We produce new reconstructions of Northern Hemisphere annually averaged temperature anomalies back to 1000 AD, and explore the effects of including external climate forcings within the reconstruction and of accounting for short-memory and long-memory features. Our reconstructions are based on two linear models, with the first linking the latent temperature series to three main external forcings (solar irradiance, greenhouse gas concentration and volcanism), and the second linking the observed temperature proxy data (tree rings, sediment record, ice cores, etc.) to the unobserved temperature series. Uncertainty is captured with additive noise, and a rigorous statistical investigation of the correlation structure in the regression errors is conducted through systematic comparisons between reconstructions that assume no memory, short-memory autoregressive models, and long-memory fractional Gaussian noise models. We use Bayesian estimation to fit the model parameters and to perform separate reconstructions of land-only and combined land-and-marine temperature anomalies. For model formulations that include forcings, both exploratory and Bayesian data analysis provide evidence against models with no memory. Model assessments indicate that models with no memory underestimate uncertainty. However, no single line of evidence is sufficient to favor short-memory models over long-memory ones, or to favor the opposite choice. When forcings are not included, the long-memory models appear to be necessary. While including external climate forcings substantially improves the reconstruction, accurate reconstructions that exclude these forcings are vital for testing the fidelity of climate models used for future projections. Finally, we use posterior samples of model parameters to arrive at an estimate of the transient climate response to greenhouse gas forcings of 2.5°C (95% credible interval of [2.16, 2.92]°C), which is on the high end of, but consistent with, the expert-assessment-based uncertainties given in the recent Fifth Assessment Report of the IPCC.

We consider the class of all stationary Gaussian process with explicit parametric spectral density. Under some conditions on the autocovariance function, we defined a GMM estimator that satisfies consistency and asymptotic normality, using the Breuer-Major theorem and previous results on ergodicity. This result is applied to the joint estimation of the three parameters of a stationary Ornstein-Uhlenbeck (fOU) process driven by a fractional Brownian motion. The asymptotic normality of its GMM estimator applies for any $H$ in $(0,1)$ and under some restrictions on the remaining parameters. A numerical study is performed in the fOU case, to illustrate the estimator’s practical performance when the number of datapoints is moderate.

Successful partnerships between researchers, experts, and public health authorities have been critical to navigate the challenges of the Covid-19 pandemic worldwide. In this collaboration, mathematical models have played a decisive role in informing public policy, with findings effectively translated into public health measures that have shaped the pandemic in Costa Rica. As a result of interdisciplinary and cross-institutional collaboration, we constructed a multilayer network model that incorporates a diverse contact structure for each individual. In July 2020, we used this model to test the effect of lifting restrictions on population mobility after a so-called “epidemiological fence” imposed to contain the country’s first big wave of cases. Later, in August 2020, we used it to predict the effects of an open and close strategy (the Hammer and Dance). Scenarios constructed in July 2020 showed that lifting restrictions on population mobility after less than three weeks of epidemiological fence would produce a sharp increase in cases. Results from scenarios in August 2020 indicated that the Hammer and Dance strategy would only work with 50% of the population adhering to mobility restrictions. The development, evolution, and applications of a multilayer network model of Covid-19 in Costa Rica has guided decision-makers to anticipate implementing sanitary measures and contributed to gain valuable time to increase hospital capacity.

Climate has been an important factor in shaping the distribution and incidence of dengue cases in tropical and subtropical countries. In Costa Rica, a tropical country with distinctive micro-climates, dengue has been endemic since its introduction in 1993, inflicting substantial economic, social, and public health repercussions. Using the number of dengue reported cases and climate data from 2007-2017, we fitted a prediction model applying a Generalized Additive Model (GAM) and Random Forest (RF) approach, which allowed us to retrospectively predict the relative risk of dengue in five climatological diverse municipalities around the country.