Detecting Parameter Redundancy in Ecological State-Space Models Diana Cole and Rachel McCrea National Centre for Statistical Ecology, University of Kent.

Slides:

Advertisements

Similar presentations

Coding Transit Itineraries Frank Milthorpe Transport and Population Data Centre.

Advertisements

Recent Advances in Statistical Ecology using Computationally Intensive Methods Ruth King.

Demography of southern leatherside chub in the presence and absence of an introduced predator Mark C. Belk, Eric Billman, Josh Rasmussen, Karen Mock, Jerald.

Workshop on Parameter Redundancy Part II Diana Cole.

The Problem with Parameter Redundancy Diana Cole, University of Kent.

Spatio-temporal variation in pike demography and dispersal: effects of harvest intensity and population density Thrond O Haugen.

MAT 4830 Mathematical Modeling 4.4 Matrix Models of Base Substitutions II

Parameter Redundancy and Identifiability in Ecological Models Diana Cole, University of Kent.

Parameter Redundancy and Identifiability Diana Cole and Byron Morgan University of Kent Initial work supported by an EPSRC grant to the National Centre.

Detecting Parameter Redundancy in Complex Ecological Models Diana Cole and Byron Morgan University of Kent.

Species interaction models. Goal Determine whether a site is occupied by two different species and if they affect each others' detection and occupancy.

Parameter Redundancy in Ecological Models Diana Cole, University of Kent Byron Morgan, University of Kent Rachel McCrea, University of Kent Ben Hubbard,

Monthly Analysis of Teal Ring- Recovery Data Diana Cole, Takis Besbeas, and Byron Morgan.

1/30 Stochastic Models for Yeast Prion Propagation Diana Cole 1, Lee Byrne 2, Byron Morgan 1, Martin Ridout 1, Mick Tuite Institute of Mathematics,

Determining Parameter Redundancy of Multi-state Mark- Recapture Models for Sea Birds Diana Cole University of Kent.

C82MCP Diploma Statistics School of Psychology University of Nottingham 1 Overview Central Limit Theorem The Normal Distribution The Standardised Normal.

Uses of Population Censuses and Household Sample Surveys for Vital Statistics in South Africa United Nations Expert Group Meeting on International Standards.

Adding individual random effects results in models that are no longer parameter redundant Diana Cole, University of Kent Rémi Choquet, Centre d'Ecologie.

Embedding population dynamics models in inference S.T. Buckland, K.B. Newman, L. Thomas and J Harwood (University of St Andrews) Carmen Fernández (Oceanographic.

Simon Thornley Meta-analysis: pooling study results.

Advanced Higher Statistics Data Analysis and Modelling Hypothesis Testing Statistical Inference AH.

Detecting Parameter Redundancy in Integrated Population Models Diana Cole and Rachel McCrea National Centre for Statistical Ecology, School of Mathematics,

Integrated Population Modeling a natural tool for population dynamics Integrated Population Modeling a natural tool for population dynamics Jean-Dominique.

A Hybrid Symbolic-Numerical Method for Determining Model Structure Diana Cole, NCSE, University of Kent Rémi Choquet, Centre d'Ecologie Fonctionnelle et.

Math 22 Introductory Statistics Chapter 8 - The Binomial Probability Distribution.

1 Demographic and environmental stochasticity in population processes 1) Population dynamics 2) Community dynamics 3) Selection in fluctuating environments.

Introducing model-data fusion to graduate students in ecology Topics of discussion: The impact of NEON on ecology What are the desired outcomes from a.

Population and Sample The entire group of individuals that we want information about is called population. A sample is a part of the population that we.

Integral projection models

Chapter One Section 1.1 Note: This is the only section we are doing in chapter one.

Population dynamics across multiple sites Multiple populations How many populations are needed to ensure a high probability of survival for a species?

Assessing Estimability of Latent Class Models Using a Bayesian Estimation Approach Elizabeth S. Garrett Scott L. Zeger Johns Hopkins University Departments.

Trond Reitan (Division of statistics and insurance mathematics, Department of Mathematics, University of Oslo) Statistical modelling and latent variables.

Estimating age-specific survival rates from historical ring-recovery data Diana J. Cole and Stephen N. Freeman Mallard Dawn Balmer (BTO) Sandwich Tern.

CLASSICAL NORMAL LINEAR REGRESSION MODEL (CNLRM )

Demographic PVA’s Based on vital rates. Basic types of vital rates Fertility rates Survival rates State transition, or growth rates.

Parameter Redundancy in Mark-Recapture and Ring-Recovery Models with Missing Data Diana Cole University of Kent.

Section 1.1 Note: This is the only section we are doing in chapter one.

MAT 2720 Discrete Mathematics Section 3.3 Relations

Multistate models UF Outline  Description of the model  Data structure and types of analyses  Multistate with 2 and 3 states  Assumptions 

Estimation of Vital Rates: Use of Index Statistics? Relevance of Detection Probability.

Matrix Population Models for Wildlife Conservation and Management 27 February - 5 March 2016 Jean-Dominique LEBRETON Jim NICHOLS Madan OLI Jim HINES.

Pollock’s Robust Design: Model Extensions. Estimation of Temporary Emigration Temporary Emigration: = individual emigrated from study area, but only temporarily.

3.1 Statistical Distributions. Random Variable Observation = Variable Outcome = Random Variable Examples: – Weight/Size of animals – Animal surveys: detection.

Pollock’s Robust Design: Extensions II. Quick overview 1.Separation of Recruitment Components in a single patch context (Source-Sink) 2.Separation of.

Additional multistate model applications. Unobservable States single observable state, single unobservable state.

1 Occupancy models extension: Species Co-occurrence.

 Multi-state Occupancy. Multiple Occupancy States Rather than just presence/absence of the species at a sampling unit, ‘occupancy’ could be categorized.

Capture-recapture Models for Open Populations Multiple Ages.

 Occupancy Model Extensions. Number of Patches or Sample Units Unknown, Single Season So far have assumed the number of sampling units in the population.

Multi-state Occupancy. Multiple Occupancy States Rather than just presence/absence of the species at a sampling unit, ‘occupancy’ could be categorized.

Combining pin-point and Braun-Blanquet plant cover data

Hierarchical Models. Conceptual: What are we talking about? – What makes a statistical model hierarchical? – How does that fit into population analysis?

Capture-recapture Models for Open Populations Abundance, Recruitment and Growth Rate Modeling 6.15 UF-2015.

Trace-Contrast models for capture-recapture without capture histories Rachel Fewster Ben Stevenson, David Borchers St Andrews Helen Nathan UoA.

Tatiana Varatnitskaya Belаrussian State University, Minsk

Advanced Higher Statistics

Discrete Probability Distributions

Frequency and Distribution

School of Mathematical Sciences, University of Nottingham.

Extension to the Hybrid Symbolic-Numeric Method for Investigating Identifiability Diana Cole, University of Kent, UK Rémi Choquet, CEFE, CNRS, France.

Statistical Modeling of Ancestral Processes

Parameter Redundancy and Identifiability in Ecological Models

Probability & Statistics Probability Theory Mathematical Probability Models Event Relationships Distributions of Random Variables Continuous Random.

Multistate models Lecture 10.

From Simulations to the Central Limit Theorem

CHAPTER 15 SUMMARY Chapter Specifics

Integrated research framework, bounded by population and ecology of care axes running from highly selected to managed care populations (Y-axis) and from.

Statistical Inference

Chap. 1: Introduction to Statistics

Presentation transcript:

Detecting Parameter Redundancy in Ecological State-Space Models Diana Cole and Rachel McCrea National Centre for Statistical Ecology, University of Kent

Lapwing Example

Symbolic Method for Detecting Parameter Redundancy

Parameter Redundancy in State-Space Models

Lapwing Example State-Space Model

Integrated Models

Lapwing Example State-Space Model Combined with Ring-Recovery Data

Extended Symbolic Method

Multi-Site Model McCrea et al (2010) consider a multi-site state-space model for great cormorants (Phalacrocorax carbo). Census data consisted of annual nest counts at 2 different sites (simplification of 3 sites). State-space model, where  1,k survival prob. of immature animals,  2,k survival prob. of breeders, ρ k productivity,  k prob. becoming a breeder and  kj transition prob. (site k). new born immature breeders

Multi-Site Model

Discussion Parameter redundancy of state-space models can be investigate by expanding the expectation of the observation process. It is not always necessary to combine state-space models with other types of data, even when not all states are observed. It is often possible to estimate more than expected. It is possible to investigate parameter redundancy in integrated models by combining exhaustive summaries for each data set. The reparameterisation theorem and extension theorem have been combined to create a simpler method to investigate parameter redundancy in integrated models.

References Besbeas, P., Freeman, S. N., Morgan, B. J. T. and Catchpole, E. A. (2002) Integrating Mark-Recapture-Recovery and Census Data to Estimate Animal Abundance and Demographic Parameters. Biometrics, 58, Catchpole, E. A. and Morgan, B. J. T. (1997) Detecting parameter redundancy. Biometrika, 84, Catchpole, E. A., Morgan, B. J. T and Freeman, S. N. (1998) Estimation in parameter redundant models. Biometrika, 85, Cole, D. J., Morgan, B. J. T. and Titterington, D. M. (2010) Determining the parametric structure of models. Mathematical Biosciences, 228, Cole, D. J. and McCrea, R. S. (2012) Parameter Redundancy in Discrete State-Space and Integrated Models. Cole, D.J., Morgan, B.J.T., Catchpole, E.A. and Hubbard, B. A. (2012) Parameter Redundancy in Mark-Recovery Models. Biometrical Journal, 54, McCrea, R. S., Morgan, B. J. T., Gimenez, O, Besbeas, P., Lebreton, J. D., Bregnballe, T. (2010) Multi-Site Integrated Population Modelling. JABES, 15,