ISM Symposium on
Environmental Statistics
2013

Date & Time: Jan. 25(Fri), 2013
Venue: The Institute of Statistical Mathematics,
10-3 Midori-cho Tachikawa, Tokyo 190-8562, Japan

Aim of Symposium:
In order to enhance the understanding of the global environment, statisticalscience is extremely important. Centered around the topic of directional
statistics, we are holding a symposium in order to better develop research on
statistical theory which can be applied to solve specific issues in the fields ofenvironmental and ecological data.
Host Organization:
The Institute of Statistical Mathematics
Organizing Committee:Koji Kanefuji(ISM)
Kunio Shimizu(Keio University, ISM)
Atsushi Yoshimoto(ISM)
Kenichiro Shimatani(ISM)Program
Opening Address：Junji Nakano(ISM)

13:00-13:05[1]Alan Welsh(The Australian National University)
Is it there? Analysing occupancy surveys

13:05-13:50[2]Janice Scealy(The Australian National University)
13:50-14:35
Fitting Kent models to compositional data with small concentration[3]Toshihiro Abe(Tokyo University of Science)
14:35-15:05
Circular and axial distributions with an application for fallen tree data

Coffee Break

15:05-15:20[4] Shuangzhe Liu(University of Canberra) ， Min-zhen Wang (KeioUniversity), K. Shimizu (Keio University) , and A. SenGupta (IndianStatistical Institute)
15:20-16:05
Influence diagnostics in asymmetric circular-linear multivariate regression
models[5]Kenichiro Shimatani(ISM)
16:05-16:35
Circular statistics for animal movement ecology and movement ecology forcircular statistics[6]Min-zhen Wang and Kunio Shimizu (Keio University)
16-35-17:05
Cylindrical Distributions with Application to Environmental Data
Closing address：Tomoyuki Higuchi(ISM: Director-General)

17:05-17:10

Abstract[1]Alan Welsh
Is it there? Analysing occupancy surveys
We will discuss some general methods which deal with nondetection andthen consider a currently popular method called occupancy modelling in
more detail. We will show how we use statistical thinking to understandoccupancy modelling and evaluate its properties. It is obviously important tounderstand when a method will or will not work well and to understand its
limitations. We will see that occupancy models are more difficult to fit andinterpret than is generally appreciated because the estimating equations
often have multiple solutions and the estimates are unstable when the data
are sparse. When the abundance of a species varies from site to site thestandard analysis runs into difficulties and in this case, occupancy modelling
can be just as poor as analyses which ignore nondetection completely. This
raises broader philosophical questions about the use of incorrect models andthe value of trying to make complicated adjustments in difficult problems.

[2]Janice Scealy
Fitting Kent models to compositional data with small concentration
Compositional data can be transformed to directional data by the squareroot transformation and then modelled by using the Kent distribution. The
current approach for estimating the parameters in the Kent model forcompositional data relies on a large concentration assumption whichassumes that the majority of the transformed data is not distributed too
close to the boundaries of the positive orthant. When the data is distributed
close to the boundaries with large variance significant folding may result. To
treat this case we propose new estimators of the parameters derived basedon the actual folded Kent distribution which are obtained via the EMalgorithm. We show that these new estimators significantly reduce the bias
in the current estimators when both the sample size and amount of folding ismoderately large. We also propose using a saddlepoint density
approximation for the Kent distribution normalising constant in order tomore accurately estimate the shape paramet ers when the concentration issmall or only moderately large.

[3]Toshihiro Abe
Circular and axial distributions with an application for fallen tree data
We present a retrospective method for studying forest disturbance regimes,
and especially the role of windthrows, based on circular and axial statisticalmodels of directions of fallen logs. This approach was applied to fallen log
data from three areas of pristine Picea abies-dominated boreal forests innorthern Europe. The data consisted of 5 plots from each of the three areas,
totaling 15 plots and covering an area of 24 ha.The disturbance history of theplots, which varied from area to area, was known from previous detailed
studies. Our results suggested the utility of circular and axial distributionsof fallen logs and their statistical models for retrospective assessments offorest disturbance regimes.[4] Shuangzhe Liu(University of Canberra) ， Min-zhen Wang (KeioUniversity), K. Shimizu (Keio University), and A. SenGupta (IndianStatistical Institute)Influence diagnostics in asymmetric circular-linear multivariate regression
modelsDistributional studies and regression models have played important roles
in statistical analysis of circular data. Asymmetric circular-linear
multivariate regression models (SenGupta and Ugwuowo, 2006) aremotivated by and applied to predict some environmental characteristics
based on both circular and linear predictors. In this paper, we consider alikelihood approach (Cook, 1986) to study influence diagnostic analysis forthese models, using the maximum likelihood estimation and influencediagnostics methods. The observed information matrices and normal
curvatures are derived. Simulated and real data examples are then provided
to illustrate our approach and establish the utility of our results.

[5] Kenichiro Shimatani
Circular statistics for animal movement ecology and movement ecology forcircular statistics
Animal movement ecology will advance in parallel to developments incircular statistics, and the development of circular statistics will be promotedby the practical demands made from movement ecology. Here I will present
an example of such studies. Movement trajectories of an animal are often
more oriented or tortuous than expected from simple (correlated) random
models. On the basis of the recently developed circular auto-regressive model,
a new movement model was introduced and applied to GPS trajectories of aseabird. The proposed model enables us to evaluate the effects of external
factors on movements separately from the animal’s internal state. For
example, maximum likelihood estimates and model selection by AIC
suggested that in one homing flight section, the seabird intended to fly
toward the home island, but misjudged its navigation and was driven
off-course by winds, while in the subsequent flight section, the seabird resetthe focal direction, navigated the flight under strong wind conditions, andsucceeded in approaching the nest.

[6]Min-zhen Wang and Kunio Shimizu
Cylindrical Distributions with Application to Environmental Data
A cylindrical distribution means the joint distribution of a linear randomvariable and a circular random variable such as wind speed and directionand the concentration of a pollutant and wind direction. A pair of realization
may be identified with a point on the cylinder. Johnson and Wehrly (1978)
and Mardia and Sutton (1978) give fundamental models on the cylinder, andKato and Shimizu (2008) extend some of the Mardia-Sutton andJohnson-Wehrly models. In this talk we introduce some cylindrical
distributions and fit them to the periwinkle dataset in Fisher (1993).
References
1. Fisher, N. I. (1993). Statistical Analysis of Circular Data, Cambridge
University Press, Cambridge.
2. Johnson, R. A. and Wehrly, T. E. (1978). Some angular-linear
distributions and related regression models, Journal of the American
Statistical Association, 73, 602-606.
3. Kato, S. and Shimizu, K. (2008). Dependent models for observations
which include angular ones, Journal of Statistical Planning and Inference,
138, 3538-3549.
4. Mardia, K. V. and Sutton, T. W. (1978). A model for cylindrical variables
with applications, Journal of the Royal Statistical Society, B40, 229-233.