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Modern Applied Statistics With S

Population-level analyses often use average quantities to describe heterogeneous systems, particularly when variation does not arise from identifiable groups. A prominent example, central to our current understanding of epidemic spread, is the basic reproductive number, R(0), which is defined as the mean number of infections caused by an infected individual in a susceptible population. Population estimates of R(0) can obscure considerable individual variation in infectiousness, as highlighted during the global emergence of severe acute respiratory syndrome (SARS) by numerous 'superspreading events' in which certain individuals infected unusually large numbers of secondary cases. For diseases transmitted by non-sexual direct contacts, such as SARS or smallpox, individual variation is difficult to measure empirically, and thus its importance for outbreak dynamics has been unclear. Here we present an integrated theoretical and statistical analysis of the influence of individual variation in infectiousness on disease emergence. Using contact tracing data from eight directly transmitted diseases, we show that the distribution of individual infectiousness around R(0) is often highly skewed. Model predictions accounting for this variation differ sharply from average-based approaches, with disease extinction more likely and outbreaks rarer but more explosive. Using these models, we explore implications for outbreak control, showing that individual-specific control measures outperform population-wide measures. Moreover, the dramatic improvements achieved through targeted control policies emphasize the need to identify predictive correlates of higher infectiousness. Our findings indicate that superspreading is a normal feature of disease spread, and to frame ongoing discussion we propose a rigorous definition for superspreading events and a method to predict their frequency.

/pdf/superspreading-and-the-effect-of-individual-variation-on-1hf80n09pb.pdf

Superspreading and the effect of individual variation on disease emergence

The Use of Partial Least Squares Structural Equation Modeling in Strategic Management Research: A Review of Past Practices and Recommendations for Future Applications

Preface. Acknowledgments. 1 Complex Electricity Markets. 1.1 Liberalization. 1.2 The Marketplace. 1.2.1 Power Pools and Power Exchanges. 1.2.2 Nodal and Zonal Pricing. 1.2.3 Market Structure. 1.2.4 Traded Products. 1.3 Europe. 1.3.1 The England and Wales Electricity Market. 1.3.2 The Nordic Market. 1.3.3 Price Setting at Nord Pool. 1.3.4 Continental Europe 13. 1.4 North America. 1.4.1 PJM Interconnection. 1.4.2 California and the Electricity Crisis. 1.4.3 Alberta and Ontario. 1.5 Australia and New Zealand. 1.6 Summary. 1.7 Further Reading. 2 Stylized Facts of Electricity Loads and Prices. 2.1 Introduction. 2.2 Price Spikes. 2.2.1 Case Study: The June 1998 Cinergy Price Spike. 2.2.2 When Supply Meets Demand. 2.2.3 What is Causing the Spikes?. 2.2.4 The Definition. 2.3 Seasonality. 2.3.1 Measuring Serial Correlation. 2.3.2 Spectral Analysis and the Periodogram. 2.3.3 Case Study: Seasonal Behavior of Electricity Prices and Loads. 2.4 Seasonal Decomposition. 2.4.1 Differencing. 2.4.2 Mean or Median Week. 2.4.3 Moving Average Technique. 2.4.4 Annual Seasonality and Spectral Decomposition. 2.4.5 Rolling Volatility Technique. 2.4.6 Case Study: Rolling Volatility in Practice. 2.4.7 Wavelet Decomposition. 2.4.8 Case Study: Wavelet Filtering of Nord Pool Hourly System Prices. 2.5 Mean Reversion. 2.5.1 R/S Analysis. 2.5.2 Detrended Fluctuation Analysis. 2.5.3 Periodogram Regression. 2.5.4 Average Wavelet Coefficient. 2.5.5 Case Study: Anti-persistence of Electricity Prices. 2.6 Distributions of Electricity Prices. 2.6.1 Stable Distributions. 2.6.2 Hyperbolic Distributions. 2.6.3 Case Study: Distribution of EEX Spot Prices. 2.6.4 Further Empirical Evidence and Possible Applications. 2.7 Summary. 2.8 Further Reading. 3 Modeling and Forecasting Electricity Loads. 3.1 Introduction. 3.2 Factors Affecting Load Patterns. 3.2.1 Case Study: Dealing with Missing Values and Outliers. 3.2.2 Time Factors. 3.2.3 Weather Conditions. 3.2.4 Case Study: California Weather vs Load. 3.2.5 Other Factors. 3.3 Overview of Artificial Intelligence-Based Methods. 3.4 Statistical Methods. 3.4.1 Similar-Day Method. 3.4.2 Exponential Smoothing. 3.4.3 Regression Methods. 3.4.4 Autoregressive Model. 3.4.5 Autoregressive Moving Average Model. 3.4.6 ARMA Model Identification. 3.4.7 Case Study: Modeling Daily Loads in California. 3.4.8 Autoregressive Integrated Moving Average Model. 3.4.9 Time Series Models with Exogenous Variables. 3.4.10 Case Study: Modeling Daily Loads in California with Exogenous Variables. 3.5 Summary. 3.6 Further Reading. 4 Modeling and Forecasting Electricity Prices. 4.1 Introduction. 4.2 Overview of Modeling Approaches. 4.3 Statistical Methods and Price Forecasting. 4.3.1 Exogenous Factors. 4.3.2 Spike Preprocessing. 4.3.3 How to Assess the Quality of Price Forecasts. 4.3.4 ARMA-type Models. 4.3.5 Time Series Models with Exogenous Variables. 4.3.6 Autoregressive GARCH Models. 4.3.7 Case Study: Forecasting Hourly CalPX Spot Prices with Linear Models. 4.3.8 Case Study: Is Spike Preprocessing Advantageous?. 4.3.9 Regime-Switching Models. 4.3.10 Calibration of Regime-Switching Models. 4.3.11 Case Study: Forecasting Hourly CalPX Spot Prices with Regime-Switching Models. 4.3.12 Interval Forecasts. 4.4 Quantitative Models and Derivatives Valuation. 4.4.1 Jump-Diffusion Models. 4.4.2 Calibration of Jump-Diffusion Models. 4.4.3 Case Study: A Mean-Reverting Jump-Diffusion Model for Nord Pool Spot Prices. 4.4.4 Hybrid Models. 4.4.5 Case Study: Regime-Switching Models for Nord Pool Spot Prices. 4.4.6 Hedging and the Use of Derivatives. 4.4.7 Derivatives Pricing and the Market Price of Risk. 4.4.8 Case Study: Asian-Style Electricity Options. 4.5 Summary. 4.6 Further Reading. Bibliography. Index.

Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach

Regression Analysis of Count Data: Preface

In spatial count data analysis, modeling with a multilateral lattice structure presents some important challenges. They include both the model construction and the estimation of the model parameters, since the structure accommodates the left, right, top, bottom, and diagonal site effects. Thus, the multilateral spatial process unifies all the popular spatial subclasses that include the unilateral, Rook, Bishop, and Queen models and, hence, makes it suitable for a wide variety of applications. This paper introduces a first-order multilateral integer-valued spatial process, based on a binomial thinning mechanism and some innovation term, under both stationary and nonstationary conditions. The estimation of parameters is handled by the conditional maximum likelihood estimation (CML) approach. Simulation experiments are implemented to assess the consistency of the CML estimators in the stationary and nonstationary multilateral spatial model and its subclasses, based on different grid sizes and under both covariate and noncovariate designs. The proposed model, along with its subclasses are applied to real datasets. 

The Multilateral Spatial Integer‐valued Process of order 1

If the assumed model does not accurately capture the underlying structure of the data, a statistical method is likely to yield sub-optimal results, and so model selection is crucial in order to conduct any statistical analysis. However, in case of massive datasets, the selection of an appropriate model from a large pool of candidates becomes computationally challenging, and limited research has been conducted on data selection for model selection. In this study, we conduct subdata selection based on the A-optimality criterion, allowing to perform model selection on a smaller subset of the data. We evaluate our approach based on the probability of selecting the best model and on the estimation efficiency through simulation experiments and two real data applications.

Optimal subdata selection for linear model selection

We propose a statistical modeling approach as a viable alternative to traditional transportation models concerning inference on origin-destination (OD) matrices. To this end we utilize Poisson mixtures in order to model a large over-dispersed OD matrix derived from the 2001 Belgian travel census. Bayesian methods are using a novel Poisson-inverse Gaussian model. As shown the model has desirable attributes both in its marginal and in its hierarchical form.

Poisson mixture regression for Bayesian inference on large over-dispersed transportation origin-destination matrices

Over the past few years, interest has increased in models defined on positive and negative integers. Several application areas lead to data that are differences between positive integers. Some important examples are price changes measured discretely in financial applications, pre- and posttreatment measurements of discrete outcomes in clinical trials, the difference in the number of goals in sports events, and differencing of count-valued time series. This review aims at bringing together a wide range of models that have appeared in the literature in recent decades. We provide an extensive review on discrete distributions defined for integer data and then consider univariate and multivariate time-series models, including the class of autoregressive models, stochastic processes, and ARCH-GARCH– (autoregressive conditionally heteroskedastic–generalized autoregressive conditionally heteroskedastic–) type models. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 10 is March 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

https://www.annualreviews.org/doi/pdf/10.1146/annurev-statistics-032921-022516

Dimitris Karlis

Papers

The Multilateral Spatial Integer‐valued Process of order 1

Optimal subdata selection for linear model selection

Poisson mixture regression for Bayesian inference on large over-dispersed transportation origin-destination matrices

Models for Integer Data

Reply to the letter to the editor 'ESMO-MCBS v1.1: statistical and patient relevant shortcomings' by Emprechtinger et al.