This is one of two volumes that sets forth invited papers from the International Indian Statistical Association Conference. This volume emphasizes advancements in methodology and applications of probability and statistics. The chapters, each representing the ideas of experts, explore a range of areas, including applied probability, models and applications, estimation and testing, robust inference, regression and design, and sample size methodology. They also describe applications of these new ideas in industry, ecology, biology, health, economics, and management. Along with those in probability and statistics, this volume will benefit researchers and graduate students in mathematical analysis.