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The paper obtains analytical results for the asymptotic properties of Model Selection Criteria – widely used in practice – for a general family of hidden Markov models (HMMs), thereby substantially extending the related theory beyond typical ‘i.i.d.-like’ model structures and filling in an important gap in the relevant literature. In particular, we look at the Bayesian and Akaike Information Criteria (BIC and AIC) and the model evidence. In the setting of nested classes of models, we prove that BIC and the evidence are strongly consistent for HMMs (under regularity conditions), whereas AIC is not weakly consistent. Numerical experiments support our theoretical results.

Monitoring time-varying vaccine effectiveness (e.g., due to waning of immunity and the emergence of novel variants) provides crucial information for outbreak control. Existing studies of time-varying vaccine effectiveness have used individual-level data, most importantly dates of vaccination and variant classification, which are often not available in a timely manner or from a wide range of population groups. We present a novel Bayesian framework for estimating the waning of variant-specific vaccine effectiveness in the presence of multi-variant circulation from population-level surveillance data. Applications to simulated outbreak and COVID-19 epidemic in Japan are also presented. Our results show that variant-specific waning vaccine effectiveness estimated from population-level surveillance data could approximately reproduce the estimates from previous test-negative design studies, allowing for rapid, if crude, assessment of the epidemic situation before fine-scale studies are made available.Author summaryThe emergence of immunity-escaping SARS-CoV-2 variants and the waning of vaccine effectiveness have highlighted the need for near-real-time monitoring of variant-specific protection in the population to guide control efforts. However, standard epidemiological studies to this end typically require access to detailed individual-level dataset, which may not be timely available in an ongoing outbreak. A more convenient and less resource-intensive approach using routinely-collected data could complement such studies by providing tentative estimates of waning vaccine effectiveness until the conclusive evidence becomes available. In this paper, we propose a novel Bayesian framework for estimating waning vaccine effectiveness against multiple co-circulating variants that requires only population-level surveillance data. Using simulated outbreak data of multiple variants,we showed that the proposed method can plausibly recover the ground truth from population-level data. We also applied the proposed method to empirical COVID-19 data in Japan, which yielded estimates that are overall in line with those derived from studies using individual-level data.

We introduce a novel methodology for robust Bayesian estimation with robust divergence (e.g., density power divergence or $$\gamma $$ γ -divergence), indexed by tuning parameters. It is well known that the posterior density induced by robust divergence gives highly robust estimators against outliers if the tuning parameter is appropriately and carefully chosen. In a Bayesian framework, one way to find the optimal tuning parameter would be using evidence (marginal likelihood). However, we theoretically and numerically illustrate that evidence induced by the density power divergence does not work to select the optimal tuning parameter since robust divergence is not regarded as a statistical model. To overcome the problems, we treat the exponential of robust divergence as an unnormalisable statistical model, and we estimate the tuning parameter by minimising the Hyvarinen score. We also provide adaptive computational methods based on sequential Monte Carlo samplers, enabling us to obtain the optimal tuning parameter and samples from posterior distributions simultaneously. The empirical performance of the proposed method through simulations and an application to real data are also provided.

While robust divergence such as density power divergence and $\gamma$-divergence is helpful for robust statistical inference in the presence of outliers, the tuning parameter that controls the degree of robustness is chosen in a rule-of-thumb, which may lead to an inefficient inference. We here propose a selection criterion based on an asymptotic approximation of the Hyvarinen score applied to an unnormalized model defined by robust divergence. The proposed selection criterion only requires first and second-order partial derivatives of an assumed density function with respect to observations, which can be easily computed regardless of the number of parameters. We demonstrate the usefulness of the proposed method via numerical studies using normal distributions and regularized linear regression., Comment: 15 pages

We introduce a methodology for online estimation of smoothing expectations for a class of additive functionals, in the context of a rich family of diffusion processes (that may include jumps) -- observed at discrete-time instances. We overcome the unavailability of the transition density of the underlying SDE by working on the augmented pathspace. The new method can be applied, for instance, to carry out online parameter inference for the designated class of models. Algorithms defined on the infinite-dimensional pathspace have been developed in the last years mainly in the context of MCMC techniques. There, the main benefit is the achievement of mesh-free mixing times for the practical time-discretised algorithm used on a PC. Our own methodology sets up the framework for infinite-dimensional online filtering -- an important positive practical consequence is the construct of estimates with the variance that does not increase with decreasing mesh-size. Besides regularity conditions, our method is, in principle, applicable under the weak assumption -- relatively to restrictive conditions often required in the MCMC or filtering literature of methods defined on pathspace -- that the SDE covariance matrix is invertible.