Measuring Instantaneous Frequency of Local Field Potential Oscillations using the Kalman Smoother

Rhythmic local field potentials (LFPs) arise from coordinated neural activity. Inference of neural function based on the properties of brain rhythms remains a challenging data analysis problem. Algorithms that characterize non-stationary rhythms with high temporal and spectral resolution may be useful for interpreting LFP activity on the timescales in which they are generated. We propose a Kalman smoother based dynamic autoregressive model for tracking the instantaneous frequency (iFreq) and frequency modulation (FM) of noisy and non-stationary sinusoids such as those found in LFP data. We verify the performance of our algorithm using simulated data with broad spectral content, and demonstrate its application using real data recorded from behavioral learning experiments. In analyses of ripple oscillations (100–250 Hz) recorded from the rodent hippocampus, our algorithm identified novel repetitive, short timescale frequency dynamics. Our results suggest that iFreq and FM may be useful measures for the quantification of small timescale LFP dynamics.National Institutes of Health (U.S.) (NIH/NIMH R01 MH59733)National Institutes of Health (U.S.) (NIH/NIHLB R01 HL084502)Massachusetts Institute of Technology (Henry E. Singleton Presidential Graduate Fellowship Award

Contributions to statistical analysis methods for neural spiking activity

With the technical advances in neuroscience experiments in the past few decades, we have seen a massive expansion in our ability to record neural activity. These advances enable neuroscientists to analyze more complex neural coding and communication properties, and at the same time, raise new challenges for analyzing neural spiking data, which keeps growing in scale, dimension, and complexity. This thesis proposes several new statistical methods that advance statistical analysis approaches for neural spiking data, including sequential Monte Carlo (SMC) methods for efficient estimation of neural dynamics from membrane potential threshold crossings, state-space models using multimodal observation processes, and goodness-of-fit analysis methods for neural marked point process models. In a first project, we derive a set of iterative formulas that enable us to simulate trajectories from stochastic, dynamic neural spiking models that are consistent with a set of spike time observations. We develop a SMC method to simultaneously estimate the parameters of the model and the unobserved dynamic variables from spike train data. We investigate the performance of this approach on a leaky integrate-and-fire model. In another project, we define a semi-latent state-space model to estimate information related to the phenomenon of hippocampal replay. Replay is a recently discovered phenomenon where patterns of hippocampal spiking activity that typically occur during exploration of an environment are reactivated when an animal is at rest. This reactivation is accompanied by high frequency oscillations in hippocampal local field potentials. However, methods to define replay mathematically remain undeveloped. In this project, we construct a novel state-space model that enables us to identify whether replay is occurring, and if so to estimate the movement trajectories consistent with the observed neural activity, and to categorize the content of each event. The state-space model integrates information from the spiking activity from the hippocampal population, the rhythms in the local field potential, and the rat's movement behavior. Finally, we develop a new, general time-rescaling theorem for marked point processes, and use this to develop a general goodness-of-fit framework for neural population spiking models. We investigate this approach through simulation and a real data application

A fully Bayesian approach to financial forecasting and portfolio selection

PhD ThesisThe movements of share prices has long been of interest to both academic researchers as well as market practitioners. The statistical research in this field dates back to the work of Bachelier (1900) and there have been many approaches adopted subsequently. This thesis considers a Bayesian approach to multivariate forecasting of financial time series based on dynamic linear models. We will also consider the forecasting of the returns distribution using stochastic volatility models. We will then look at combining these two model structures. We will also demonstrate how the posterior forecast distribution can be simulated and how this may be used directly in order to implement a fully Bayesian decision theoretic approach to selection of optimal stock portfolios. These methods are first illustrated on simulated data and then applied to real data for selected shares from the Standard and Poor 500.University of Newcastle upon Tyne

Experimental evaluation of confidence interval procedures in sequential steady-state simulation

Sequential analysis of simulation output is generally accepted as the most efficient way for securing representativeness of samples of collected observations. In this scenario a simulation experiment is stopped when the relative precision of estimates, defined as the relative width of confidence intervals at an assumed confidence level, reaches the required level. This paper deals with the statistical correctness of the methods proposed for estimating confidence intervals for mean values in sequential steady-state stochastic simulation. We formulate basic rules that should be followed in proper experimental analysis of coverage of different steadystate interval estimators. Our main argument is that such analysis should be done sequentially. The numerical results of our preliminary coverage analysis of the method of Spectral Analysis (SA/HW) and Nonoverlapping Batch Means are presented, and compared with those obtained by traditional, non-sequential approaches

Linear State Models for Volatility Estimation and Prediction

This report covers the important topic of stochastic volatility modelling with an emphasis on linear state models. The approach taken focuses on comparing models based on their ability to fit the data and their forecasting performance. To this end several parsimonious stochastic volatility models are estimated using realised volatility, a volatility proxy from high frequency stock price data. The results indicate that a hidden state space model performs the best among the realised volatility-based models under consideration. For the state space model different sampling intervals are compared based on in-sample prediction performance. The comparisons are partly based on the multi-period prediction results that are derived in this report

Automatic outlier detection in automated water quality measurement stations

Des stations de mesure de la qualité de l’eau sont utilisées pour mesurer la qualité de l'eau à haute fréquence. Pour une gestion efficace de ces mesures, la qualité des données doit être vérifiée. Dans une méthode univariée précédemment développée, des points aberrants et des fautes étaient détectés dans les données mesurées par ces stations en employant des modèles à lissage exponentiel pour prédire les données au moment suivant avec l’intervalle de confiance. Dans la présente étude, ne considérant que le cas univarié, la détection de points aberrants est améliorée par l’identification d’un modèle autorégressif à moyenne mobile sur une fenêtre mobile de données pour prédire la donnée au moment suivant. Les données de turbidité mesurées à l'entrée d'une station d'épuration municipale au Danemark sont utilisées comme étude de cas pour comparer la performance de l’utilisation des deux modèles. Les résultats montrent que le nouveau modèle permet de prédire la donnée au moment suivant avec plus de précision. De plus, l’inclusion du nouveau modèle dans la méthode univariée présente une performance satisfaisante pour la détection de points aberrants et des fautes dans les données de l'étude de cas.Water quality monitoring stations are used to measure water quality at high frequency. For effective data management, the quality of the data must be evaluated. In a previously developed univariate method both outliers and faults were detected in the data measured by these stations by using exponential smoothing models that give one-step ahead forecasts and their confidence intervals. In the present study, the outlier detection step of the univariate method is improved by identifying an auto-regressive moving average model for a moving window of data and forecasting one-step ahead. The turbidity data measured at the inlet of a municipal treatment plant in Denmark is used as case study to compare the performance of the use of the two models. The results show that the forecasts made by the new model are more accurate. Also, inclusion of the new forecasting model in the univariate method shows satisfactory performance for detecting outliers and faults in the case study data