 1 9 9 100200300400500 A r r o w t o Recall Linear Simulation Results SE(Intcpt) SE(Slope) GLM 0.41874441 0.03495611 Finite Difference 0.33607883 0.02814508 Bootstrap Data 0.57623950 0.04390691 Bootstrap Residuals 0.40904021 0.03241597 b1 p.b1 0.3 0.4 0.5 0.6 0.7 0.0 0.01 0.02 0.03 0.04 Exact, Finite Diff, Boot Data, Boot Resid b1 p.b1 0.3 0.4 0.5 0.6 0.7 0.0 0.01 0.02 0.03 0.04 Exact, Finite Diff, Bayes, LikelihoodProfile A suite of methods for exploring uncertainty Application to logistic model biomass.obs = function(param,data=arrowtooth) { Binf = param[1] k = param[2] Bobs = data$Bobs Cobs = data$Cobs B = Bobs[1] n = length(Bobs) Time = seq(n) dP = rep(0,n) for(i in Time[-n])...
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This note was uploaded on 04/17/2010 for the course STSCI 3200 taught by Professor Sullivan during the Spring '10 term at Cornell University (Engineering School).

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Lec21.Nonlin3 - Nonlinear Regression III Return of the Arrowtooth Flounder Y e a r Biom ass(Thousands of mt 1 9 8 2 1 9 8 4 1 9 8 6 1 9 8 8 1 9 9 0

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