Relevant states and memory in Markov chain bootstrapping and simulation

Markov chain theory is proving to be a powerful approach to bootstrap and simulate highly nonlinear time series. In this work, we provide a method to estimate the memory of a Markov chain (i.e. its order) and to identify its relevant states. In particular, the choice of memory lags and the aggregation of irrelevant states are obtained by looking for regularities in the transition probabilities. Our approach is based on an optimization model. More specifically, we consider two competing objectives that a researcher will in general pursue when dealing with bootstrapping and simulation: preserving the “structural” similarity between the original and the resampled series, and assuring a controlled diversification of the latter. A discussion based on information theory is developed to define the desirable properties for such optimal criteria. Two numerical tests are developed to verify the effectiveness of the proposed method

Approximating Markov Chains for Bootstrapping and Simulation

In this work we develop a bootstrap method based on the theory of Markov chains. The method moves from the two competing objectives that a researcher pursues when performing a bootstrap procedure: (i) to preserve the structural similarity -in statistical sense- between the original and the bootstrapped sample; (ii) to assure a diversification of the latter with respect to the former. The original sample is assumed to be driven by a Markov chain. The approach we follow is to implement an optimization problem to estimate the memory of a Markov chain (i.e. its order) and to identify its relevant states. The basic ingredients of the model are the transition probabilities, whose distance is measured through a suitably defined functional. We apply the method to the series of electricity prices in Spain. A comparison with the Variable Length Markov Chain bootstrap, which is a well established bootstrap method, shows the superiority of our proposal in reproducing the dependence among data

A Tabu Search Heuristic Procedure in Markov Chain Bootstrapping

Markov chain theory is proving to be a powerful approach to bootstrap nite states processes, especially where time dependence is non linear. In this work we extend such approach to bootstrap discrete time continuous-valued processes. To this purpose we solve a minimization problem to partition the state space of a continuous-valued process into a nite number of intervals or unions of intervals (i.e. its states) and identify the time lags which provide \memory" to the process. A distance is used as objective function to stimulate the clustering of the states having similar transition probabilities. The problem of the exploding number of alternative partitions in the solution space (which grows with the number of states and the order of the Markov chain) is addressed through a Tabu Search algorithm. The method is applied to bootstrap the series of the German and Spanish electricity prices. The analysis of the results conrms the good consistency properties of the method we propose

A Computational Approach to Sequential Decision Optimization in Energy Storage and Trading

Due to recent technical progress, battery energy storages are becoming a viable option in the power sector. Their optimal operational management focuses on load shift and shaving of price spikes. However, this requires optimally responding to electricity demand, intermittent generation, and volatile electricity prices. More importantly, such optimization must take into account the so-called deep discharge costs, which have a significant impact on battery lifespan. We present a solution to a class of stochastic optimal control problems associated with these applications. Our numerical techniques are based on efficient algorithms which deliver a guaranteed accurac

A mixed integer linear program to compress transition probability matrices in Markov chain bootstrapping

Bootstrapping time series is one of the most acknowledged tools to study the statistical properties of an evolutive phenomenon. An important class of bootstrapping methods is based on the assumption that the sampled phenomenon evolves according to a Markov chain. This assumption does not apply when the process takes values in a continuous set, as it frequently happens with time series related to economic and financial phenomena. In this paper we apply the Markov chain theory for bootstrapping continuous-valued processes, starting from a suitable discretization of the support that provides the state space of a Markov chain of order k≥1. Even for small k, the number of rows of the transition probability matrix is generally too large and, in many practical cases, it may incorporate much more information than it is really required to replicate the phenomenon satisfactorily. The paper aims to study the problem of compressing the transition probability matrix while preserving the “law” characterising the process that generates the observed time series, in order to obtain bootstrapped series that maintain the typical features of the observed time series. For this purpose, we formulate a partitioning problem of the set of rows of such a matrix and propose a mixed integer linear program specifically tailored for this particular problem. We also provide an empirical analysis by applying our model to the time series of Spanish and German electricity prices, and we show that, in these medium size real-life instances, bootstrapped time series reproduce the typical features of the ones under observation. This is a post-peer-review, pre-copyedit version of an article published in Annals of Operations Research volume. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10479-016-2181-

Modified percutaneous ethanol injection of parathyroid adenoma in primary hyperparathyroidism.

Surgery is the treatment of choice for symptomatic primary hyperparathyroidism; unlikely few patients do not meet established surgical criteria or have comorbid conditions that prohibit surgery. In these subjects, medical therapy alone offers little hope for a sustained long normocalcemic period. However percutaneous ethanol injection (PEI) may represent an alternative therapeutic procedure. It is currently in use for the treatment of secondary or tertiary hyperparathyroidism, however, few studies or case reports suggest it for the treatment of primary hyperparathyroidism. Moreover, little information is available about the long-term follow-up, where incomplete necrosis or the spreading of ethanol in the surrounding tissues is often reported. We believe that many of the side effects could be correlated to procedure itself. Taking these experiences into account, we have reasoned that in order to limit these side effects, we had to modify the standard PEI procedure. We reported this preliminary experience describing our modified PEI procedure

Feasibility and Predictive Performance of a Triage System for Patients with Cancer During the COVID-19 Pandemic

Background: Triage procedures have been implemented to limit hospital access and minimize infection risk among patients with cancer during the coronavirus disease (COVID-19) outbreak. In the absence of prospective evidence, we aimed to evaluate the predictive performance of a triage system in the oncological setting. Materials and Methods: This retrospective cohort study analyzes hospital admissions to the oncology and hematology department of Udine, Italy, during the COVID-19 pandemic (March 30 to April 30, 2020). A total of 3,923 triage procedures were performed, and data of 1,363 individual patients were reviewed. Results: A self-report triage questionnaire identified 6% of triage-positive procedures, with a sensitivity of 66.7% (95% confidence interval [CI], 43.0%–85.4%), a specificity of 94.3% (95% CI, 93.5%–95.0%), and a positive predictive value of 5.9% (95% CI, 4.3%–8.0%) for the identification of patients who were not admitted to the hospital after medical review. Patients with thoracic cancer (odds ratio [OR], 1.69; 95% CI, 1.13–2.53, p =.01), younger age (OR, 1.52; 95% CI, 1.15–2.01, p <.01), and body temperature at admission ≥37°C (OR, 9.52; 95% CI, 5.44–16.6, p <.0001) had increased risk of positive triage. Direct hospital access was warranted to 93.5% of cases, a further 6% was accepted after medical evaluation, whereas 0.5% was refused at admission. Conclusion: A self-report questionnaire has a low positive predictive value to triage patients with cancer and suspected severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) symptoms. Differential diagnosis with tumor- or treatment-related symptoms is always required to avoid unnecessary treatment delays. Body temperature measurement improves the triage process's overall sensitivity, and widespread SARS-CoV-2 testing should be implemented to identify asymptomatic carriers. Implications for Practice: This is the first study to provide data on the predictive performance of a triage system in the oncological setting during the coronavirus disease outbreak. A questionnaire-based triage has a low positive predictive value to triage patients with cancer and suspected severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) symptoms, and a differential diagnosis with tumor- or treatment-related symptoms is mandatory to avoid unnecessary treatment delays. Consequently, adequate recourses should be reallocated for a triage implementation in the oncological setting. Of note, body temperature measurement improves the overall sensitivity of the triage process, and widespread testing for SARS-CoV-2 infection should be implemented to identify asymptomatic carriers

Neutrophil-to-lymphocyte and lymphocyte-to-monocyte ratios in breast cancer

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593pthe seneca study prognostic role of serum biomarkers in elderly metastatic colorectal cancer patients

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