Probability of informed trading and volatility for an ETF

We use the new procedure developed by Easley et al. to estimate the Probability of Informed Trading (PIN), based on the volume imbalance: Volume-Synchronized Probability of Informed Trading (VPIN). Unlike the previous method, this one does not require the use of numerical methods to estimate unobservable parameters. We also relate the VPIN metric to volatility measures. However, we use most efficient estimators of volatility which consider the number of jumps. Moreover, we add the VPIN to a Heterogeneous Autoregressive model of Realized Volatility to further investigate its relation with volatility. For the empirical analysis we use data on the exchange traded fund (SPY)

Efficient posterior sampling for high-dimensional imbalanced logistic regression

High-dimensional data are routinely collected in many areas. We are particularly interested in Bayesian classification models in which one or more variables are imbalanced. Current Markov chain Monte Carlo algorithms for posterior computation are inefficient as $n$ and/or $p$ increase due to worsening time per step and mixing rates. One strategy is to use a gradient-based sampler to improve mixing while using data sub-samples to reduce per-step computational complexity. However, usual sub-sampling breaks down when applied to imbalanced data. Instead, we generalize piece-wise deterministic Markov chain Monte Carlo algorithms to include importance-weighted and mini-batch sub-sampling. These approaches maintain the correct stationary distribution with arbitrarily small sub-samples, and substantially outperform current competitors. We provide theoretical support and illustrate gains in simulated and real data applications.Comment: 4 figure

Estimation and prediction of road traffic flow using particle filter for real-time traffic control

Real-data testing results of a real-time state estimator and predictor are presented with particular focus on the feature of enabling of detector fault alarms and also its relation to queue-length based traffic control. A parameter and state estimator/predictor is developed by using particle filter. The simulation testing results are quite satisfactory and promising for further work on developing a hybrid model of traffic flow that captures the transition between low and high intensity. By using this hybrid model, it may be more feasible to achieve the significant feature of automatic adaptation to changing system condition

Efficient estimation of blocking probabilities in non-stationary loss networks

This paper considers estimation of blocking probabilities in a nonstationary loss network. Invoking the so called MOL (Modified Offered Load) approximation, the problem is transformed into one requiring the solution of blocking probabilities in a sequence of stationary loss networks with time varying loads. To estimate the blocking probabilities Monte Carlo simulation is used and to increase the efficiency of the simulation, we develop a likelihood ratio method that enables samples drawn at a one time point to be used at later time points. This reduces the need to draw new samples every time independently as a new time point is considered, thus giving substantial savings in the computational effort of evaluating time dependent blocking probabilities. The accuracy of the method is analyzed by using Taylor series approximations of the variance indicating the direct dependence of the accuracy on the rate of change of the actual load. Finally, three practical applications of the method are provided along with numerical examples to demonstrate the efficiency of the method

Multiscale autocorrelation function: a new approach to anisotropy studies

We present a novel catalog-independent method, based on a scale dependent approach, to detect anisotropy signatures in the arrival direction distribution of the ultra highest energy cosmic rays (UHECR). The method provides a good discrimination power for both large and small data sets, even in presence of strong contaminating isotropic background. We present some applications to simulated data sets of events corresponding to plausible scenarios for charged particles detected by world-wide surface detector-based observatories, in the last decades.Comment: 18 pages, 9 figure

Sampling and Inference for Beta Neutral-to-the-Left Models of Sparse Networks

Empirical evidence suggests that heavy-tailed degree distributions occurring in many real networks are well-approximated by power laws with exponents $\eta$ that may take values either less than and greater than two. Models based on various forms of exchangeability are able to capture power laws with $\eta < 2$, and admit tractable inference algorithms; we draw on previous results to show that $\eta > 2$ cannot be generated by the forms of exchangeability used in existing random graph models. Preferential attachment models generate power law exponents greater than two, but have been of limited use as statistical models due to the inherent difficulty of performing inference in non-exchangeable models. Motivated by this gap, we design and implement inference algorithms for a recently proposed class of models that generates $\eta$ of all possible values. We show that although they are not exchangeable, these models have probabilistic structure amenable to inference. Our methods make a large class of previously intractable models useful for statistical inference.Comment: Accepted for publication in the proceedings of Conference on Uncertainty in Artificial Intelligence (UAI) 201

Sequential Bayesian inference for implicit hidden Markov models and current limitations

Hidden Markov models can describe time series arising in various fields of science, by treating the data as noisy measurements of an arbitrarily complex Markov process. Sequential Monte Carlo (SMC) methods have become standard tools to estimate the hidden Markov process given the observations and a fixed parameter value. We review some of the recent developments allowing the inclusion of parameter uncertainty as well as model uncertainty. The shortcomings of the currently available methodology are emphasised from an algorithmic complexity perspective. The statistical objects of interest for time series analysis are illustrated on a toy "Lotka-Volterra" model used in population ecology. Some open challenges are discussed regarding the scalability of the reviewed methodology to longer time series, higher-dimensional state spaces and more flexible models.Comment: Review article written for ESAIM: proceedings and surveys. 25 pages, 10 figure