Markov Chain Monte Carlo (MCMC) is a method for drawing samples from non-standard probability distributions. Hamiltonian Monte Carlo (HMC) is a popular variant of MCMC that uses gradient information to explore the target distribution. The Sequential Monte Carlo (SMC) sampler is an alternative sampling method which, unlike MCMC, can readily utilise parallel computing architectures. It is typical within SMC literature to target a tempered distribution using a proposal with an accept/reject mechanism. In this letter, we show how the proposal used in the No-U-Turn Sampler (NUTS), an advanced variant of HMC, can be incorporated into an SMC sampler without an accept/reject mechanism. Empirical results show that this can remove the need for tempering and gives rise to accurate estimates being generated in fewer iterations which motivates this technique being deployed on parallel hardware.

The emergence of the novel coronavirus (COVID-19) generated a need to quickly and accurately assemble up-to-date information related to its spread. In this research article, we propose two methods in which Twitter is useful when modelling the spread of COVID-19: (1) machine learning algorithms trained in English, Spanish, German, Portuguese and Italian are used to identify symptomatic individuals derived from Twitter. Using the geo-location attached to each tweet, we map users to a geographic location to produce a time-series of potential symptomatic individuals. We calibrate an extended SEIRD epidemiological model with combinations of low-latency data feeds, including the symptomatic tweets, with death data and infer the parameters of the model. We then evaluate the usefulness of the data feeds when making predictions of daily deaths in 50 US States, 16 Latin American countries, 2 European countries and 7 NHS (National Health Service) regions in the UK. We show that using symptomatic tweets can result in a 6% and 17% increase in mean squared error accuracy, on average, when predicting COVID-19 deaths in US States and the rest of the world, respectively, compared to using solely death data. (2) Origin/destination (O/D) matrices, for movements between seven NHS regions, are constructed by determining when a user has tweeted twice in a 24 h period in two different locations. We show that increasing and decreasing a social connectivity parameter within an SIR model affects the rate of spread of a disease.

This paper analyses the Taylor rule and its application to monetary policy in the United Kingdom and Euro area. The analysis uses a linear regression on quarterly economic data from 1993Q1 to 2017Q4 for the United Kingdom and 2000Q1 to 2016Q4 for the Euro area. The results show that the Taylor rule does not fully describe the monetary policy actions made by the Bank of England and European Central Bank over the period analysed; and, that both central banks engage in a significant level of interest rate smoothing. The results also suggest that the Taylor rule does not provide the rationale for quantitative easing within the two regions and that interest rates should be higher than they currently are.