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The results of a simulation-based evaluation of several policies for vaccine rollout are reported, particularly focusing on the effects of delaying the second dose of two-dose vaccines. In the presence of limited vaccine supply, the specific policy choice is a pressing issue for several countries worldwide, and the adopted course of action will affect the extension or easing of non-pharmaceutical interventions in the next months. We employ a suitably generalised, age-structure, stochastic SEIR (Susceptible → Exposed → Infectious → Removed) epidemic model that can accommodate quantitative descriptions of the major effects resulting from distinct vaccination strategies. The different rates of social contacts among distinct age-groups (as well as some other model parameters) are informed by a recent survey conducted in Greece, but the conclusions are much more widely applicable. The results are summarised and evaluated in terms of the total number of deaths and infections as well as life years lost. The optimal strategy is found to be one based on fully vaccinating the elderly/at risk as quickly as possible, while extending the time-interval between the two vaccine doses to 12 weeks for all individuals below 75 years old, in agreement with epidemic theory which suggests targeting a combination of susceptibility and infectivity. This policy, which is similar to the approaches adopted in the UK and in Canada, is found to be effective in reducing deaths and life years lost in the period while vaccination is still being carried out.

The problem of determining the best achievable performance of arbitrary lossless compression algorithms is examined, when correlated side information is available at both the encoder and decoder. For arbitrary source-side information pairs, the conditional information density is shown to provide a sharp asymptotic lower bound for the description lengths achieved by an arbitrary sequence of compressors. This implies that for ergodic source-side information pairs, the conditional entropy rate is the best achievable asymptotic lower bound to the rate, not just in expectation but with probability one. Under appropriate mixing conditions, a central limit theorem and a law of the iterated logarithm are proved, describing the inevitable fluctuations of the second-order asymptotically best possible rate. An idealised version of Lempel-Ziv coding with side information is shown to be universally first- and second-order asymptotically optimal, under the same conditions. These results are in part based on a new almost-sure invariance principle for the conditional information density, which may be of independent interest.

Partly motivated by entropy-estimation problems in neuroscience, we present a detailed and extensive comparison between some of the most popular and effective entropy estimation methods used in practice: The plug-in method, four different estimators based on the Lempel-Ziv (LZ) family of data compression algorithms, an estimator based on the Context-Tree Weighting (CTW) method, and the renewal entropy estimator. METHODOLOGY: Three new entropy estimators are introduced; two new LZ-based estimators, and the “renewal entropy estimator,†which is tailored to data generated by a binary renewal process. For two of the four LZ-based estimators, a bootstrap procedure is described for evaluating their standard error, and a practical rule of thumb is heuristically derived for selecting the values of their parameters in practice. THEORY: We prove that, unlike their earlier versions, the two new LZ-based estimators are universally consistent, that is, they converge to the entropy rate for every finite-valued, stationary and ergodic process. An effective method is derived for the accurate approximation of the entropy rate of a finite-state hidden Markov model (HMM) with known distribution. Heuristic calculations are presented and approximate formulas are derived for evaluating the bias and the standard error of each estimator. SIMULATION: All estimators are applied to a wide range of data generated by numerous different processes with varying degrees of dependence and memory. The main conclusions drawn from these experiments include: (i) For all estimators considered, the main source of error is the bias. (ii) The CTW method is repeatedly and consistently seen to provide the most accurate results. (iii) The performance of the LZ-based estimators is often comparable to that of the plug-in method. (iv) The main drawback of the plug-in method is its computational inefficiency; with small word-lengths it fails to detect longer-range structure in the data, and with longer word-lengths the empirical distribution is severely undersampled, leading to large biases.