In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

discuss the production of low rank smoothers for d greater than or equal to 1 dimensional data, which can be fitted by regression or penalized regression methods. The smoothers are constructed by a simple transformation and truncation of the basis that arises from the solution of the thin plate spline smoothing problem and are optimal in the sense that the truncation is designed to result in the minimum possible perturbation of the thin plate spline smoothing problem given the dimension of the basis used to construct the smoother. By making use of Lanczos iteration the basis change and truncation are computationally efficient. The smoothers allow the use of approximate thin plate spline models with large data sets, avoid the problems that are associated with 'knot placement' that usually complicate modelling with regression splines or penalized regression splines, provide a sensible way of modelling interaction terms in generalized additive models, provide low rank approximations to generalized smoothing spline models, appropriate for use with large data sets, provide a means for incorporating smooth functions of more than one variable into non-linear models and improve the computational efficiency of penalized likelihood models incorporating thin plate splines. Given that the approach produces spline-like models with a sparse basis, it also provides a natural way of incorporating unpenalized spline-like terms in linear and generalized linear models, and these can be treated just like any other model terms from the point of view of model selection, inference and diagnostics

Thin plate regression splines

Summary
1. Distance sampling is a widely used technique for estimating the size or density of biological populations. Many distance sampling designs and most analyses use the software Distance.

2. We briefly review distance sampling and its assumptions, outline the history, structure and capabilities of Distance, and provide hints on its use.

3. Good survey design is a crucial prerequisite for obtaining reliable results. Distance has a survey design engine, with a built-in geographic information system, that allows properties of different proposed designs to be examined via simulation, and survey plans to be generated.

4. A first step in analysis of distance sampling data is modelling the probability of detection. Distance contains three increasingly sophisticated analysis engines for this: conventional distance sampling, which models detection probability as a function of distance from the transect and assumes all objects at zero distance are detected; multiple-covariate distance sampling, which allows covariates in addition to distance; and mark–recapture distance sampling, which relaxes the assumption of certain detection at zero distance.

5. All three engines allow estimation of density or abundance, stratified if required, with associated measures of precision calculated either analytically or via the bootstrap.

6. Advanced analysis topics covered include the use of multipliers to allow analysis of indirect surveys (such as dung or nest surveys), the density surface modelling analysis engine for spatial and habitat modelling, and information about accessing the analysis engines directly from other software.

7.Synthesis and applications. Distance sampling is a key method for producing abundance and density estimates in challenging field conditions. The theory underlying the methods continues to expand to cope with realistic estimation situations. In step with theoretical developments, state-of-the-art software that implements these methods is described that makes the methods accessible to practising ecologists.

/pdf/distance-software-design-and-analysis-of-distance-sampling-5edm5dww9q.pdf

Distance software: design and analysis of distance sampling surveys for estimating population size.

Introduction.- Data management and software.- Advice for teachers.- Exploration.- Linear regression.- Generalised linear modelling.- Additive and generalised additive modelling.- Introduction to mixed modelling.- Univariate tree models.- Measures of association.- Ordination--first encounter.- Principal component analysis and redundancy analysis.- Correspondence analysis and canonical correspondence analysis.- Introduction to discriminant analysis.- Principal coordinate analysis and non-metric multidimensional scaling.- Time series analysis--Introduction.- Common trends and sudden changes.- Analysis and modelling lattice data.- Spatially continuous data analysis and modelling.- Univariate methods to analyse abundance of decapod larvae.- Analysing presence and absence data for flatfish distribution in the Tagus estuary, Portugual.- Crop pollination by honeybees in an Argentinean pampas system using additive mixed modelling.- Investigating the effects of rice farming on aquatic birds with mixed modelling.- Classification trees and radar detection of birds for North Sea wind farms.- Fish stock identification through neural network analysis of parasite fauna.- Monitoring for change: using generalised least squares, nonmetric multidimensional scaling, and the Mantel test on western Montana grasslands.- Univariate and multivariate analysis applied on a Dutch sandy beach community.- Multivariate analyses of South-American zoobenthic species--spoilt for choice.- Principal component analysis applied to harbour porpoise fatty acid data.- Multivariate analysis of morphometric turtle data--size and shape.- Redundancy analysis and additive modelling applied on savanna tree data.- Canonical correspondence analysis of lowland pasture vegetation in the humid tropics of Mexico.- Estimating common trends in Portuguese fisheries landings.- Common trends in demersal communities on the Newfoundland-Labrador Shelf.- Sea level change and salt marshes in the Wadden Sea: a time series analysis.- Time series analysis of Hawaiian waterbirds.- Spatial modelling of forest community features in the Volzhsko-Kamsky reserve.

Analysing Ecological Data

Species distribution modelling is central to both fundamental and applied research in biogeography. Despite widespread use of models, there are still important conceptual ambiguities as well as biotic and algorithmic uncertainties that need to be investigated in order to increase confidence in model results. We identify and discuss five areas of enquiry that are of high importance for species distribution modelling: (1) clarification of the niche concept; (2) improved designs for sampling data for building models; (3) improved parameterization; (4) improved model selection and predictor contribution; and (5) improved model evaluation. The challenges discussed in this essay do not preclude the need for developments of other areas of research in this field. However, they are critical for allowing the science of species distribution modelling to move forward.

Five (or so) challenges for species distribution modelling

1. Introductory concepts 2. Assumptions and modelling philosophy 3. Statistical theory 4. Line transects 5. Point transects 6. Related methods 7. Study design and field methods 8. Illustrative examples

Introduction to Distance Sampling: Estimating Abundance of Biological Populations

Live-trapping capture-recapture studies of animal populations with fixed trap locations inevitably have a spatial component: animals close to traps are more likely to be caught than those far away. This is not addressed in conventional closed-population estimates of abundance and without the spatial component, rigorous estimates of density cannot be obtained. We propose new, flexible capture-recapture models that use the capture locations to estimate animal locations and spatially referenced capture probability. The models are likelihood-based and hence allow use of Akaike's information criterion or other likelihood-based methods of model selection. Density is an explicit parameter, and the evaluation of its dependence on spatial or temporal covariates is therefore straightforward. Additional (nonspatial) variation in capture probability may be modeled as in conventional capture-recapture. The method is tested by simulation, using a model in which capture probability depends only on location relative to traps. Point estimators are found to be unbiased and standard error estimators almost unbiased. The method is used to estimate the density of Red-eyed Vireos (Vireo olivaceus) from mist-netting data from the Patuxent Research Refuge, Maryland, U.S.A. Estimates agree well with those from an existing spatially explicit method based on inverse prediction. A variety of additional spatially explicit models are fitted; these include models with temporal stratification, behavioral response, and heterogeneous animal home ranges.

Spatially explicit maximum likelihood methods for capture-recapture studies.

1. The status of small cetaceans in the North Sea and adjacent waters has been of concern for many years. Shipboard and aerial line transect surveys were conducted to provide accurate and precise estimates of abundance as a basis for conservation strategy in European waters. 2. The survey, known as SCANS (Small Cetacean Abundance in the North Sea), was conducted in summer 1994 and designed to generate precise and unbiased abundance estimates. Thus the intensity of survey was high, and data collection and analysis methods allowed for the probability of detection of animals on the transect line being less than unity and, for shipboard surveys, also allowed for animal movement in response to the survey platform. 3. Shipboard transects covered 20 000 km in an area of 890 000 km2. Aerial transects covered 7000 km in an area of 150 000 km2. 4. Three species dominated the data. Harbour porpoise Phocoena phocoena were encountered throughout the survey area except in the Channel and the southern North Sea. Whitebeaked dolphin Lagenorhynchus albirostris and minke whale Balaenoptera acutorostrata were found mainly in the north-western North Sea. 5. Phocoena phocoena abundance for the entire survey area was estimated as 341 366 [coefficient of variation (CV) = 0.14; 95% confidence interval (CI) = 260 000-449 000]. The estimated number of B. acutorostrata was 8445 (CV = 0.24; 95% CI 5000-13 500). The estimate for L. albirostris based on confirmed sightings of this species was 7856 (CV = 0.30; 95% CI = 4000-13 000). When Atlantic whitesided dolphin Lagenorhynchus acutus and Lagenorhynchus spp. sightings were included, this estimate increased to 11 760 (CV = 0.26; 95% CI 5900-18 500). 6. Shortbeaked common dolphin Delphinus delphis were found almost exclusively in the Celtic Sea. Abundance was estimated as 75 450 (CV = 0.67; 95% CI = 23 000-149 000). 7. Current assessments and recommendations by international fora concerning the impact on P. phocoena of bycatch in gillnet fisheries in the North Sea and adjacent waters are based on these estimates.

/pdf/abundance-of-harbour-porpoise-and-other-cetaceans-in-the-23kyaqspxq.pdf

Abundance of harbour porpoise and other cetaceans in the North Sea and adjacent waters

1. Introduction to advanced distance sampling 2. General formulation for distance sampling 3. Covariate models 4. Spatial distance sampling models 5. Temporal inferences from distance sampling surveys 6. Methods for incomplete detection at distance zero 7. Design of distance sampling surveys and Geographic Information Systems 8. Adaptive distance sampling surveys 9. Passive approaches to detection in distance sampling 10. Assessment of distance sampling estimators 11. Further topics in distance sampling References Index

/pdf/advanced-distance-sampling-sak0cbmfhg.pdf

David L. Borchers

Papers

Introduction to Distance Sampling: Estimating Abundance of Biological Populations

Spatially explicit maximum likelihood methods for capture-recapture studies.

Abundance of harbour porpoise and other cetaceans in the North Sea and adjacent waters

Advanced distance sampling

Estimating Animal Abundance