Abstract We present a new framework to estimate excess cause‐specific mortality by integrating relative survival into a multi‐state model, motivated by the question of how vaccination and infection impacted different components of excess mortality for the older Dutch population during the first two years of the COVID‐19 pandemic in the Netherlands. The proportion of the study population who died from COVID‐19, 0.98%, was nearly three times the excess proportion of all‐cause mortality, 0.34%, reflecting a mortality substitution effect: other causes of death occurred less than expected. COVID‐19 infection increased short‐term mortality across all causes of death, with residual risk beyond 28 days postinfection. Vaccination was associated with reduced COVID‐19 mortality risk in both the acute and long‐term infection phases, with consistent results across landmark times. Results suggest a healthy vaccinee bias, specifically for cardiovascular diseases, mental & neurological disorders and neoplasms. However, this bias seems far smaller than the impact of vaccination on reduction of COVID‐19 mortality.
Abstract Additional states in a hidden Markov model (HMM) can compensate for restrictive emission distributions without representing additional scientific regimes. We study this distinction using the established representation of mixture components as refined states. Under compactness, mixture identifiability and positive aggregate transitions, we prove that a simple‐emission HMM with too few components has an observed‐law Kullback–Leibler loss that grows at least linearly with sequence length. An exact refinement, or an aggregate HMM with mixture emissions, removes this approximation gap. Simulations illustrate the resulting incentive to add states. An analysis of tumor allele fractions on chromosome 1 then compares five Gaussian states with three regional profiles containing five Gaussian components. The fitted emissions and regional assignments are nearly the same after grouping the Gaussian states, while the mixture model uses 14 fewer parameters. This example illustrates how additional states can describe variation within a regional profile rather than additional regional regimes. The number of fitted states alone therefore does not determine the number of scientifically distinct regimes.
When a sampling distribution is discrete, the coverage of a confidence interval follows a sequence of peaks and troughs when plotted against the value of the parameter of interest. Then methods of forming a confidence interval must either be conservative, with a coverage that is almost always above the nominal confidence level, or give a coverage that is sometimes below the nominal level. Many methods have been proposed that adopt the latter policy, so the requirements of a confidence interval are often tempered. Garthwaite et al. (2024) suggest that the definition of a confidence interval should be relaxed in a clearly defined way if the definition is not strictly adhered to. For one-sided intervals, they define locally correct confidence intervals as intervals whose average coverage between consecutive peaks is no smaller than the nominal level. Two-sided locally correct confidence intervals are formed from two one-sided intervals. They propose a method for forming locally correct intervals for a binomial proportion that minimizes the average length of such intervals. In this article, we generalize the method so that it can be used with other discrete sampling models. The method is illustrated through examples and compared with alternative methods.
Intraday transaction-level data on financial assets constitute high-frequency, irregularly spaced time series, posing challenges for volatility modeling. Traditional stochastic volatility models, designed for regularly spaced time series, are not directly applicable in this setting. This paper introduces two hierarchical Bayesian models-the irregular basic multivariate stochastic volatility autoregressive conditional duration model and the irregular dynamic multivariate stochastic volatility autoregressive conditional duration model to address these challenges and effectively model volatility in irregular intra-day data. These models incorporate the autoregressive conditional duration model to account for irregular gaps between transactions, improving the understanding of market microstructure and future dynamics. The analysis is conducted within a Bayesian framework using the Hamiltonian Monte Carlo algorithm with No-U-turn sampler in R via the cmdstanr package. We demonstrate the efficacy of our methodology through simulation studies and an illustrative example using intra-day prices of healthcare stocks traded on the New York Stock Exchange at the microsecond level. Utilizing the refresh time sampling technique, we synchronize transactions, compute synchronized log-returns and gaps, and use these for modeling purposes.
We study the admissibility of generalized Bayes estimators for regression coefficients in normal linear models under hierarchical -priors. While admissibility results are available for canonical normal means problems with unknown variance, their applicability to the regression problem is nontrivial. We explore the admissibility of regression-induced generalized Bayes estimators under scaled quadratic loss with arbitrary positive definite weight matrices by carefully transporting recent normal means results to the regression parameter. Explicit conditions on the hyperparameters governing the prior on are derived. Our results provide a decision-theoretic justification for generalized Bayes estimators of regression coefficients under hierarchical g-priors.
