SlideShare a Scribd company logo
Using informative priors to improve parameters
estimation in capture-recapture models
Blaise Piédallu
PhD Student
Supervisors :
Olivier Gimenez
Pierre-Yves Quenette
Population of interest
-Brown bears (Ursus arctos) in the French and Spanish
Pyrénées
-Population size : about 25 individuals in 2013
-Individuals are detected and identified through different
methods (camera pictures, genetic sampling of hair and
faeces)
-2 population cores or « Regions » (Western and Central-
Eastern), without communication (Western – 2 individuals
in 2013 – and Central-Eastern – ~23 individuals in 2013)
Population of interest
Objectives :
- Estimate population size, test for difference in Regions
- Since the population is small, use an informative prior to improve
the precision
Dataset
 Capture-Recapture data during 25 years (1989 – 2013)
 A Jolly-Seber model is used to estimate population size
- Capture-Recapture on n different occasions (here, n=25)
- Open population: immigrations (births/reintroductions) and
emigrations (deaths)
State-Space Model :
Detected (= 1)
Not detected (= 0)
p
1 - p
1 Not detected (= 0)
Survived
Time t
Died
f
1 - f
Hidden information Observed information
Dataset
 Capture-Recapture data during 25 years (1989 – 2013)
 A Jolly-Seber model is used to estimate population size
- Capture-Recapture on n different occasions (here, n=25)
- Open population: immigrations (births/reintroductions) and
emigrations (deaths)
State-Space Model :
Detected (= 1)
Not detected (= 0)
p
1 - p
1 Not detected (= 0)
Survived
Time t
Died
f
1 - f
Hidden information Observed information
Model Selection
The Bayesian computation was performed with the softwares -R- and JAGS.
Tested models
Survival Detection
r
.
r + T + r.T
r + T
r
T
.
r : « Region » effect
T : Time effect
. : no effect
Survival probability :
logit(phi[i,t]) <- alpha[1] + alpha[2]*cov.region[i]
Detection probability :
logit(p[i,t]) <- alpha[3] + alpha[4]*cov.region[i] + alpha[5]*t
+ alpha[6]*t*cov.region[i] + eps[i]
Model Selection
Model selection by estimating posterior model probabilities (Kuo
and Mallick, 1998)
Survival probability :
logit(phi[i,t]) <- alpha[1] + w[1]*alpha[2]*cov.region[i]
Detection probability :
logit(p[i,t]) <- alpha[3] + w[2]*alpha[4]*cov.region[i] +
w[3]*alpha[5]*t + w[4]*alpha[6]*t*cov.region[i] + eps[i]
Indicator variables - w ~ dbern(0.5)
Multiplies every relevant parameter
Model Selection
MCMC sampling
Posterior model probability =
Number of iterations using this model
Total number of iterations
Model Selection
Results :
r .
r + T + r.T 0,01027 0,05487
r + T 0,06833 0,36239
r 0,04008 0,18398
T 0,01216 0,05809
. 0,02383 0,12107
Survival
Capture
Model selected : Survival = f(.), Capture = f(r+T)
Some models with no
significance are
ignored: the intersect
of r and T only has a
meaning if both r and
T are used
Theoretical number
of models = 24 = 16
Estimated survival
Estimated density
with an uninformative
prior U(0,1)
f = 0.94 ± 0.015
Using informative priors
Two priors for Survival were used for the next simulations :
-A non informative prior
U(0,1)
-An informative prior
B(a,b), with a and b chosen
in order to get a mean of
0.9 and a standard
deviation of 0.025
Using informative priors
Entire dataset
n = 25 years
Both population cores
No difference in
population size
estimation
No difference in
standard deviation
Using informative Priors - Splitting the dataset
Dataset split
n = 25 years
Eastern population only
No difference in
population size
estimation
No difference in
standard deviation
Using informative Priors - Splitting the dataset
Dataset split
n = 25 years
Western population only
No difference in
population size
estimation
No difference in
standard deviation
Using informative Priors - Splitting the dataset
Dataset split
n = 15 years (89-03)
Both population cores
Improvement in
standard deviation by
using informative
priors
Using informative Priors - Splitting the dataset
Dataset split
n = 15 years (04-13)
Both population cores
Improvement in
standard deviation by
using informative
priors
Difference in
population size
estimation
Conclusion
What can we say about informative priors ?
-Even relatively small datasets may contain enough data in order to
be used
- In the case of the French Brown Bear, the information seems to
come from the length of the study (over 25 years)
-In the last 10 years, monitoring of the population has greatly
increased – more people involved, improving the search for genetic
samples in the Pyrénées
-Informative priors are useful to create a more complex model
including more parameters on a smaller timeframe
Conclusion
What to do next ?
Check if an informative prior has influences model selection
Check the influence of an informative prior on a more complex
model :
-Add more age classes
-Add gender
Use the parameter estimates in order to check the influence of future
reintroductions
Perform a viability analysis of the population using the informative
priors
The End
From Pyrénée, written by Régis Loisel, drawn by Philippe Sternis
THANK YOU FOR YOUR
ATTENTION !

More Related Content

Similar to Talk by Blaise Piédallu at ISEC 2014 on improving abundance estimates by using informative priors.

A basic Introduction To Statistics with examples
A basic Introduction To Statistics with examplesA basic Introduction To Statistics with examples
A basic Introduction To Statistics with examples
ShibsekharRoy1
 
Introduction to Biostatistics
Introduction to BiostatisticsIntroduction to Biostatistics
Introduction to Biostatistics
RamFeg
 
LECTURE 3-PREVALENCE& DISEASES OUTBREAK.pdf
LECTURE 3-PREVALENCE& DISEASES OUTBREAK.pdfLECTURE 3-PREVALENCE& DISEASES OUTBREAK.pdf
LECTURE 3-PREVALENCE& DISEASES OUTBREAK.pdf
SamuelGitonga10
 
Ph250b.14 measures of disease part 2 fri sep 5 2014
Ph250b.14 measures of disease part 2  fri sep 5 2014 Ph250b.14 measures of disease part 2  fri sep 5 2014
Ph250b.14 measures of disease part 2 fri sep 5 2014
A M
 
San diego
San diegoSan diego
San diego
Gianluca Baio
 
Statics for management
Statics for managementStatics for management
Statics for management
parth06
 
Sampling Theory Part 1
Sampling Theory Part 1Sampling Theory Part 1
Sampling Theory Part 1
FellowBuddy.com
 
Bio stat
Bio statBio stat
Bio stat
AbhishekDas15
 
Sampling
SamplingSampling
Statistics for management assignment
Statistics for management assignmentStatistics for management assignment
Statistics for management assignment
GIEDEEAM SOLAR and Gajanana Publications, LIC
 
Seminar-2015
Seminar-2015Seminar-2015
Seminar-2015
Dongfeng Wu
 
SP and R.pptx
SP and R.pptxSP and R.pptx
SP and R.pptx
ssuserfc98db
 
Introduction to Statistics (Part -I)
Introduction to Statistics (Part -I)Introduction to Statistics (Part -I)
Introduction to Statistics (Part -I)
YesAnalytics
 
STAT 101 Lecture collegeINTRODUCTION.pdf
STAT 101 Lecture collegeINTRODUCTION.pdfSTAT 101 Lecture collegeINTRODUCTION.pdf
STAT 101 Lecture collegeINTRODUCTION.pdf
Sharon608481
 
Statistical Estimation
Statistical Estimation Statistical Estimation
Statistical Estimation
Remyagharishs
 
Sampling techniques new
Sampling techniques newSampling techniques new
Sampling techniques new
Geeta80373
 
Sampling techniques new
Sampling techniques newSampling techniques new
Sampling techniques new
babita jangra
 
STATISTICS-AND-PROBABLITY-A-REVIEW-FOR-SHS.pdf
STATISTICS-AND-PROBABLITY-A-REVIEW-FOR-SHS.pdfSTATISTICS-AND-PROBABLITY-A-REVIEW-FOR-SHS.pdf
STATISTICS-AND-PROBABLITY-A-REVIEW-FOR-SHS.pdf
MariaCatherineErfeLa
 
BIOMETRYc(1).pptx
BIOMETRYc(1).pptxBIOMETRYc(1).pptx
BIOMETRYc(1).pptx
dawudkuro
 
BIOMETRYc(1).pptx
BIOMETRYc(1).pptxBIOMETRYc(1).pptx
BIOMETRYc(1).pptx
dawudkuro
 

Similar to Talk by Blaise Piédallu at ISEC 2014 on improving abundance estimates by using informative priors. (20)

A basic Introduction To Statistics with examples
A basic Introduction To Statistics with examplesA basic Introduction To Statistics with examples
A basic Introduction To Statistics with examples
 
Introduction to Biostatistics
Introduction to BiostatisticsIntroduction to Biostatistics
Introduction to Biostatistics
 
LECTURE 3-PREVALENCE& DISEASES OUTBREAK.pdf
LECTURE 3-PREVALENCE& DISEASES OUTBREAK.pdfLECTURE 3-PREVALENCE& DISEASES OUTBREAK.pdf
LECTURE 3-PREVALENCE& DISEASES OUTBREAK.pdf
 
Ph250b.14 measures of disease part 2 fri sep 5 2014
Ph250b.14 measures of disease part 2  fri sep 5 2014 Ph250b.14 measures of disease part 2  fri sep 5 2014
Ph250b.14 measures of disease part 2 fri sep 5 2014
 
San diego
San diegoSan diego
San diego
 
Statics for management
Statics for managementStatics for management
Statics for management
 
Sampling Theory Part 1
Sampling Theory Part 1Sampling Theory Part 1
Sampling Theory Part 1
 
Bio stat
Bio statBio stat
Bio stat
 
Sampling
SamplingSampling
Sampling
 
Statistics for management assignment
Statistics for management assignmentStatistics for management assignment
Statistics for management assignment
 
Seminar-2015
Seminar-2015Seminar-2015
Seminar-2015
 
SP and R.pptx
SP and R.pptxSP and R.pptx
SP and R.pptx
 
Introduction to Statistics (Part -I)
Introduction to Statistics (Part -I)Introduction to Statistics (Part -I)
Introduction to Statistics (Part -I)
 
STAT 101 Lecture collegeINTRODUCTION.pdf
STAT 101 Lecture collegeINTRODUCTION.pdfSTAT 101 Lecture collegeINTRODUCTION.pdf
STAT 101 Lecture collegeINTRODUCTION.pdf
 
Statistical Estimation
Statistical Estimation Statistical Estimation
Statistical Estimation
 
Sampling techniques new
Sampling techniques newSampling techniques new
Sampling techniques new
 
Sampling techniques new
Sampling techniques newSampling techniques new
Sampling techniques new
 
STATISTICS-AND-PROBABLITY-A-REVIEW-FOR-SHS.pdf
STATISTICS-AND-PROBABLITY-A-REVIEW-FOR-SHS.pdfSTATISTICS-AND-PROBABLITY-A-REVIEW-FOR-SHS.pdf
STATISTICS-AND-PROBABLITY-A-REVIEW-FOR-SHS.pdf
 
BIOMETRYc(1).pptx
BIOMETRYc(1).pptxBIOMETRYc(1).pptx
BIOMETRYc(1).pptx
 
BIOMETRYc(1).pptx
BIOMETRYc(1).pptxBIOMETRYc(1).pptx
BIOMETRYc(1).pptx
 

More from olivier gimenez

Making sense of citizen science data: A review of methods
Making sense of citizen science data: A review of methodsMaking sense of citizen science data: A review of methods
Making sense of citizen science data: A review of methods
olivier gimenez
 
Dealing with observer bias when mapping species distribution using citizen sc...
Dealing with observer bias when mapping species distribution using citizen sc...Dealing with observer bias when mapping species distribution using citizen sc...
Dealing with observer bias when mapping species distribution using citizen sc...
olivier gimenez
 
Individual Heterogeneity in Capture-Recapture Models
Individual Heterogeneity in Capture-Recapture ModelsIndividual Heterogeneity in Capture-Recapture Models
Individual Heterogeneity in Capture-Recapture Models
olivier gimenez
 
Talk by Laetitia Blanc at ISEC 2014 on improving abundance estimates by combi...
Talk by Laetitia Blanc at ISEC 2014 on improving abundance estimates by combi...Talk by Laetitia Blanc at ISEC 2014 on improving abundance estimates by combi...
Talk by Laetitia Blanc at ISEC 2014 on improving abundance estimates by combi...
olivier gimenez
 
My talk at EURING 2013 on individual variability in capture-recapture models
My talk at EURING 2013 on individual variability in capture-recapture modelsMy talk at EURING 2013 on individual variability in capture-recapture models
My talk at EURING 2013 on individual variability in capture-recapture models
olivier gimenez
 
My CNRS interview to get a senior scientist position (directeur de recherche)
My CNRS interview to get a senior scientist position (directeur de recherche)My CNRS interview to get a senior scientist position (directeur de recherche)
My CNRS interview to get a senior scientist position (directeur de recherche)
olivier gimenez
 
HDR Olivier Gimenez
HDR Olivier GimenezHDR Olivier Gimenez
HDR Olivier Gimenez
olivier gimenez
 
My talk at ISEC 2014 (http://isec2014.sciencesconf.org/) on how to model occu...
My talk at ISEC 2014 (http://isec2014.sciencesconf.org/) on how to model occu...My talk at ISEC 2014 (http://isec2014.sciencesconf.org/) on how to model occu...
My talk at ISEC 2014 (http://isec2014.sciencesconf.org/) on how to model occu...
olivier gimenez
 

More from olivier gimenez (8)

Making sense of citizen science data: A review of methods
Making sense of citizen science data: A review of methodsMaking sense of citizen science data: A review of methods
Making sense of citizen science data: A review of methods
 
Dealing with observer bias when mapping species distribution using citizen sc...
Dealing with observer bias when mapping species distribution using citizen sc...Dealing with observer bias when mapping species distribution using citizen sc...
Dealing with observer bias when mapping species distribution using citizen sc...
 
Individual Heterogeneity in Capture-Recapture Models
Individual Heterogeneity in Capture-Recapture ModelsIndividual Heterogeneity in Capture-Recapture Models
Individual Heterogeneity in Capture-Recapture Models
 
Talk by Laetitia Blanc at ISEC 2014 on improving abundance estimates by combi...
Talk by Laetitia Blanc at ISEC 2014 on improving abundance estimates by combi...Talk by Laetitia Blanc at ISEC 2014 on improving abundance estimates by combi...
Talk by Laetitia Blanc at ISEC 2014 on improving abundance estimates by combi...
 
My talk at EURING 2013 on individual variability in capture-recapture models
My talk at EURING 2013 on individual variability in capture-recapture modelsMy talk at EURING 2013 on individual variability in capture-recapture models
My talk at EURING 2013 on individual variability in capture-recapture models
 
My CNRS interview to get a senior scientist position (directeur de recherche)
My CNRS interview to get a senior scientist position (directeur de recherche)My CNRS interview to get a senior scientist position (directeur de recherche)
My CNRS interview to get a senior scientist position (directeur de recherche)
 
HDR Olivier Gimenez
HDR Olivier GimenezHDR Olivier Gimenez
HDR Olivier Gimenez
 
My talk at ISEC 2014 (http://isec2014.sciencesconf.org/) on how to model occu...
My talk at ISEC 2014 (http://isec2014.sciencesconf.org/) on how to model occu...My talk at ISEC 2014 (http://isec2014.sciencesconf.org/) on how to model occu...
My talk at ISEC 2014 (http://isec2014.sciencesconf.org/) on how to model occu...
 

Recently uploaded

A hot-Jupiter progenitor on a super-eccentric retrograde orbit
A hot-Jupiter progenitor on a super-eccentric retrograde orbitA hot-Jupiter progenitor on a super-eccentric retrograde orbit
A hot-Jupiter progenitor on a super-eccentric retrograde orbit
Sérgio Sacani
 
Rice Genome Project a complete saga .(1).pptx
Rice Genome  Project a complete saga .(1).pptxRice Genome  Project a complete saga .(1).pptx
Rice Genome Project a complete saga .(1).pptx
SoumyaDixit11
 
Burn child health Nursing 3rd year presentation..pptx
Burn child health Nursing 3rd year presentation..pptxBurn child health Nursing 3rd year presentation..pptx
Burn child health Nursing 3rd year presentation..pptx
sohil4260
 
End of pipe treatment: Unlocking the potential of RAS waste - Carlos Octavio ...
End of pipe treatment: Unlocking the potential of RAS waste - Carlos Octavio ...End of pipe treatment: Unlocking the potential of RAS waste - Carlos Octavio ...
End of pipe treatment: Unlocking the potential of RAS waste - Carlos Octavio ...
Faculty of Applied Chemistry and Materials Science
 
Review Article:- A REVIEW ON RADIOISOTOPES IN CANCER THERAPY
Review Article:- A REVIEW ON RADIOISOTOPES IN CANCER THERAPYReview Article:- A REVIEW ON RADIOISOTOPES IN CANCER THERAPY
Review Article:- A REVIEW ON RADIOISOTOPES IN CANCER THERAPY
niranjangiri009
 
Concept of Balanced Diet & Nutrients.pdf
Concept of Balanced Diet & Nutrients.pdfConcept of Balanced Diet & Nutrients.pdf
Concept of Balanced Diet & Nutrients.pdf
SELF-EXPLANATORY
 
Post RN - Biochemistry (Unit 7) Metabolism
Post RN - Biochemistry (Unit 7) MetabolismPost RN - Biochemistry (Unit 7) Metabolism
Post RN - Biochemistry (Unit 7) Metabolism
Areesha Ahmad
 
The Next-Gen Innovative Therapeutic Potential of Probiotics: Insights into Gu...
The Next-Gen Innovative Therapeutic Potential of Probiotics: Insights into Gu...The Next-Gen Innovative Therapeutic Potential of Probiotics: Insights into Gu...
The Next-Gen Innovative Therapeutic Potential of Probiotics: Insights into Gu...
Dr. Lenin Kumar Bompalli
 
17. 20240529_Ingrid Olesen_MariGreen summer school.pdf
17. 20240529_Ingrid Olesen_MariGreen summer school.pdf17. 20240529_Ingrid Olesen_MariGreen summer school.pdf
17. 20240529_Ingrid Olesen_MariGreen summer school.pdf
marigreenproject
 
Types of Hypersensitivity Reactions.pptx
Types of Hypersensitivity Reactions.pptxTypes of Hypersensitivity Reactions.pptx
Types of Hypersensitivity Reactions.pptx
Isha Pandey
 
Traditional, current and future use of fish and seaweed for fertilisation - ...
Traditional, current and future use of fish and seaweed for fertilisation -  ...Traditional, current and future use of fish and seaweed for fertilisation -  ...
Traditional, current and future use of fish and seaweed for fertilisation - ...
Faculty of Applied Chemistry and Materials Science
 
Fish in the Loop: Exploring RAS - Julie Hansen Bergstedt
Fish in the Loop: Exploring RAS - Julie Hansen BergstedtFish in the Loop: Exploring RAS - Julie Hansen Bergstedt
Fish in the Loop: Exploring RAS - Julie Hansen Bergstedt
Faculty of Applied Chemistry and Materials Science
 
All-domain Anomaly Resolution Office Supplement to Oak Ridge National Laborat...
All-domain Anomaly Resolution Office Supplement to Oak Ridge National Laborat...All-domain Anomaly Resolution Office Supplement to Oak Ridge National Laborat...
All-domain Anomaly Resolution Office Supplement to Oak Ridge National Laborat...
Sérgio Sacani
 
Surface properties of the seas of Titan as revealed by Cassini mission bistat...
Surface properties of the seas of Titan as revealed by Cassini mission bistat...Surface properties of the seas of Titan as revealed by Cassini mission bistat...
Surface properties of the seas of Titan as revealed by Cassini mission bistat...
Sérgio Sacani
 
Phytoremediation: Harnessing Nature's Power with Phytoremediation
Phytoremediation: Harnessing Nature's Power with PhytoremediationPhytoremediation: Harnessing Nature's Power with Phytoremediation
Phytoremediation: Harnessing Nature's Power with Phytoremediation
Gurjant Singh
 
Ancient Theory, Abiogenesis , Biogenesis
Ancient Theory, Abiogenesis , BiogenesisAncient Theory, Abiogenesis , Biogenesis
Ancient Theory, Abiogenesis , Biogenesis
SoniaBajaj10
 
VIII-Geography FOR CBSE CLASS 8 INDIA.pdf
VIII-Geography FOR CBSE CLASS 8 INDIA.pdfVIII-Geography FOR CBSE CLASS 8 INDIA.pdf
VIII-Geography FOR CBSE CLASS 8 INDIA.pdf
poorvarajgolkar
 
Celebrity Girls Call Navi Mumbai 🎈🔥9920725232 🔥💋🎈 Provide Best And Top Girl S...
Celebrity Girls Call Navi Mumbai 🎈🔥9920725232 🔥💋🎈 Provide Best And Top Girl S...Celebrity Girls Call Navi Mumbai 🎈🔥9920725232 🔥💋🎈 Provide Best And Top Girl S...
Celebrity Girls Call Navi Mumbai 🎈🔥9920725232 🔥💋🎈 Provide Best And Top Girl S...
bellared2
 
Analytical methods for blue residues characterization - Oana Crina Bujor
Analytical methods for blue residues characterization - Oana Crina BujorAnalytical methods for blue residues characterization - Oana Crina Bujor
Analytical methods for blue residues characterization - Oana Crina Bujor
Faculty of Applied Chemistry and Materials Science
 
Speed-accuracy trade-off for the diffusion models
Speed-accuracy trade-off for the diffusion modelsSpeed-accuracy trade-off for the diffusion models
Speed-accuracy trade-off for the diffusion models
sosukeito
 

Recently uploaded (20)

A hot-Jupiter progenitor on a super-eccentric retrograde orbit
A hot-Jupiter progenitor on a super-eccentric retrograde orbitA hot-Jupiter progenitor on a super-eccentric retrograde orbit
A hot-Jupiter progenitor on a super-eccentric retrograde orbit
 
Rice Genome Project a complete saga .(1).pptx
Rice Genome  Project a complete saga .(1).pptxRice Genome  Project a complete saga .(1).pptx
Rice Genome Project a complete saga .(1).pptx
 
Burn child health Nursing 3rd year presentation..pptx
Burn child health Nursing 3rd year presentation..pptxBurn child health Nursing 3rd year presentation..pptx
Burn child health Nursing 3rd year presentation..pptx
 
End of pipe treatment: Unlocking the potential of RAS waste - Carlos Octavio ...
End of pipe treatment: Unlocking the potential of RAS waste - Carlos Octavio ...End of pipe treatment: Unlocking the potential of RAS waste - Carlos Octavio ...
End of pipe treatment: Unlocking the potential of RAS waste - Carlos Octavio ...
 
Review Article:- A REVIEW ON RADIOISOTOPES IN CANCER THERAPY
Review Article:- A REVIEW ON RADIOISOTOPES IN CANCER THERAPYReview Article:- A REVIEW ON RADIOISOTOPES IN CANCER THERAPY
Review Article:- A REVIEW ON RADIOISOTOPES IN CANCER THERAPY
 
Concept of Balanced Diet & Nutrients.pdf
Concept of Balanced Diet & Nutrients.pdfConcept of Balanced Diet & Nutrients.pdf
Concept of Balanced Diet & Nutrients.pdf
 
Post RN - Biochemistry (Unit 7) Metabolism
Post RN - Biochemistry (Unit 7) MetabolismPost RN - Biochemistry (Unit 7) Metabolism
Post RN - Biochemistry (Unit 7) Metabolism
 
The Next-Gen Innovative Therapeutic Potential of Probiotics: Insights into Gu...
The Next-Gen Innovative Therapeutic Potential of Probiotics: Insights into Gu...The Next-Gen Innovative Therapeutic Potential of Probiotics: Insights into Gu...
The Next-Gen Innovative Therapeutic Potential of Probiotics: Insights into Gu...
 
17. 20240529_Ingrid Olesen_MariGreen summer school.pdf
17. 20240529_Ingrid Olesen_MariGreen summer school.pdf17. 20240529_Ingrid Olesen_MariGreen summer school.pdf
17. 20240529_Ingrid Olesen_MariGreen summer school.pdf
 
Types of Hypersensitivity Reactions.pptx
Types of Hypersensitivity Reactions.pptxTypes of Hypersensitivity Reactions.pptx
Types of Hypersensitivity Reactions.pptx
 
Traditional, current and future use of fish and seaweed for fertilisation - ...
Traditional, current and future use of fish and seaweed for fertilisation -  ...Traditional, current and future use of fish and seaweed for fertilisation -  ...
Traditional, current and future use of fish and seaweed for fertilisation - ...
 
Fish in the Loop: Exploring RAS - Julie Hansen Bergstedt
Fish in the Loop: Exploring RAS - Julie Hansen BergstedtFish in the Loop: Exploring RAS - Julie Hansen Bergstedt
Fish in the Loop: Exploring RAS - Julie Hansen Bergstedt
 
All-domain Anomaly Resolution Office Supplement to Oak Ridge National Laborat...
All-domain Anomaly Resolution Office Supplement to Oak Ridge National Laborat...All-domain Anomaly Resolution Office Supplement to Oak Ridge National Laborat...
All-domain Anomaly Resolution Office Supplement to Oak Ridge National Laborat...
 
Surface properties of the seas of Titan as revealed by Cassini mission bistat...
Surface properties of the seas of Titan as revealed by Cassini mission bistat...Surface properties of the seas of Titan as revealed by Cassini mission bistat...
Surface properties of the seas of Titan as revealed by Cassini mission bistat...
 
Phytoremediation: Harnessing Nature's Power with Phytoremediation
Phytoremediation: Harnessing Nature's Power with PhytoremediationPhytoremediation: Harnessing Nature's Power with Phytoremediation
Phytoremediation: Harnessing Nature's Power with Phytoremediation
 
Ancient Theory, Abiogenesis , Biogenesis
Ancient Theory, Abiogenesis , BiogenesisAncient Theory, Abiogenesis , Biogenesis
Ancient Theory, Abiogenesis , Biogenesis
 
VIII-Geography FOR CBSE CLASS 8 INDIA.pdf
VIII-Geography FOR CBSE CLASS 8 INDIA.pdfVIII-Geography FOR CBSE CLASS 8 INDIA.pdf
VIII-Geography FOR CBSE CLASS 8 INDIA.pdf
 
Celebrity Girls Call Navi Mumbai 🎈🔥9920725232 🔥💋🎈 Provide Best And Top Girl S...
Celebrity Girls Call Navi Mumbai 🎈🔥9920725232 🔥💋🎈 Provide Best And Top Girl S...Celebrity Girls Call Navi Mumbai 🎈🔥9920725232 🔥💋🎈 Provide Best And Top Girl S...
Celebrity Girls Call Navi Mumbai 🎈🔥9920725232 🔥💋🎈 Provide Best And Top Girl S...
 
Analytical methods for blue residues characterization - Oana Crina Bujor
Analytical methods for blue residues characterization - Oana Crina BujorAnalytical methods for blue residues characterization - Oana Crina Bujor
Analytical methods for blue residues characterization - Oana Crina Bujor
 
Speed-accuracy trade-off for the diffusion models
Speed-accuracy trade-off for the diffusion modelsSpeed-accuracy trade-off for the diffusion models
Speed-accuracy trade-off for the diffusion models
 

Talk by Blaise Piédallu at ISEC 2014 on improving abundance estimates by using informative priors.

  • 1. Using informative priors to improve parameters estimation in capture-recapture models Blaise Piédallu PhD Student Supervisors : Olivier Gimenez Pierre-Yves Quenette
  • 2. Population of interest -Brown bears (Ursus arctos) in the French and Spanish Pyrénées -Population size : about 25 individuals in 2013 -Individuals are detected and identified through different methods (camera pictures, genetic sampling of hair and faeces) -2 population cores or « Regions » (Western and Central- Eastern), without communication (Western – 2 individuals in 2013 – and Central-Eastern – ~23 individuals in 2013)
  • 3. Population of interest Objectives : - Estimate population size, test for difference in Regions - Since the population is small, use an informative prior to improve the precision
  • 4. Dataset  Capture-Recapture data during 25 years (1989 – 2013)  A Jolly-Seber model is used to estimate population size - Capture-Recapture on n different occasions (here, n=25) - Open population: immigrations (births/reintroductions) and emigrations (deaths) State-Space Model : Detected (= 1) Not detected (= 0) p 1 - p 1 Not detected (= 0) Survived Time t Died f 1 - f Hidden information Observed information
  • 5. Dataset  Capture-Recapture data during 25 years (1989 – 2013)  A Jolly-Seber model is used to estimate population size - Capture-Recapture on n different occasions (here, n=25) - Open population: immigrations (births/reintroductions) and emigrations (deaths) State-Space Model : Detected (= 1) Not detected (= 0) p 1 - p 1 Not detected (= 0) Survived Time t Died f 1 - f Hidden information Observed information
  • 6. Model Selection The Bayesian computation was performed with the softwares -R- and JAGS. Tested models Survival Detection r . r + T + r.T r + T r T . r : « Region » effect T : Time effect . : no effect Survival probability : logit(phi[i,t]) <- alpha[1] + alpha[2]*cov.region[i] Detection probability : logit(p[i,t]) <- alpha[3] + alpha[4]*cov.region[i] + alpha[5]*t + alpha[6]*t*cov.region[i] + eps[i]
  • 7. Model Selection Model selection by estimating posterior model probabilities (Kuo and Mallick, 1998) Survival probability : logit(phi[i,t]) <- alpha[1] + w[1]*alpha[2]*cov.region[i] Detection probability : logit(p[i,t]) <- alpha[3] + w[2]*alpha[4]*cov.region[i] + w[3]*alpha[5]*t + w[4]*alpha[6]*t*cov.region[i] + eps[i] Indicator variables - w ~ dbern(0.5) Multiplies every relevant parameter
  • 8. Model Selection MCMC sampling Posterior model probability = Number of iterations using this model Total number of iterations
  • 9. Model Selection Results : r . r + T + r.T 0,01027 0,05487 r + T 0,06833 0,36239 r 0,04008 0,18398 T 0,01216 0,05809 . 0,02383 0,12107 Survival Capture Model selected : Survival = f(.), Capture = f(r+T) Some models with no significance are ignored: the intersect of r and T only has a meaning if both r and T are used Theoretical number of models = 24 = 16
  • 10. Estimated survival Estimated density with an uninformative prior U(0,1) f = 0.94 ± 0.015
  • 11. Using informative priors Two priors for Survival were used for the next simulations : -A non informative prior U(0,1) -An informative prior B(a,b), with a and b chosen in order to get a mean of 0.9 and a standard deviation of 0.025
  • 12. Using informative priors Entire dataset n = 25 years Both population cores No difference in population size estimation No difference in standard deviation
  • 13. Using informative Priors - Splitting the dataset Dataset split n = 25 years Eastern population only No difference in population size estimation No difference in standard deviation
  • 14. Using informative Priors - Splitting the dataset Dataset split n = 25 years Western population only No difference in population size estimation No difference in standard deviation
  • 15. Using informative Priors - Splitting the dataset Dataset split n = 15 years (89-03) Both population cores Improvement in standard deviation by using informative priors
  • 16. Using informative Priors - Splitting the dataset Dataset split n = 15 years (04-13) Both population cores Improvement in standard deviation by using informative priors Difference in population size estimation
  • 17. Conclusion What can we say about informative priors ? -Even relatively small datasets may contain enough data in order to be used - In the case of the French Brown Bear, the information seems to come from the length of the study (over 25 years) -In the last 10 years, monitoring of the population has greatly increased – more people involved, improving the search for genetic samples in the Pyrénées -Informative priors are useful to create a more complex model including more parameters on a smaller timeframe
  • 18. Conclusion What to do next ? Check if an informative prior has influences model selection Check the influence of an informative prior on a more complex model : -Add more age classes -Add gender Use the parameter estimates in order to check the influence of future reintroductions Perform a viability analysis of the population using the informative priors
  • 19. The End From Pyrénée, written by Régis Loisel, drawn by Philippe Sternis THANK YOU FOR YOUR ATTENTION !