A New MCMC Sampling Based Segment Model for Radar Target Recognition

One of the main tools in radar target recognition is high resolution range profile (HRRP)‎. ‎However‎, ‎it is very sensitive to the aspect angle‎. ‎One solution to this problem is to assume the consecutive samples of HRRP identically independently distributed (IID) in small frames of aspect angles‎, ‎an assumption which is not true in reality‎. ‎However, b‎‎ased on this assumption‎, ‎some models have been developed to characterize the sequential information contained in the multi-aspect radar echoes‎. ‎Therefore‎, ‎they only consider the short dependency between consecutive samples‎. ‎Here‎, ‎we propose an alternative model‎, ‎the segment model‎, ‎to address the shortcomings of these assumptions‎. ‎In addition‎, ‎using a Markov chain Monte-Carlo (MCMC) based Gibbs sampler as an iterative approach to estimate the parameters of the segment model‎, ‎we will show that the proposed method is able to estimate the parameters with quite satisfying accuracy and computational load‎

A Bayesian approach for inferring neuronal connectivity from calcium fluorescent imaging data

Deducing the structure of neural circuits is one of the central problems of modern neuroscience. Recently-introduced calcium fluorescent imaging methods permit experimentalists to observe network activity in large populations of neurons, but these techniques provide only indirect observations of neural spike trains, with limited time resolution and signal quality. In this work we present a Bayesian approach for inferring neural circuitry given this type of imaging data. We model the network activity in terms of a collection of coupled hidden Markov chains, with each chain corresponding to a single neuron in the network and the coupling between the chains reflecting the network's connectivity matrix. We derive a Monte Carlo Expectation--Maximization algorithm for fitting the model parameters; to obtain the sufficient statistics in a computationally-efficient manner, we introduce a specialized blockwise-Gibbs algorithm for sampling from the joint activity of all observed neurons given the observed fluorescence data. We perform large-scale simulations of randomly connected neuronal networks with biophysically realistic parameters and find that the proposed methods can accurately infer the connectivity in these networks given reasonable experimental and computational constraints. In addition, the estimation accuracy may be improved significantly by incorporating prior knowledge about the sparseness of connectivity in the network, via standard L$_1$ penalization methods.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS303 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Analyzing Single-Molecule Protein Transportation Experiments via Hierarchical Hidden Markov Models

To maintain proper cellular functions, over 50% of proteins encoded in the genome need to be transported to cellular membranes. The molecular mechanism behind such a process, often referred to as protein targeting, is not well understood. Single-molecule experiments are designed to unveil the detailed mechanisms and reveal the functions of different molecular machineries involved in the process. The experimental data consist of hundreds of stochastic time traces from the fluorescence recordings of the experimental system. We introduce a Bayesian hierarchical model on top of hidden Markov models (HMMs) to analyze these data and use the statistical results to answer the biological questions. In addition to resolving the biological puzzles and delineating the regulating roles of different molecular complexes, our statistical results enable us to propose a more detailed mechanism for the late stages of the protein targeting process

Analyzing Single-Molecule Protein Transportation Experiments via Hierarchical Hidden Markov Models

To maintain proper cellular functions, over 50% of proteins encoded in the genome need to be transported to cellular membranes. The molecular mechanism behind such a process, often referred to as protein targeting, is not well understood. Single-molecule experiments are designed to unveil the detailed mechanisms and reveal the functions of different molecular machineries involved in the process. The experimental data consist of hundreds of stochastic time traces from the fluorescence recordings of the experimental system. We introduce a Bayesian hierarchical model on top of hidden Markov models (HMMs) to analyze these data and use the statistical results to answer the biological questions. In addition to resolving the biological puzzles and delineating the regulating roles of different molecular complexes, our statistical results enable us to propose a more detailed mechanism for the late stages of the protein targeting process

Discrete- and Continuous-Time Probabilistic Models and Algorithms for Inferring Neuronal UP and DOWN States

UP and DOWN states, the periodic fluctuations between increased and decreased spiking activity of a neuronal population, are a fundamental feature of cortical circuits. Understanding UP-DOWN state dynamics is important for understanding how these circuits represent and transmit information in the brain. To date, limited work has been done on characterizing the stochastic properties of UP-DOWN state dynamics. We present a set of Markov and semi-Markov discrete- and continuous-time probability models for estimating UP and DOWN states from multiunit neural spiking activity. We model multiunit neural spiking activity as a stochastic point process, modulated by the hidden (UP and DOWN) states and the ensemble spiking history. We estimate jointly the hidden states and the model parameters by maximum likelihood using an expectation-maximization (EM) algorithm and a Monte Carlo EM algorithm that uses reversible-jump Markov chain Monte Carlo sampling in the E-step. We apply our models and algorithms in the analysis of both simulated multiunit spiking activity and actual multi- unit spiking activity recorded from primary somatosensory cortex in a behaving rat during slow-wave sleep. Our approach provides a statistical characterization of UP-DOWN state dynamics that can serve as a basis for verifying and refining mechanistic descriptions of this process.National Institutes of Health (U.S.) (Grant R01-DA015644)National Institutes of Health (U.S.) (Director Pioneer Award DP1- OD003646)National Institutes of Health (U.S.) (NIH/NHLBI grant R01-HL084502)National Institutes of Health (U.S.) (NIH institutional NRSA grant T32 HL07901

Latent variable models for understanding user behavior in software applications

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018.Cataloged from PDF version of thesis.Includes bibliographical references (pages 147-157).Understanding user behavior in software applications is of significant interest to software developers and companies. By having a better understanding of the user needs and usage patterns, the developers can design a more efficient workflow, add new features, or even automate the user's workflow. In this thesis, I propose novel latent variable models to understand, predict and eventually automate the user interaction with a software application. I start by analyzing users' clicks using time series models; I introduce models and inference algorithms for time series segmentation which are scalable to large-scale user datasets. Next, using a conditional variational autoencoder and some related models, I introduce a framework for automating the user interaction with a software application. I focus on photo enhancement applications, but this framework can be applied to any domain where segmentation, prediction and personalization is valuable. Finally, by combining sequential Monte Carlo and variational inference, I propose a new inference scheme which has better convergence properties than other reasonable baselines.by Ardavan Saeedi.Ph. D

Sequential Bayesian learning for State Space Models

This thesis explores the topic of sequential inference on a variety of novel model classes. Chapter 2 focuses on a class of discrete State Space Models (SSM) known as Hidden Semi-Markov Model (HSMM), a versatile generalization of the famous Hidden Markov Model (HMM) in which the underlying stochastic process follows a semi-Markov chain. In a case study on the VIX Index, efficient batch as well as sequential Bayesian parameter estimation schemes are contributed and validated. We benchmark HSMMs against popular discrete SSM alternatives and show how by-products that arise during the estimation process can be used for model selection and clustering. Chapter 3 centers on a new class of Susceptible-Exposed-Infected-Recovered (SEIR) type models to analyze and detect regime switches in the SARS-CoV-2 pandemic. We propose an epidemic model with the transmission rate between susceptible and infected individuals being time varying and piecewise constant. At any point in time, this parameter is linked to a latent variable that follows a HSMM. We define this model in state space formulation and demonstrate the latent states can be efficiently estimated using the Particle MCMC (PMCMC) and Sequential Monte Carlo Squared (SMC2) machinery. Moreover, a case study is conducted on the reported infection and fatalities data in the United Kingdom, during which we benchmark models with varying observation distribution specifications and determine the number of latent regimes in the data. Chapter 4 addresses Stochastic Volatility (SV) models and employs a variety of carefully selected copulas to explore the dependency structure between stocks and their volatility. This new class of models can reconstruct stylised empirical behaviours that cannot be captured by standard symmetric Gaussian innovations. In a case study on the S&P 500 and the VIX index, we examine the marginal distributions and joint dependency structure of the error terms in our proposed model. Moreover, batch and sequential Bayesian model selection are applied to analyze the suitability of the separate copula choices against standard modelling techniques

MCMC implementation for Bayesian hidden semi-Markov models with illustrative applications

Copyright © Springer 2013. The final publication is available at Springer via http://dx.doi.org/10.1007/s11222-013-9399-zHidden Markov models (HMMs) are flexible, well established models useful in a diverse range of applications. However, one potential limitation of such models lies in their inability to explicitly structure the holding times of each hidden state. Hidden semi-Markov models (HSMMs) are more useful in the latter respect as they incorporate additional temporal structure by explicit modelling of the holding times. However, HSMMs have generally received less attention in the literature, mainly due to their intensive computational requirements. Here a Bayesian implementation of HSMMs is presented. Recursive algorithms are proposed in conjunction with Metropolis-Hastings in such a way as to avoid sampling from the distribution of the hidden state sequence in the MCMC sampler. This provides a computationally tractable estimation framework for HSMMs avoiding the limitations associated with the conventional EM algorithm regarding model flexibility. Performance of the proposed implementation is demonstrated through simulation experiments as well as an illustrative application relating to recurrent failures in a network of underground water pipes where random effects are also included into the HSMM to allow for pipe heterogeneity