Top Banner
Making predictions
44

Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

May 24, 2020

Download

Documents

dariahiddleston
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Makingpredictions

Page 2: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Sofar...Build,check&selectmodelsfordetectability

Build,check&selectmodelsforabundance

Makesomeecologicalinferenceaboutsmooths

Whataboutpredictions?

Page 3: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Let'stalkaboutmaps

Page 4: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Whatdoesamapmean?Grids!

Cellsareabundanceestimate

“snapshot”

Sumcellstogetabundance

Sumasubset?

Page 5: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Goingbacktotheformula(Count)Model:

Predictions(index ):

Needto“fill-in”valuesfor , and .

= exp[ + s( ) + s( )] +nj Aj p̂j β0 yj Depthj ϵj

r

= exp[ + s( ) + s( )]nr Ar β0 yr Depthr

Ar yr Depthr

Page 6: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

PredictingWiththesevaluescanusepredictinRpredict(model, newdata=data)

Page 7: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Predictiondata x y Depth SST NPP DistToCAS EKE off.set126 547984.6 788254 153.5983 8.8812 1462.521 11788.974 0.0074 1e+08127 557984.6 788254 552.3107 9.2078 1465.410 5697.248 0.0144 1e+08258 527984.6 778254 96.8199 9.6341 1429.432 13722.626 0.0024 1e+08259 537984.6 778254 138.2376 9.6650 1424.862 9720.671 0.0027 1e+08260 547984.6 778254 505.1439 9.7905 1379.351 8018.690 0.0101 1e+08261 557984.6 778254 1317.5952 9.9523 1348.544 3775.462 0.0193 1e+08 LinkID Nhat_tw126 1 0.01417657127 2 0.05123483258 3 0.01118858259 4 0.01277096260 5 0.04180434261 6 0.45935801

Page 8: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

AquickwordaboutrastersWehavetalkedaboutrastersabit

InR,thedata.frameiskingFortunatelyas.data.frameexistsMakeour“stack”andthenconverttodata.frame

Page 9: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Predictors

Page 10: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

MakingapredictionAddanothercolumntothepredictiondata

Plottingtheneasier(inR)

predgrid$Nhat_tw <- predict(dsm_all_tw_rm, predgrid)

Page 11: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Mapsofpredictionsp <- ggplot(predgrid) + geom_tile(aes(x=x, y=y, fill=Nhat_tw)) + scale_fill_viridis() + coord_equal()print(p)

Page 12: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

TotalabundanceEachcellhasanabundance,sumtogettotal

sum(predict(dsm_all_tw_rm, predgrid))

[1] 2491.864

Page 13: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

SubsettingRsubsettingletsyoucalculate“interesting”estimates:

# how many sperm whales at depths less than 2500m?sum(predgrid$Nhat_tw[predgrid$Depth < 2500])

[1] 1006.272

# how many sperm whales North of 0?sum(predgrid$Nhat_tw[predgrid$x>0])

[1] 1383.742

Page 14: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Extrapolation

Page 15: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Whatdowemeanbyextrapolation?Predictingatvaluesoutsidethoseobserved

Whatdoes“outside”mean?

betweentransects?

outside“surveyarea”?

Page 16: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

TemporalextrapolationModelsaretemporallyimplicit(mostly)

Dynamicvariableschangeseasonally

Migrationcanbeanissue

Needtounderstandwhatthepredictionsare

Page 17: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

ExtrapolationExtrapolationisfraughtwithissues

Wanttobepredicting“insidetherug”

Ingeneral,trynottodoit!

(Thinkaboutvariancetoo!)

Page 18: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

RecapUsingpredictGetting“overall”abundance

Subsetting

PlottinginR

Extrapolation(anditsdangers)

Page 19: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Estimatingvariance

Page 20: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

NowwecanmakepredictionsNowwearedangerous.

Page 21: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Predictionsareuselesswithoutuncertainty

Page 22: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Wheredoesuncertaintycomefrom?

Page 23: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

SourcesofuncertaintyDetectionfunction

GAMparameters

Page 24: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Let'sthinkaboutsmoothsfirst

Page 25: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

UncertaintyinsmoothsDashedlinesare+/-2standarderrors

Howdowetranslateto ?N̂

Page 26: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

BacktobasesBeforeweexpressedsmoothsas:

Theorytellsusthat:

where isabitcomplicated

(derivedfromthesmoothermatrix)

s(x) = (x)∑Kk=1 βkbk

β ∼ N( , )β̂ Vβ

Vβ

Page 27: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Predictionstopredictionvariance(roughly)

“map”dataontofittedvalues

“map”predictionmatrixtopredictions

Here needtotakesmoothsintoaccount

pre-/post-multiplyby to“transformvariance”

linkscale,needtodoanothertransformforresponse

Xβ

βXp

Xp

Xp

⇒ XTp VβXp

Page 28: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Addingindetectionfunctions

Page 29: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

GAM+detectionfunctionuncertainty(Gettingalittlefast-and-loosewiththemathematics)

( ) ≈ (GAM) +CV2 N̂ CV2

(detectionfunction)CV2

Page 30: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Notthatsimple...AssumesdetectionfunctionandGAMareindependent

Maybethisisokay?

(Probablynottrue?)

Page 31: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

VariancepropagationIncludethedetectabilityasterminGAM

Randomeffect,meanzero,varianceofdetectionfunction

Uncertainty“propagated”throughthemodel

Detailsinbibliography(toomuchtodetailhere)

Underdevelopment

(Cancoverinspecialtopic)

Page 32: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Thatseemedcomplicated...

Page 33: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Rtotherescue

Page 34: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

InR...Functionsindsmtodothis

dsm.var.gamassumesspatialmodelanddetectionfunctionareindependent

dsm.var.proppropagatesuncertaintyfromdetectionfunctiontospatialmodel

onlyworksforcountmodels(moreorless)

Page 35: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

VarianceofabundanceUsingdsm.var.gam

dsm_tw_var_ind <- dsm.var.gam(dsm_all_tw_rm, predgrid, off.set=predgrid$off.set)summary(dsm_tw_var_ind)

Summary of uncertainty in a density surface model calculated analytically for GAM, with delta method

Approximate asymptotic confidence interval: 2.5% Mean 97.5% 1539.018 2491.864 4034.643 (Using log-Normal approximation)

Point estimate : 2491.864 CV of detection function : 0.2113123 CV from GAM : 0.1329 Total standard error : 622.0389 Total coefficient of variation : 0.2496

Page 36: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

VarianceofabundanceUsingdsm.var.prop

dsm_tw_var <- dsm.var.prop(dsm_all_tw_rm, predgrid, off.set=predgrid$off.set)summary(dsm_tw_var)

Summary of uncertainty in a density surface model calculated by variance propagation.

Probability of detection in fitted model and variance model Fitted.model Fitted.model.se Refitted.model1 0.3624567 0.07659373 0.3624567

Approximate asymptotic confidence interval: 2.5% Mean 97.5% 1556.898 2458.634 3882.646 (Using log-Normal approximation)

Point estimate : 2458.634 Standard error : 581.0379 Coefficient of variation : 0.2363

Page 37: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Plotting-dataprocessingCalculateuncertaintyper-cell

dsm.var.*thinkspredgridisone“region”Needtosplitdataintocells(usingsplit())(Couldbearbitrarysetsofcells,seeexercises)

Needwidthandheightofcellsforplotting

Page 38: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Plotting(code)predgrid$width <- predgrid$height <- 10*1000predgrid_split <- split(predgrid, 1:nrow(predgrid))head(predgrid_split,3)

$`1` x y Depth SST NPP DistToCAS EKE off.set126 547984.6 788254 153.5983 8.8812 1462.521 11788.97 0.0074 1e+08 LinkID Nhat_tw height width126 1 0.01417657 10000 10000

$`2` x y Depth SST NPP DistToCAS EKE off.set127 557984.6 788254 552.3107 9.2078 1465.41 5697.248 0.0144 1e+08 LinkID Nhat_tw height width127 2 0.05123483 10000 10000

$`3` x y Depth SST NPP DistToCAS EKE off.set258 527984.6 778254 96.8199 9.6341 1429.432 13722.63 0.0024 1e+08 LinkID Nhat_tw height width258 3 0.01118858 10000 10000

dsm_tw_var_map <- dsm.var.prop(dsm_all_tw_rm, predgrid_split, off.set=predgrid$off.set)

Page 39: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

CVplotp <- plot(dsm_tw_var_map, observations=FALSE, plot=FALSE) + coord_equal() + scale_fill_viridis()print(p)

Page 40: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

InterpretingCVplotsPlottingcoefficientofvariation

Standardisestandarddeviationbymean

(percell)

Canbeusefultooverplotsurveyeffort

CV = se( )/N̂ N̂

Page 41: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Effortoverplotted

Page 42: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

BigCVsHereCVsare“wellbehaved”

Notalwaysthecase(hugeCVspossible)

Thesecanbeapaintoplot

Usecut()inRtomakecategoricalvariable

e.g.c(seq(0,1, len=100), 2:4, Inf)orsomesuch

Page 43: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

RecapHowdoesuncertaintyariseinaDSM?

Estimatevarianceofabundanceestimate

Mapcoefficientofvariation

Page 44: Making predictions - GitHub · Predictions to prediction variance (roughly) “map” data onto fitted values “map” prediction matrix to predictions Here need to take smooths

Let'strythat!


Related Documents
Future prediction: Get exact future predictions free

Future prediction: Get exact future predictions free

Category: Spiritual
Icing Predictions for the Canadian Wind Energy Industry · Numerical Weather Prediction (NWP) ) • Operational model used for weather predictions in Canada – hrdps: high resolution

Icing Predictions for the Canadian Wind Energy Industry ·....

Category: Documents
Advancements in NMR Predictions- Neural Network vs. HOSE ... · PDF fileAdvancements in NMR Predictions-Neural Network vs. HOSE Code Algorithms ... Prediction Accuracy ... (ppm)-40-20

Advancements in NMR Predictions- Neural Network vs. HOSE ......

Category: Documents
APPENDIX 1 SUMMARY OF TRAFFIC INFORMATION. 2005 … · SUMMARY OF TRAFFIC INFORMATION. 2005 URBAN PREDICTION Predictions from 1998 Predictions from 1999 Differences? Road No. ...

APPENDIX 1 SUMMARY OF TRAFFIC INFORMATION. 2005 … ·...

Category: Documents
Prediction Markets: Theory and Applications · an accurate prediction. Chapter 7 extends the classical prediction elicitation setting to describe decision markets, where predictions

Prediction Markets: Theory and Applications · an accurate....

Category: Documents
Experimental Climate Monitoring and Prediction Reports/2011/Dec/WMS_Report...predictions (delivered via IRI map tool) predict 25mm- over 120mm rainfall from 29th Nov – 04th December

Experimental Climate Monitoring and Prediction...

Category: Documents
IDC FutureScape: Worldwide Financial Services 2020 Predictions€¦ · In no particular order, our 2020 predictions for the worldwide financial services market are as follows: Prediction

IDC FutureScape: Worldwide Financial Services 2020...

Category: Documents
6 1D predictions 2012 - cbs.dtu.dkblicher/Courses/6_1D_predictions_2012.pdf · 1-D Predictions Prediction of local features: Secondary structure & surface exposure 4 . Learning Objectives

6 1D predictions 2012 -...

Category: Documents
Dennis D. McCarthy Elements of Prediction. Why are we here? IERS Working Group on Predictions IERS Working Group on Predictions Definitive user requirements.

Dennis D. McCarthy Elements of Prediction. Why are we here?....

Category: Documents
Bioinformatics Gene detection and prediction Gene predictions in prokaryotes Gene predictions in eukaryotes Difficulties of gene prediction Statistical.

Bioinformatics Gene detection and prediction Gene...

Category: Documents
Prediction Map- Boundaries Type

Prediction Map- Boundaries Type

Category: Documents
Online Optimization with Predictions and Switching Costs ... · Online Optimization with Predictions and Switching ... exploring the effect of prediction, ... in many practical applications,

Online Optimization with Predictions and Switching Costs...

Category: Documents