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Title: MONTE CARLO SIMULATION OF INFINITE-DIMENSIONAL INTEGRALS
Creator: Niu, Ben
Date: 2011-04-13, 2011-05
Description: This thesis is motivated by pricing a path-dependent financial derivative, such as an Asian option, which requires the computation of the...
Show moreThis thesis is motivated by pricing a path-dependent financial derivative, such as an Asian option, which requires the computation of the expectation of a payoff function, which depends on a Brownian motion. Employing a standard series expansion of the Brownian motion, the latter problem is equivalent to the computation of the expectation of a function of the corresponding i.i.d. sequence of random coefficients. This motivates the construction and the analysis of algorithms for numerical integration with respect to a product probability measure on the infinite-dimensional sequence. The class of integrands studied in this thesis resides in the unit ball in a reproducing kernel Hilbert space obtained by superposition of weighted tensor product spaces of functions of finitely many variables. Combining tractability results for high-dimensional integration with the multi-level technique we obtain new algorithms for infinite-dimensional integration. These deterministic multi-level algorithms use variable subspace sampling and they are superior to any deterministic algorithm based on fixed subspace sampling with respect to the respective worst case error. Numerical experiment results are presented at the end.
Ph.D. in Applied Mathematics, May 2011
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Title: A NUMERICAL AND ANALYTICAL STUDY OF THE GROWTH OF SECOND PHASE PARTICLES USING A SHARP INTERFACE APPROACH
Creator: Barua, Amlan K.
Date: 2012-08-15, 2012-12
Description: Two phase alloys are quite important in materials science and metallurgy. Some common examples include nickel-aluminum system, iron-carbon...
Show moreTwo phase alloys are quite important in materials science and metallurgy. Some common examples include nickel-aluminum system, iron-carbon system etc. The most important macroscopic properties of these alloys depend on size, orientation and concentration of the second-phase precipitates. It is necessary to understand the details of formation, growth and equilibrium conditions of these micro-structures for better material production. In this dissertation we investigate the growth of the precipitates within the matrix using a sharp interface approach. We consider the effects of elastic fields on the evolution of the precipitates. The elastic fields can either be applied at the far field or can simply arise as a result of crystallographic difference between matrix and precipitate phase. The precipitates exhibit complicated morphology because of the Mullins-Sekerka instability. Our investigation is based on both analytical and numerical techniques. We use linear analysis to understand the qualitative behavior of the problem, at least for short time. To simulate the long time dynamics of the problem and to understand the effects of nonlinearity, we use highly accurate boundary integral methods. Our main contribution in this thesis is threefold. First, starting from linear analysis, we focus on the conditions under which stable growth, in presence of elastic field, is possible for a single precipitate. Finding such conditions are important in material production and simple conditions like constant material flux and constant elastic fields produce precipitates with complicated shapes. Second, we propose a space-time rescaling of the original boundary integral equations of the problem. The rescaling enables us to accurately simulate very long time behavior of the system comprising of multiple precipitates growing under different mass flux and elasticity. It also helps us to understand the long time interaction of precipitates. Third, we xiii implement an adaptive treecode to reduce the computational complexity of the iterative solver from O(N2) to O(N logN) where N is the dimension of the discrete problem. The efficiency of the treecode is demonstrated by performing simulations. Also a parallelization strategy for the treecode is discussed. The speed-up from the parallelization is demonstrated using moderate number of cores. xiv
PH.D in Applied Mathematics, December 2012
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Title: RELIABLE QUASI-MONTE CARLO WITH CONTROL VARIATES
Creator: Li, Da
Date: 2016, 2016-07
Description: Recently, Quasi-Monte Carlo (QMC) methods have been implemented in a reliable adaptive algorithm. This raises the possibility of combining...
Show moreRecently, Quasi-Monte Carlo (QMC) methods have been implemented in a reliable adaptive algorithm. This raises the possibility of combining adaptive QMC with efficiency improvement techniques for independent and identically distributed (IID) Monte Carlo (MC) such as control variates (CV). The challenge for adding CV to QMC is that the optimal CV coefficient for QMC is generally not the same as that for MC. Here we propose a method for imple- menting CV in a reliable adaptive QMC algorithm. One merit of using CV with MC is that theoretically the efficiency is always no worse than vanilla MC. Our method is implemented in an efficient way so that the extra cost for CV is tolerable, and the overall time savings can be substantial. We test our algorithm on various problems including option pricing and mul- tivariate normal probability estimation for dimensions from 4 to 64. The same tests are performed on adaptive QMC algorithm without CV as a comparison. Our results show that with good CV, the cost of adaptive QMC is greatly reduced compared to vanilla QMC.
M.S. in Applied Mathematics, July 2016
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Title: A Dynamic Model of Central Counterparty Risk and Liquidity Risk Measures
Creator: Feng, Shibi
Date: 2019
Description: The thesis consists of two major parts, and it contributes to two topics in risk models - a dynamic model of central counterparty risk and...
Show moreThe thesis consists of two major parts, and it contributes to two topics in risk models - a dynamic model of central counterparty risk and liquidity risk measures.Chapter 2 is devoted to the first part of the thesis, where we propose a dynamic model of central counterparty risk by introducing a dynamic model of the default waterfall of derivatives Central Counterparties (CCPs) and by designing a risk sensitive method for sizing the initial margin (IM), and the default fund (DF) and its allocation among clearing members. Using a Markovian structure model of joint credit migrations, our evaluation of DF takes into account the joint credit quality of clearing members as they evolve over time. Another important aspect of the proposed methodology is the use of the time consistent dynamic risk measures for computation of IM and DF. We carry out a comprehensive numerical study, where, in particular, we analyze the advantages of the proposed methodology and its comparison with the currently prevailing methods used in industry. The second part of the thesis is divided into four chapters, and the primary goal of this part is to develop a general framework for liquidity risk management in an order driven market. Chapter 3 describes the essential elements of an order driven market and introduces the notions that are of critical financial meaning, for instance, trading strategy and its corresponding value process. Moreover, we propose a model for the dynamics of the limit order book by using marked point process. Chapter 4 is devoted to the identification and measurement of liquidity risk. We describe the importance of demand for liquidity in measuring liquidity risk and we introduce the concept of liquidity provision. By considering a trader who is subject to liquidity provision only, we demonstrate that liquidity provision impacts the valuation of the portfolio through the trading costs of the foreseen transactions. Then, we propose two portfolio liquidity risk measures to account for the liquidity risk introduced by the liquidity provision. Besides measuring the liquidity risk of a portfolio, we also design a method to measure the liquidity provision adjusted risk for any contingent claim in the financial market established in Chapter 3. Chapter 5 attends to the hedging problem under liquidity provision. We prove the existence of an optimal hedging strategy in terms of minimizing the hedging error under liquidity provision. We demonstrate that the optimal hedging strategy can be solved in terms of associated Bellman equations.
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Title: A BOUNDARY INTEGRAL METHOD FOR COMPUTING THE FORCES OF MOVING BEADS IN A THREE-DIMENSIONAL LINEAR VISCOELASTIC FLOW
Creator: Hernandez, Francisco
Date: 2019
Description: Computing the forces acting on particles in fluids is fundamental to understanding particle dynamics and interactions. In this thesis, we...
Show moreComputing the forces acting on particles in fluids is fundamental to understanding particle dynamics and interactions. In this thesis, we study the dynamics of a two-particle system in a three-dimensional linear viscoelastic flow. Using a correspondence principle between unsteady Stokes flow and viscoelastic flow, we reformulate the problem and derive a boundary integral formulation that solves the Brinkman’s equation in the Fourier domain. We show that computational costs can be reduced by carefully eliminating the double-layer potential, and that a unique solution can be obtained by desingularizing the equation. We develop a highly accurate numerical integration scheme to evaluate the resulting boundary integrals. We solve the backward problem by making use of our numerical integration scheme, variable transformations, generalized minimum residual (GMRES) method, and spherical harmonic interpolations. In particular, spherical harmonic interpolations ensure that this numerical scheme is of high accuracy. Our method also has the advantage of working for both unsteady Stokes and linear viscoelastic flow by appropriately adjusting the oscillation frequency. Our numerical results are in agreement with the exact solution for a single-particle system, as well as the asymptotic solution for large particle separation in the two-particle system. Last, we analyze the numerical results for high oscillation frequencies and small particle separation. Our numerical method is shown to only depend on the frequency parameter and the distance between the particles. We find that for high frequencies, the forces on the particles behave differently for unsteady Stokes and linear viscoelastic flows.
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Title: GUARANTEED, ADAPTIVE, AUTOMATIC ALGORITHMS FOR UNIVARIATE INTEGRATION: METHODS, COSTS AND IMPLEMENTATIONS
Creator: Zhang, Yizhi
Date: 2018
Description: This thesis investigates how to solve univariate integration problems using numerical methods, including the trapezoidal rule and the Simpson...
Show moreThis thesis investigates how to solve univariate integration problems using numerical methods, including the trapezoidal rule and the Simpson's rule. Most existing guaranteed algorithms are not adaptive and require too much a priori information. Most existing adaptive algorithms do not have valid justification for their results. The goal is to create adaptive algorithms utilizing the two above-mentioned methods with guarantees. The classes of integrands studied in this thesis are cones. The algorithms are analytically proved to be a success if the integrand lies in the cone. The algorithms are adaptive and automatically adjust the computational costs based on the integrand values. The lower and upper bounds on the computational costs for both algorithms are derived. The lower bounds on the complexity of the problems are derived as well. By comparing the upper bounds on the computational cost and the lower bounds on the complexity, our algorithms are shown to be asymptotically optimal. Numerical experiments are implemented.
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Title: Statistical Experimental Design and Modeling for Complex Data
Creator: Huang, Xiao
Date: 2018
Description: The ability to handle complex data is essential for new research findings and business success today. With increased complexity, data can...
Show moreThe ability to handle complex data is essential for new research findings and business success today. With increased complexity, data can either be difficult to collect with designed experiments or be difficult to analyze with statistical models. Both kinds of difficulties are addressed in this dissertation.The first part of this dissertation (Chapter 2 and 3) addresses the issue of complex data collection by considering two design of experiment problems. In chapter 2, we consider Bayesian A-optimal design problem under a hierarchical probabilistic model involving both quantitative and qualitative response variables. The objective function was derived and an efficient optimization algorithm was developed. In chapter 3, we consider the A/B-testing problem and propose a novel discrepancy-based approach for designing such an experiment. As the numerical examples show, the A/B-testing experiments designed in this way achieve better group balance and parametric estimation results.In the second part of this dissertation (Chapter 4 and 5), we focus on analyzing complex data with Gaussian process (GP) models. Gaussian process model is widely used for analyzing data with highly nonlinear relationships and emulating complex systems. In Chapter 4, we apply and extend GP model to analyze the in-cylinder pressure data resulted from experiments on a newly-developed dual fuel engine. The resulted model incorporates different data types and achieves good prediction accuracy. In Chapter 5, a generalized functional ANOVA GP model is proposed to tackle the difficulty resulted from high-dimensional feature space, and we develop an efficient algorithm for building such a model from the perspective of multiple kernel learning. The proposed approach outperforms traditional MLE-based GP models on both computational efficiency and prediction accuracy.
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Title: Gaussian Process Assisted Active Learning of Physical Laws
Creator: Chen, Jiuhai
Date: 2020
Description: In many areas of science and engineering, discovering the governing differential equations from the noisy experimental data is an essential...
Show moreIn many areas of science and engineering, discovering the governing differential equations from the noisy experimental data is an essential challenge. It is also a critical step in understanding the physical phenomena and prediction of the future behaviors of the systems. However, in many cases, it is expensive or time-consuming to collect experimental data. This article provides an active learning approach to estimate the unknown differential equations accurately with reduced experimental data size. We propose an adaptive design criterion combining the D-optimality and the maximin space-filling criterion. The D-optimality involves the unknown solution of the differential equations and derivatives of the solution. Gaussian process models are estimated using the available experimental data and used as surrogates of these unknown solution functions. The derivatives of the estimated Gaussian process models are derived and used to substitute the derivatives of the solution. Variable-selection-based regression methods are used to learn the differential equations from the experimental data. The proposed active learning approach is entirely data-driven and requires no tuning parameters. Through three case studies, we demonstrate the proposed approach outperforms the standard randomized design in terms of model accuracy and data economy.
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Title: Learning Stochastic Governing Laws from Noisy Data Using Normalizing Flows
Creator: McClure, William Jacob
Date: 2021
Description: With the increasing availability of massive collections of data, researchers in all sciences need tools to synthesize useful and pertinent...
Show moreWith the increasing availability of massive collections of data, researchers in all sciences need tools to synthesize useful and pertinent descriptors of the systems they study. Perhaps the most fundamental knowledge of a dynamical system is its governing laws, which describe its evolution through time and can be lever-aged for a number of analyses about its behavior. We present a novel technique for learning the infinitesimal generator of a Markovian stochastic process from large, noisy datasets generated by a stochastic system. Knowledge of the generator in turn allows us to find the governing laws for the process. This technique relies on normalizing flows, neural networks that estimate probability densities, to learn the density of time-dependent stochastic processes. We establish the efficacy of this technique on multiple systems with Brownian noise, and use our learned governing laws to perform analysis on one system by solving for its mean exit time. Our approach also allows us to learn other dynamical behaviors such as escape probability and most probable pathways in a system. The potential impact of this technique is far-reaching, since most stochastic processes in various fields are assumed to be Markovian, and the only restriction for applying our method is available data from a time near the beginning of an experiment or recording.
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Title: WIENER-HOPF FACTORIZATION FOR TIME-INHOMOGENEOUS MARKOV CHAINS AND BAYESIAN ESTIMATIONS FOR DIAGONALIZABLE BILINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
Creator: Cheng, Ziteng
Date: 2021
Description: This thesis consists of two major parts, and contributes to two areas of research in stochastic analysis: (i) Wiener-Hopf factorization (WHf)...
Show moreThis thesis consists of two major parts, and contributes to two areas of research in stochastic analysis: (i) Wiener-Hopf factorization (WHf) for Markov Chains, (ii) statistical inference for Stochastic Partial Differential Equations (SPDEs).WHf for Markov chains is a methodology concerned with computation of expectation of some types of functionals of the underlying Markov chain. Most results in WHf for Markov chains are done in the framework of time-homogeneous Markov chains. The major contribution of this thesis in the area of WHf for Markov chains are: • We extend the classical theory to the framework of time-inhomogeneous Markov chains. • In particular, we establish the existence and uniqueness of solutions for a new class of operator Riccati equations. • We connect the solution of the Riccati equation to some expectations of interest related to a time-inhomogeneous Markov chain. Statistical inference for SPDEs regards estimating parameters of a SPDE based on available and relevant observations of the underlying phenomenon that is modeled by the given SPDE. We summarize the contribution of this thesis in the area statistical inference for SPDEs as follows: • We conduct the statistical inference for a diagonalizable SPDE driven by a multiplicative noise of special structure, using spectral approach. We show that the corresponding statistical model fits the classical uniform asymptotic normality (UAN) paradigm. • We prove a Bernstein-Von Mises type result that strengthens the existing results in the literature. • We prove the asymptotic consistency, asymptotic normality and asymptotic efficiency of two Bayesian type estimators.
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Title: Binary hidden Markov models and varieties, AS2012 Special Volume, part 2: This issue includes a second series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics in the Alleghenies Conference at Penn State, which took place in July 2012.
Creator: Critch, Andrew
Date: 2013, 2013
Description: This paper closely examines HMMs in which all the hidden random variables are...
Show moreThis paper closely examines HMMs in which all the hidden random variables are binary. Its main contributions are (1) a birational parametrization for every such HMM, with an explicit inverse for recovering the hidden parameters in terms of observables, (2) a semialgebraic model membership test for every such HMM, and (3) minimal dening equations for the 4-node fully binary model, comprising 21 quadrics and 29 cubics, which were computed using Grobner bases in the cumulant coordinates of Sturmfels and Zwiernik. The new model parameters in (1) are rationally identiable in the sense of Sullivant, Garcia-Puente, and Spielvogel, and each model's Zariski closure is therefore a rational projective variety of dimension 5. Grobner basis computations for the model and its graph are found to be considerably faster using these parameters. In the case of two hidden states, item (2) supersedes a previous algorithm of Schonhuth which is only generically dened, and the dening equations (3) yield new invariants for HMMs of all lengths 4. Such invariants have been used successfully in model selection problems in phylogenetics, and one can hope for similar applications in the case of HMMs.
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Collection: Journal of Algebraic Statistics

Title: On Polyhedral Approximations of Polytopes for Learning Bayesian Networks, AS2012 Special Volume, part 2: This issue includes a second series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics in the Alleghenies Conference at Penn State, which took place in July 2012.
Creator: Studeny, Milan, Haws, David C.
Date: 2013, 2013
Description: The motivation for this paper is the geometric approach to statistical learning Bayesiannetwork (BN) structures. We review three vector...
Show moreThe motivation for this paper is the geometric approach to statistical learning Bayesiannetwork (BN) structures. We review three vector encodings of BN structures. The first one has been used by Jaakkola et al. [9] and also by Cussens [4], the other two use special integral vectors formerly introduced, called imsets [18, 20]. The topic is the comparison of outer polyhedral approximations of the corresponding polytopes. We show how to transform the inequalities suggested by Jaakkola et al. [9] into the framework of imsets. The result of our comparison is the observation that the implicit polyhedral approximation of the standard imset polytope suggested in [21] gives a tighter approximation than the (transformed) explicit polyhedral approximation from [9]. As a consequence, we confirm a conjecture from [21] that the above-mentioned implicit polyhedral approximation of the standard imset polytope is an LP relaxation of that polytope. In the end, we review recent attempts to apply the methods of integer programming to learning BN structures and discuss the task of finding suitable explicit LP relaxation in the imset-based approach.
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Collection: Journal of Algebraic Statistics

Title: Learning Coefficient in Bayesian Estimation of Restricted Boltzmann Machine, AS2012 Special Volume, part 2: This issue includes a second series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics in the Alleghenies Conference at Penn State, which took place in July 2012.
Creator: Aoyagi, Miki
Date: 2013, 2013
Description: We consider the real log canonical threshold for the learning model in Bayesian estimation. This threshold corresponds to a learning...
Show moreWe consider the real log canonical threshold for the learning model in Bayesian estimation. This threshold corresponds to a learning coefficient of generalization error in Bayesian estimation, which serves to measure learning efficiency in hierarchical learning models [30, 31, 33]. In this paper, we clarify the ideal which gives the log canonical threshold of the restricted Boltzmann machine and consider the learning coefficients of this model.
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Collection: Journal of Algebraic Statistics

Title: Phylogenetic invariants for group-based models, AS2012 Special Volume, part 1: This issue includes a second series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics in the Alleghenies Conference at Penn State, which took place in July 2012.
Creator: Donten-Bury, Maria, Michalek, Mateusz
Date: 2012, 2012
Description: In this paper we investigate properties of algebraic varieties representing group-based phylogenetic models. We propose a method of generating...
Show moreIn this paper we investigate properties of algebraic varieties representing group-based phylogenetic models. We propose a method of generating many phylogenetic invariants. We prove that we obtain all invariants for any tree for the two-state Jukes-Cantor model. We conjecture that for a large class of models our method can give all phylogenetic invariants for any tree. We show that for 3-Kimura our conjecture is equivalent to the conjecture of Sturmfels and Sullivant [22, Conjecture 2]. This, combined with the results in [22], would make it possible to determine all phylogenetic invariants for any tree for 3-Kimura model, and also other phylogenetic models. Next we give the (first) examples of non-normal varieties associated to general group-based model for an abelian group. Following Kubjas [17] we prove that for many group-based models varieties associated to trees with the same number of leaves do not have to be deformation equivalent.
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Collection: Journal of Algebraic Statistics

Title: Properties of semi-elementary imsets as sums of elementary imsets
Creator: Kashimura, Takuya, Sei, Tomonari, Takemura, Akimichi, Tanaka, Kentaro
Date: 2011, 2011
Description: We study properties of semi-elementary imsets and elementary imsets introduced by Studeny [10]. The rules of the semi-graphoid axiom ...
Show moreWe study properties of semi-elementary imsets and elementary imsets introduced by Studeny [10]. The rules of the semi-graphoid axiom (decomposition, weak union and contraction) for conditional independence statements can be translated into a simple identity among three semi-elementary imsets. By recursively applying the identity, any semi-elementary imset can be written as a sum of elementary imsets, which we call a representation of the semi-elementary imset. A semi-elementary imset has many representations. We study properties of the set of possible representations of a semi-elementary imset and prove that all representations are connected by relations among four elementary imsets.
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Collection: Journal of Algebraic Statistics

Title: Higher Connectivity of Fiber Graphs of Gröbner Bases, AS2012 Special Volume, part 2: This issue includes a second series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics in the Alleghenies Conference at Penn State, which took place in July 2012.
Creator: Potka, Samu
Date: 2013, 2013
Description: Fiber graphs of Gröbner bases from contingency tables are important in statistical hypothesis testing, where one studies random walks on these...
Show moreFiber graphs of Gröbner bases from contingency tables are important in statistical hypothesis testing, where one studies random walks on these graphs using the Metropolis-Hastings algorithm. The connectivity of the graphs has implications on how fast the algorithm converges. In this paper, we study a class of ber graphs with elementary combinatorial techniques and provide results that support a recent conjecture of Engström: the connectivity is given by the minimum vertex degree.
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Collection: Journal of Algebraic Statistics

Title: An Iterative Method Converging to a Positive Solution of Certain Systems of Polynomial Equations
Creator: Cartwright, Dustin
Date: 2011, 2011
Description: We present a numerical algorithm for finding real non-negative solutions to a certain class of polynomial equations. Our methods are based on...
Show moreWe present a numerical algorithm for finding real non-negative solutions to a certain class of polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find maximum likelihood parameters for certain classes of statistical models. Since our algorithm works by iteratively improving an approximate solution, we find approximate solutions in the cases when there are no exact solutions, such as overconstrained systems.
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Collection: Journal of Algebraic Statistics

Title: Geometry of Higher-Order Markov Chains, AS2012 Special Volume, part 1: This issue includes a second series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics in the Alleghenies Conference at Penn State, which took place in July 2012.
Creator: Sturmfels, Bernd
Date: 2012, 2012
Description: We determine an explicit Gr ?obner basis, consisting of linear forms and determinantal quadrics, for the prime ideal of Raftery’s mixture...
Show moreWe determine an explicit Gr ?obner basis, consisting of linear forms and determinantal quadrics, for the prime ideal of Raftery’s mixture transition distribution model for Markov chains. When the states are binary, the corresponding projective variety is a linear space, the model itself consists of two simplices in a cross-polytope, and the likelihood function typically has two local maxima. In the general non-binary case, the model corresponds to a cone over a Segre variety.
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Collection: Journal of Algebraic Statistics

Title: Betti Numbers of Cut Ideals of Trees, AS2012 Special Volume, part 2: This issue includes a second series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics in the Alleghenies Conference at Penn State, which took place in July 2012.
Creator: Potka, Samu, Sarmiento, Camilo
Date: 2013, 2013
Description: Cut ideals, introduced by Sturmfels and Sullivant, are used in phylogenetics and algebraic statistics. We study the minimal free resolutions...
Show moreCut ideals, introduced by Sturmfels and Sullivant, are used in phylogenetics and algebraic statistics. We study the minimal free resolutions of cut ideals of tree graphs. By employing basic methods from topological combinatorics, we obtain upper bounds for the Betti numbers of this type of ideals. These take the form of simple formulas on the number of vertices, which arise from the enumeration of induced subgraphs of certain incomparability graphs associated to the edge sets of trees.
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Collection: Journal of Algebraic Statistics

Title: The geometry of Sloppiness
Creator: Dufresne, Emilie, Harrington , Heather A, Raman, Dhruva V
Date: 2018, 2018-09-24
Description: The use of mathematical models in the sciences often requires the estimation of unknown parameter values from data. Sloppiness provides...
Show moreThe use of mathematical models in the sciences often requires the estimation of unknown parameter values from data. Sloppiness provides information about the uncertainty of this task. In this paper, we develop a precise mathematical foundation for sloppiness and define rigorously its key concepts, such as `model manifold', in relation to concepts of structural identifiability. We redefine sloppiness conceptually as a comparison between the premetric on parameter space induced by measurement noise and a reference metric. This opens up the possibility of alternative quantification of sloppiness, beyond the standard use of the Fisher Information Matrix, which assumes that parameter space is equipped with the usual Euclidean and the measurement error is infinitesimal. Applications include parametric statistical models, explicit time dependent models, and ordinary differential equation models.
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Collection: Journal of Algebraic Statistics

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