Conference Agenda

In this talk, we consider the problem of monitoring changes in the covariance matrices of a sequence of multivariate normally distributed random vectors. Therefore, we introduce a Multivariate Exponentially Weighted Moving Average (MEWMA) control chart in which, at each time step, the empirical covariance matrix is computed and vectorized. The control limit and the corresponding Average Run Length (ARL) are determined not only by Monte Carlo simulation, but also by numerically solving an integral equation for the ARL. In order to set up this integral equation, the exact transition density of the monitoring statistic is approximated by its asymptotic transition density. This approximation exploits the fact that the asymptotic transition density is invariant under rotations of the sample covariance matrix. Finally, we provide an outlook on an application of the proposed control chart to data from a bridge monitoring project.

There are indeed many EWMA control charts for various parameters available. However, there is none for monitoring the linear correlation coefficient ρ. Despite it is known for a long time, the usage of he explicit distribution of the estimator of ρ while setting up a control chart seems to be non-existent. Here, we build an EWMA chart utilizing this estimator, namely the Pearson correlation, and calculate the most popular performance measure, the zero-state average run length (ARL), by means of various numerical methods. Less surprisingly, the two standard methods work poorly for certain chart designs. We solve these problems by utilizing piece-wise collocation. Moreover, we examine further configuration details and provide some guidelines. Two applications illustrate the usefulness of monitoring the ρ level.

Biodiversity underpins life on Earth, yet it is declining at an accelerating pace, sharpening the need for interventions that can slow, halt, or reverse these losses. Designing such interventions requires clear insight into the processes driving population declines in particular species—and into the relative importance of those processes—insight most directly generated by population dynamics models. Yet appropriate population dynamics models for quantifying declines and guiding conservation management of wild herbivore populations remain scarce, leaving a critical gap in both evidence and practice. To address this gap, we develop an integrated Bayesian state-space population dynamics model, using the Mara-Serengeti hartebeest population as a case study. The model extends and generalizes an earlier framework we developed and illustrated for the Mara-Serengeti topi (Mukhopadhyay et al. 2024), adding multiple features designed to improve realism, inference, and management relevance.

The model fuses ground demographic surveys with aerial monitoring data, explicitly representing population age–sex structure and key life-history traits and strategies. It links birth rates, age-specific survival rates, and sex ratios to meteorological covariates, prior population density, environmental seasonality, predation risk, and several environmental and anthropogenic covariates. Operating on a monthly time step, it enables fine-grained estimation of reproductive seasonality, phenology, synchrony, and birth prolificacy, as well as juvenile and adult recruitment dynamics. We evaluate performance using balanced bootstrap sampling and by comparing model predictions with empirical aerial estimates of population size. We perform detailed assessment of model robustness, including by checking for parameter redundancy, estimability and identifiability, performing sensitivity analysis of the priors and running multiple MCMC chains. Implemented as a hierarchical Bayesian model using MCMC methods for parameter estimation, prediction, and inference, the model reproduces several well-established features of the hartebeest population, including a steep and persistent decline, weakly seasonal births, and juvenile and adult recruitment patterns. The framework is general and flexible and easily adaptable for other species.

References Mukhopadhyay, S., Piepho, H. P., Bhattacharya, S., Dublin, H. T., & Ogutu, J. O. (2024). Hierarchical Bayesian integrated modeling of age-and sex-structured wildlife population dynamics. Journal of Agricultural, Biological and Environmental Statistics, 1-26.

Joseph O. Ogutu, Hans-Peter Piepho et al.

University of Hohenheim, Institute of Crop Science, Biostatistics Unit, Fruwirthstrasse 23, 70599 Stuttgart, Germany

The basic results concerning with the asymptotic theory of estimation and testing, Le Cam (1960) introduced so-called locally asymptotically normal (LAN) family of distributions. The convolution theorem for LAN case is obtained by Hájek (1970). The convolution result was extended by Le Cam (1972) to more general situations than that of LAN case. These results sometimes called the Hájek-Le Cam asymptotic minimax theorem. In this talk we derive the second order generalization of Hájek's convolution theorem. Furthermore, as a application of the second order Hájek's convolution theorem, we lead to the second order Hájek-Le Cam asymptotic minimax theorem. It automatically provides the conditions that the second order asymptotic efficient estimators should satisfy.