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Seminar on Probability and Statistics
Seminar information archive ～12/10｜Next seminar｜Future seminars 12/11～
| Organizer(s) | Nakahiro Yoshida, Teppei Ogihara, Yuta Koike |
|---|
Seminar information archive
2023/03/08
14:00- Room # (Graduate School of Math. Sci. Bldg.)
Evgeny Spodarev ( Ulm University, Germany)
Non-ergodic statistics for hamonizable stable processes (English)
https://docs.google.com/forms/d/e/1FAIpQLSet6w12XsqdCGQ8yEe4sOqRlCOhhrJXeKl5H7lMaRy4LZhmqQ/viewform
Evgeny Spodarev ( Ulm University, Germany)
Non-ergodic statistics for hamonizable stable processes (English)
[ Abstract ]
We consider stationary real harmonizable symmetric α-stable processes X={X(t):t∈ℝ} with a finite control measure. Assuming the control measure is symmetric and absolutely continuous with respect to the Lebesgue measure on the real line, we refer to its density function as the spectral density of X. Standard methods for statistical inference on stable processes cannot be applied as harmonizable stable processes are non-ergodic.
A stationary real harmonizable symmetric α-stable process X admits a LePage series representation and is conditionally Gaussian which allows us to derive the non-ergodic limit of sample functions on X. In particular, we give an explicit expression for the non-ergodic limits of the empirical characteristic function of X and the lag process {X(t+h)−X(t):t∈ℝ} with h>0, respectively.
The process admits an equivalent representation as a series of sinusoidal waves with random frequencies whose probability density function is in fact the (normalized) spectral density of X. Using the strongly consistent frequency estimation via periodograms we present a strongly consistent estimator of the spectral density which is based only on one sampled path of X. The periodogram computation is fast and efficient, and our method is not affected by the non-ergodicity of X. Most notably no prior knowledge on parameters of the process such as its index of stability α is needed.
References:
[1] L.V. Hoang, E. Spodarev, "Inversion of alpha-sine and alpha-cosine transforms on R", Inverse Problems 37 (2021), 085008
[2] L.V. Hoang, E. Spodarev, "Non-ergodic statistics and spectral density estimation for stationary real harmonizable symmetric α-stable processes", Preprint arXiv:2209.04315, submitted, 2022.
[ Reference URL ]We consider stationary real harmonizable symmetric α-stable processes X={X(t):t∈ℝ} with a finite control measure. Assuming the control measure is symmetric and absolutely continuous with respect to the Lebesgue measure on the real line, we refer to its density function as the spectral density of X. Standard methods for statistical inference on stable processes cannot be applied as harmonizable stable processes are non-ergodic.
A stationary real harmonizable symmetric α-stable process X admits a LePage series representation and is conditionally Gaussian which allows us to derive the non-ergodic limit of sample functions on X. In particular, we give an explicit expression for the non-ergodic limits of the empirical characteristic function of X and the lag process {X(t+h)−X(t):t∈ℝ} with h>0, respectively.
The process admits an equivalent representation as a series of sinusoidal waves with random frequencies whose probability density function is in fact the (normalized) spectral density of X. Using the strongly consistent frequency estimation via periodograms we present a strongly consistent estimator of the spectral density which is based only on one sampled path of X. The periodogram computation is fast and efficient, and our method is not affected by the non-ergodicity of X. Most notably no prior knowledge on parameters of the process such as its index of stability α is needed.
References:
[1] L.V. Hoang, E. Spodarev, "Inversion of alpha-sine and alpha-cosine transforms on R", Inverse Problems 37 (2021), 085008
[2] L.V. Hoang, E. Spodarev, "Non-ergodic statistics and spectral density estimation for stationary real harmonizable symmetric α-stable processes", Preprint arXiv:2209.04315, submitted, 2022.
https://docs.google.com/forms/d/e/1FAIpQLSet6w12XsqdCGQ8yEe4sOqRlCOhhrJXeKl5H7lMaRy4LZhmqQ/viewform
2023/01/10
10:50-11:30 Room # (Graduate School of Math. Sci. Bldg.)
井口優雅 (University College London)
Parameter Estimation with Increased Precision for Elliptic and Hypo-elliptic Diffusions
(現地参加) https://forms.gle/qwssLccVgsAWcfps7 (Zoom参加) (1/8迄) https://docs.google.com/forms/d/e/1FAIpQLSe7OYeMDfaZ7pTLO42k43Tn5dWKpsyw
井口優雅 (University College London)
Parameter Estimation with Increased Precision for Elliptic and Hypo-elliptic Diffusions
[ Abstract ]
Parametric inference for multi-dimensional diffusion processes has been studied over the past decades. Established approaches for likelihood-based estimation invoke a numerical time-discretisation scheme for the approximation of the (typically intractable) transition dynamics of the Stochastic Differential Equation (SDE) over finite time periods. Especially in the setting of some class of hypo-elliptic models, recent research (Ditlevsen and Samson 2019, Gloter and Yoshida 2021) has highlighted the critical effect of the choice of numerical scheme on the behaviour of derived parameter estimates. In our work, first, we develop two weak second order ‘sampling schemes' (to cover both the hypo-elliptic and elliptic classes) and generate accompanying ‘transition density schemes' of the SDE (i.e., approximations of the SDE transition density). Then, we produce a collection of analytic results, providing a complete theoretical framework that solidifies the proposed schemes and showcases advantages from their incorporation within SDE calibration methods, in both high and low frequency observations regime. We also present numerical results from carrying out classical or Bayesian inference. This is a joint work with Alexandros Beskos and Matthew Graham, and the preprint is available at https://arxiv.org/abs/2211.16384.
[ Reference URL ]Parametric inference for multi-dimensional diffusion processes has been studied over the past decades. Established approaches for likelihood-based estimation invoke a numerical time-discretisation scheme for the approximation of the (typically intractable) transition dynamics of the Stochastic Differential Equation (SDE) over finite time periods. Especially in the setting of some class of hypo-elliptic models, recent research (Ditlevsen and Samson 2019, Gloter and Yoshida 2021) has highlighted the critical effect of the choice of numerical scheme on the behaviour of derived parameter estimates. In our work, first, we develop two weak second order ‘sampling schemes' (to cover both the hypo-elliptic and elliptic classes) and generate accompanying ‘transition density schemes' of the SDE (i.e., approximations of the SDE transition density). Then, we produce a collection of analytic results, providing a complete theoretical framework that solidifies the proposed schemes and showcases advantages from their incorporation within SDE calibration methods, in both high and low frequency observations regime. We also present numerical results from carrying out classical or Bayesian inference. This is a joint work with Alexandros Beskos and Matthew Graham, and the preprint is available at https://arxiv.org/abs/2211.16384.
(現地参加) https://forms.gle/qwssLccVgsAWcfps7 (Zoom参加) (1/8迄) https://docs.google.com/forms/d/e/1FAIpQLSe7OYeMDfaZ7pTLO42k43Tn5dWKpsyw
2022/12/05
14:40-15:50 Room # (Graduate School of Math. Sci. Bldg.)
Michael Choi (National University of Singapore and Yale-NUS College)
A binary branching model with Moran-type interactions (English)
(Zoom参加) 12/1締切https://docs.google.com/forms/d/e/1FAIpQLSdyluSozvNOGmDcXzGv496v2AQNiPePqIerLaBN9pD4wxEmnw/viewform (現地参加) 先着20名https://forms.gle/rS9rjhL2jXo6eGgt5
Michael Choi (National University of Singapore and Yale-NUS College)
A binary branching model with Moran-type interactions (English)
[ Abstract ]
Branching processes naturally arise as pertinent models in a variety of applications such as population size dynamics, neutron transport and cell proliferation kinetics. A key result for understanding the behaviour of such systems is the Perron Frobenius decomposition, which allows one to characterise the large time average behaviour of the branching process via its leading eigenvalue and corresponding left and right eigenfunctions. However, obtaining estimates of these quantities can be challenging, for example when the branching process is spatially dependent with inhomogeneous rates. In this talk, I will introduce a new interacting particle model that combines the natural branching behaviour of the underlying process with a selection and resampling mechanism, which allows one to maintain some control over the system and more efficiently estimate the eigenelements. I will then present the main result, which provides an explicit relation between the particle system and the branching process via a many-to-one formula and also quantifies the L^2 distance between the occupation measures of the two systems. Finally, I will discuss some examples in order to illustrate the scope and possible extensions of the model, and to provide some comparisons with the Fleming Viot interacting particle system. This is based on work with Alex Cox (University of Bath) and Denis Villemonais (Université de Lorraine).
[ Reference URL ]Branching processes naturally arise as pertinent models in a variety of applications such as population size dynamics, neutron transport and cell proliferation kinetics. A key result for understanding the behaviour of such systems is the Perron Frobenius decomposition, which allows one to characterise the large time average behaviour of the branching process via its leading eigenvalue and corresponding left and right eigenfunctions. However, obtaining estimates of these quantities can be challenging, for example when the branching process is spatially dependent with inhomogeneous rates. In this talk, I will introduce a new interacting particle model that combines the natural branching behaviour of the underlying process with a selection and resampling mechanism, which allows one to maintain some control over the system and more efficiently estimate the eigenelements. I will then present the main result, which provides an explicit relation between the particle system and the branching process via a many-to-one formula and also quantifies the L^2 distance between the occupation measures of the two systems. Finally, I will discuss some examples in order to illustrate the scope and possible extensions of the model, and to provide some comparisons with the Fleming Viot interacting particle system. This is based on work with Alex Cox (University of Bath) and Denis Villemonais (Université de Lorraine).
(Zoom参加) 12/1締切https://docs.google.com/forms/d/e/1FAIpQLSdyluSozvNOGmDcXzGv496v2AQNiPePqIerLaBN9pD4wxEmnw/viewform (現地参加) 先着20名https://forms.gle/rS9rjhL2jXo6eGgt5
2022/10/21
①14:30-15:40- ②16:20-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Estate Khmaladze (Victoria University of Wellington)
On the theory of distribution free testing of statistical hypothesis
①Empirical processes for discrete and continuous observations: structure, difficulties and resolution.
②Further testing problems: parametric regression and Markov chains. (ENGLISH)
https://docs.google.com/forms/d/e/1FAIpQLScxh_wNRs3WbMUG4S3cGlGAu1ZkP4trLbc08CBrvUDO66hwNg/viewform?usp=sf_link
Estate Khmaladze (Victoria University of Wellington)
On the theory of distribution free testing of statistical hypothesis
①Empirical processes for discrete and continuous observations: structure, difficulties and resolution.
②Further testing problems: parametric regression and Markov chains. (ENGLISH)
[ Abstract ]
The concept of distribution free testing is familiar to all. Everybody, who heard about rank statistics, knows that the distribution of ranks is independent from the distribution of underlying random variables, provided this later is a continuous distribution on the real line. Everybody, who ever used classical goodness of fit tests like Kolmogorov - Smirnov test or Cram\'er-von Mises test, knows that the distribution of statistics of these tests is independent from the distribution of the underlying random variables, again, provided this distribution is a continuous distribution on the real line.
Development in subsequent decades revealed many cracks in existing theory and difficulties in extending the concept of distribution free testing to majority of interesting models. It gradually became clear that the new starting point is needed to expand the theory to these models.
In our lectures we first describe the current situation in empirical and related processes. Then we describe how the new approaches have been developed and what progress has been made.
Then we hope to show how the new approach can be naturally extended to the domain of stochastic processes, and how the important probabilistic models of the processes can be tested in distribution free way. In discrete time, results for Markov chains have been published in 2021. Extension to continuous time will be explored during the current visit to University of Tokyo.
[ Reference URL ]The concept of distribution free testing is familiar to all. Everybody, who heard about rank statistics, knows that the distribution of ranks is independent from the distribution of underlying random variables, provided this later is a continuous distribution on the real line. Everybody, who ever used classical goodness of fit tests like Kolmogorov - Smirnov test or Cram\'er-von Mises test, knows that the distribution of statistics of these tests is independent from the distribution of the underlying random variables, again, provided this distribution is a continuous distribution on the real line.
Development in subsequent decades revealed many cracks in existing theory and difficulties in extending the concept of distribution free testing to majority of interesting models. It gradually became clear that the new starting point is needed to expand the theory to these models.
In our lectures we first describe the current situation in empirical and related processes. Then we describe how the new approaches have been developed and what progress has been made.
Then we hope to show how the new approach can be naturally extended to the domain of stochastic processes, and how the important probabilistic models of the processes can be tested in distribution free way. In discrete time, results for Markov chains have been published in 2021. Extension to continuous time will be explored during the current visit to University of Tokyo.
https://docs.google.com/forms/d/e/1FAIpQLScxh_wNRs3WbMUG4S3cGlGAu1ZkP4trLbc08CBrvUDO66hwNg/viewform?usp=sf_link
2022/10/19
10:30-11:40 Room # (Graduate School of Math. Sci. Bldg.)
Hayate Yamagishi (Graduate School of Mathematical Sciences, The University of Tokyo)
https://docs.google.com/forms/d/e/1FAIpQLSd3i_gFci4Dc8T8gjtMigm08aIoQH6gM_Yfw0bHfppM1CNmag/viewform?usp=sf_link
Hayate Yamagishi (Graduate School of Mathematical Sciences, The University of Tokyo)
[ Abstract ]
[ Reference URL ]https://docs.google.com/forms/d/e/1FAIpQLSd3i_gFci4Dc8T8gjtMigm08aIoQH6gM_Yfw0bHfppM1CNmag/viewform?usp=sf_link
2022/07/21
13:30-14:40 Room #- (Graduate School of Math. Sci. Bldg.)
( )
[ Reference URL ]
https://forms.gle/JrtVRcQNgn9pug3F7
( )
[ Reference URL ]
https://forms.gle/JrtVRcQNgn9pug3F7
2022/02/16
14:30-16:00 Room # (Graduate School of Math. Sci. Bldg.)
Teppei Ogihara (University of Tokyo)
Efficient estimation for ergodic jump-diffusion processes
https://docs.google.com/forms/d/e/1FAIpQLSeRTEo19DJgFiVsEpLrRapqzkL6LZAiUMGdA0ezK-nWYSPrGg/viewform
Teppei Ogihara (University of Tokyo)
Efficient estimation for ergodic jump-diffusion processes
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
We study the estimation problem of the parametric model for ergodic jump-diffusion processes. Shimizu and Yoshida (Stat. Inference Stoch. Process. 2006) proposed a quasi-maximum-likelihood estimator based on a thresholding likelihood function that detects the existence of jumps.
In this talk, we consider the efficiency of estimators by using local asymptotic normality (LAN). To show the LAN property, we need to specify the asymptotic behavior of log-likelihood ratios, which is complicated for the jump-diffusion model because the transition probability for no jump is quite different from that for the presence of jumps. We develop techniques to show the LAN property based on transition density approximation. By applying these techniques to the thresholding likelihood function, we obtain the LAN property for the jump-diffusion model. Moreover, we have the asymptotic efficiency of
the quasi-maximum-likelihood estimator in Shimizu and Yoshida (2006) and a Bayes-type estimator proposed in Ogihara and Yoshida (Stat.Inference Stoch. Process. 2011). This is a joint work with Yuma Uehara (Kansai University).
[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
We study the estimation problem of the parametric model for ergodic jump-diffusion processes. Shimizu and Yoshida (Stat. Inference Stoch. Process. 2006) proposed a quasi-maximum-likelihood estimator based on a thresholding likelihood function that detects the existence of jumps.
In this talk, we consider the efficiency of estimators by using local asymptotic normality (LAN). To show the LAN property, we need to specify the asymptotic behavior of log-likelihood ratios, which is complicated for the jump-diffusion model because the transition probability for no jump is quite different from that for the presence of jumps. We develop techniques to show the LAN property based on transition density approximation. By applying these techniques to the thresholding likelihood function, we obtain the LAN property for the jump-diffusion model. Moreover, we have the asymptotic efficiency of
the quasi-maximum-likelihood estimator in Shimizu and Yoshida (2006) and a Bayes-type estimator proposed in Ogihara and Yoshida (Stat.Inference Stoch. Process. 2011). This is a joint work with Yuma Uehara (Kansai University).
https://docs.google.com/forms/d/e/1FAIpQLSeRTEo19DJgFiVsEpLrRapqzkL6LZAiUMGdA0ezK-nWYSPrGg/viewform
2022/01/20
15:00-16:10 Room # (Graduate School of Math. Sci. Bldg.)
Yoshimasa Uematsu (-)
-
[ Reference URL ]
https://docs.google.com/forms/d/e/1FAIpQLSdH8oP72k7-qsHigZBBZ4F6N-bGIJ6BcOWgKLhted2ohGSBeg/viewform
Yoshimasa Uematsu (-)
-
[ Reference URL ]
https://docs.google.com/forms/d/e/1FAIpQLSdH8oP72k7-qsHigZBBZ4F6N-bGIJ6BcOWgKLhted2ohGSBeg/viewform
2022/01/19
14:30-16:00 Room # (Graduate School of Math. Sci. Bldg.)
Martin Hazelton (Otago University)
Dynamic fibre samplers for linear inverse problems
https://docs.google.com/forms/d/e/1FAIpQLSeoXt5v8xdQNFAKTDLoD0lttaHjV17_r7864x11mtxU1EQlhQ/viewform
Martin Hazelton (Otago University)
Dynamic fibre samplers for linear inverse problems
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Statistical inverse problems occur when we wish to learn about some random process that is observed only indirectly. Inference in such situations typically involves sampling possible values for the latent variables of interest conditional on the indirect observations. For count data, the latent variables are constrained to lie on a fibre (solution set for the linear system) comprising the integer lattice within a convex polytope.
Sampling the latent counts can be conducted using MCMC methods,through a random walk on this fibre. A major challenge is finding a set of basic moves that ensures connectedness of the walk over the fibre. In principle this can be done by computing a Markov basis of potential moves, but the resulting sampler can be hugely inefficient even when such a basis is computable. In this talk I will describe some current work on developing a dynamic Markov basis that generates moves on the fly. This approach can guarantee irreducibility of the sampler while gaining efficiency by increasing the probability of selecting serviceable sampling directions.
[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Statistical inverse problems occur when we wish to learn about some random process that is observed only indirectly. Inference in such situations typically involves sampling possible values for the latent variables of interest conditional on the indirect observations. For count data, the latent variables are constrained to lie on a fibre (solution set for the linear system) comprising the integer lattice within a convex polytope.
Sampling the latent counts can be conducted using MCMC methods,through a random walk on this fibre. A major challenge is finding a set of basic moves that ensures connectedness of the walk over the fibre. In principle this can be done by computing a Markov basis of potential moves, but the resulting sampler can be hugely inefficient even when such a basis is computable. In this talk I will describe some current work on developing a dynamic Markov basis that generates moves on the fly. This approach can guarantee irreducibility of the sampler while gaining efficiency by increasing the probability of selecting serviceable sampling directions.
https://docs.google.com/forms/d/e/1FAIpQLSeoXt5v8xdQNFAKTDLoD0lttaHjV17_r7864x11mtxU1EQlhQ/viewform
2021/12/15
14:30-16:00 Room # (Graduate School of Math. Sci. Bldg.)
Estate Khmaladze (Victoria University of Wellington)
Theory of Distribution-free Testing
https://docs.google.com/forms/d/e/1FAIpQLSdFj1XF8WJSPRmE0GFKY2QxscaGxC9msM6GkEsAf0TgD9yv2g/viewform
Estate Khmaladze (Victoria University of Wellington)
Theory of Distribution-free Testing
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
The aim of the talk is to introduce transformations of empirical-type processes by a group of unitary operators. Recall that if v_{nP} is empirical process on real line, based on a sample from P, it can be mapped into empirical process v_{nQ} by appropriate change of time
v_{nP}(h(x))=v_{nQ}(x)
where h(x) is continuous and increasing. This is the basis for distribution-free theory of goodness of fit testing. If w(\phi) is a function-parametric “empirical-type” process (i.e. has functions \phi from a space L as a time) and if K* is a unitary operator on L, then transformed process Kw we define as
Kw(\phi) = w(K*\phi)
These two formulas have good similarity, but one transformation in on the real line, while the other transformation in on functional space.This later one turns out to be of very broad use, and allows to base distribution-free theory upon it. Examples, we have specific results for, are parametric empirical
processes in R^d, regression empirical processes, those in GLM, parametric models for point processes and for Markov processes in discrete time. Hopefully, further examples will follow.
[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
The aim of the talk is to introduce transformations of empirical-type processes by a group of unitary operators. Recall that if v_{nP} is empirical process on real line, based on a sample from P, it can be mapped into empirical process v_{nQ} by appropriate change of time
v_{nP}(h(x))=v_{nQ}(x)
where h(x) is continuous and increasing. This is the basis for distribution-free theory of goodness of fit testing. If w(\phi) is a function-parametric “empirical-type” process (i.e. has functions \phi from a space L as a time) and if K* is a unitary operator on L, then transformed process Kw we define as
Kw(\phi) = w(K*\phi)
These two formulas have good similarity, but one transformation in on the real line, while the other transformation in on functional space.This later one turns out to be of very broad use, and allows to base distribution-free theory upon it. Examples, we have specific results for, are parametric empirical
processes in R^d, regression empirical processes, those in GLM, parametric models for point processes and for Markov processes in discrete time. Hopefully, further examples will follow.
https://docs.google.com/forms/d/e/1FAIpQLSdFj1XF8WJSPRmE0GFKY2QxscaGxC9msM6GkEsAf0TgD9yv2g/viewform
2021/11/17
15:30-17:00 Room # (Graduate School of Math. Sci. Bldg.)
Jean Bertoin (Institut of Mathematics, University of Zurich (UZH))
On the local times of noise reinforced Bessel processes
https://docs.google.com/forms/d/e/1FAIpQLSeuK9AOw6QUqvUge9ukw__v04j5jpfogzrGxlPLpEgNhW09kg/viewform
Jean Bertoin (Institut of Mathematics, University of Zurich (UZH))
On the local times of noise reinforced Bessel processes
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Bessel processes form a one-parameter family of self-similar diffusion on $[0,\infty)$ with the same Hurst exponent 1/2 as Brownian motion. Loosely speaking, in this setting, linear noise reinforcement with reinforcement parameter $p$ consists of repeating (if $p>0$) or counterbalancing (if $p<0$)infinitesimal increments of the process, uniformly at random and at a fixed rate as time passes. In this talk, we will investigate the effect of noise reinforcement on the local time at level $0$, that is, informally, the time that the process spends at $0$. A connection with increasing self-similar Markov processes will play a key role.
[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Bessel processes form a one-parameter family of self-similar diffusion on $[0,\infty)$ with the same Hurst exponent 1/2 as Brownian motion. Loosely speaking, in this setting, linear noise reinforcement with reinforcement parameter $p$ consists of repeating (if $p>0$) or counterbalancing (if $p<0$)infinitesimal increments of the process, uniformly at random and at a fixed rate as time passes. In this talk, we will investigate the effect of noise reinforcement on the local time at level $0$, that is, informally, the time that the process spends at $0$. A connection with increasing self-similar Markov processes will play a key role.
https://docs.google.com/forms/d/e/1FAIpQLSeuK9AOw6QUqvUge9ukw__v04j5jpfogzrGxlPLpEgNhW09kg/viewform
2021/10/13
14:30-16:00 Room # (Graduate School of Math. Sci. Bldg.)
Li Cheng (National University of Singapore (NUS))
Bayesian Fixed-domain Asymptotics for Covariance Parameters in Gaussian Random Field Models
https://docs.google.com/forms/d/e/1FAIpQLSfEWrpkVavWEELx93dPxd0g2thhkC8NtA_8We4cDeiCKI6mZg/viewform
Li Cheng (National University of Singapore (NUS))
Bayesian Fixed-domain Asymptotics for Covariance Parameters in Gaussian Random Field Models
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Gaussian random field models are commonly used for modeling spatial processes. In this work we focus on the Gaussian process with isotropic Matern covariance functions. Under fixed-domain asymptotics,it is well known that when the dimension of data is less than or equal to three, the microergodic parameter can be consistently estimated with asymptotic normality while the range (or length-scale) parameter cannot. Motivated by this frequentist result, we prove that under a Bayesian fixed-domain framework, the posterior distribution of the microergodic parameter converges in total variation norm to a normal distribution with shrinking variance, while the posterior of the range parameter does not necessarily converge. Built on this new theory, we further show that the Bayesian kriging predictor satisfies the posterior asymptotic efficiency in linear prediction. We illustrate these asymptotic results in numerical examples.
[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Gaussian random field models are commonly used for modeling spatial processes. In this work we focus on the Gaussian process with isotropic Matern covariance functions. Under fixed-domain asymptotics,it is well known that when the dimension of data is less than or equal to three, the microergodic parameter can be consistently estimated with asymptotic normality while the range (or length-scale) parameter cannot. Motivated by this frequentist result, we prove that under a Bayesian fixed-domain framework, the posterior distribution of the microergodic parameter converges in total variation norm to a normal distribution with shrinking variance, while the posterior of the range parameter does not necessarily converge. Built on this new theory, we further show that the Bayesian kriging predictor satisfies the posterior asymptotic efficiency in linear prediction. We illustrate these asymptotic results in numerical examples.
https://docs.google.com/forms/d/e/1FAIpQLSfEWrpkVavWEELx93dPxd0g2thhkC8NtA_8We4cDeiCKI6mZg/viewform
2021/09/15
14:30-16:00 Room # (Graduate School of Math. Sci. Bldg.)
Anup Biswas (Indian Institute of Science Education and Research (IISER), Pune)
Ergodic risk-sensitive control: history, new results and open problems
https://docs.google.com/forms/d/e/1FAIpQLSe-136jVBQwRDg3rgEGpgVtH2d4chXCvQuvnk_gE2fZqMGwBw/viewform
Anup Biswas (Indian Institute of Science Education and Research (IISER), Pune)
Ergodic risk-sensitive control: history, new results and open problems
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Risk-sensitive control became popular because of the robustness it provides to the optimal control. Its connection to the theory of large deviation also made it a natural candidate of mathematical interest. In this talk, we shall give an overview of the history of risk-sensitive control problems and some of its applications. We shall then (informally) discuss the ways of tackling this problem and the main questions of interest. At the end, we shall see some important open problems.
[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Risk-sensitive control became popular because of the robustness it provides to the optimal control. Its connection to the theory of large deviation also made it a natural candidate of mathematical interest. In this talk, we shall give an overview of the history of risk-sensitive control problems and some of its applications. We shall then (informally) discuss the ways of tackling this problem and the main questions of interest. At the end, we shall see some important open problems.
https://docs.google.com/forms/d/e/1FAIpQLSe-136jVBQwRDg3rgEGpgVtH2d4chXCvQuvnk_gE2fZqMGwBw/viewform
2021/08/18
14:30-16:00 Room # (Graduate School of Math. Sci. Bldg.)
Gery Geenens (The University of New South Wales (UNSW Sydney))
Dependence, Sklar's copulas and discreteness
https://docs.google.com/forms/d/e/1FAIpQLScU9_QHdHZ-JeVyUIJOKUFmYJvG697NBDFkNh735WK9Cov1Og/viewform
Gery Geenens (The University of New South Wales (UNSW Sydney))
Dependence, Sklar's copulas and discreteness
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Yet the classical copula approach, building on Sklar’s theorem, cannot be legitimised if the variables of interest are not continuous. Indeed in the presence of discreteness, copula models are (i) unidentifiable, and (ii) not margin-free, and this by construction. In spite of the serious inconsistencies that this creates, downplaying statements are widespread in the literature, where copula methods are devised and used in discrete settings. In this work we call to reconsidering this current practice. To reconcile copulas with discreteness, we argued that they should be apprehended from a more fundamental perspective. Inspired by century-old ideas of Yule, we propose a novel construction which allows all the pleasant properties of copulas for modelling dependence (in particular:‘margin-freeness’) to smoothly carry over to the discrete setting.
[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Yet the classical copula approach, building on Sklar’s theorem, cannot be legitimised if the variables of interest are not continuous. Indeed in the presence of discreteness, copula models are (i) unidentifiable, and (ii) not margin-free, and this by construction. In spite of the serious inconsistencies that this creates, downplaying statements are widespread in the literature, where copula methods are devised and used in discrete settings. In this work we call to reconsidering this current practice. To reconcile copulas with discreteness, we argued that they should be apprehended from a more fundamental perspective. Inspired by century-old ideas of Yule, we propose a novel construction which allows all the pleasant properties of copulas for modelling dependence (in particular:‘margin-freeness’) to smoothly carry over to the discrete setting.
https://docs.google.com/forms/d/e/1FAIpQLScU9_QHdHZ-JeVyUIJOKUFmYJvG697NBDFkNh735WK9Cov1Og/viewform
2021/07/14
14:30-16:00 Room # (Graduate School of Math. Sci. Bldg.)
Anirvan Chakraborty ( IISER Kolkata, India)
Statistics for Functional Data
https://docs.google.com/forms/d/e/1FAIpQLSfkHbmXT_3kHkBIUedzNSFqQ6QxuZzUQ9_qOgc8HqtZsKHTPQ/viewform
Anirvan Chakraborty ( IISER Kolkata, India)
Statistics for Functional Data
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
With the advancement in technology, statisticians often have to analyze data which are curves or functions observed over a domain. Data of this type is usually called functional data and is very common these days in various fields of science. Statistical modelling of this type of data is usually done by viewing the data as a random sample from a probability distribution on some infinite dimensional function space. This formulation, however, implies that one has to delve into the mathematical rigour and complexity of dealing with infinite dimensional objects and probability distributions in function spaces. As such, standard multivariate statistical methods are far from useful in analyzing such data. We will discuss some statistical techniques for analyzing functional data as well as outline some of the unique challenges faced and also discuss some interesting open problems in this frontline research area.
[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
With the advancement in technology, statisticians often have to analyze data which are curves or functions observed over a domain. Data of this type is usually called functional data and is very common these days in various fields of science. Statistical modelling of this type of data is usually done by viewing the data as a random sample from a probability distribution on some infinite dimensional function space. This formulation, however, implies that one has to delve into the mathematical rigour and complexity of dealing with infinite dimensional objects and probability distributions in function spaces. As such, standard multivariate statistical methods are far from useful in analyzing such data. We will discuss some statistical techniques for analyzing functional data as well as outline some of the unique challenges faced and also discuss some interesting open problems in this frontline research area.
https://docs.google.com/forms/d/e/1FAIpQLSfkHbmXT_3kHkBIUedzNSFqQ6QxuZzUQ9_qOgc8HqtZsKHTPQ/viewform
2021/07/03
10:55-17:10 Room # (Graduate School of Math. Sci. Bldg.)
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[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/statmodel/?page_id=2028
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[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/statmodel/?page_id=2028
2021/06/16
14:30-16:00 Room # (Graduate School of Math. Sci. Bldg.)
Hiroki Masuda (Kyushu University)
Levy-Ornstein-Uhlenbeck Regression
https://docs.google.com/forms/d/e/1FAIpQLSfkHbmXT_3kHkBIUedzNSFqQ6QxuZzUQ9_qOgc8HqtZsKHTPQ/viewform
Hiroki Masuda (Kyushu University)
Levy-Ornstein-Uhlenbeck Regression
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
We will present some of recent developments in parametric inference for a linear regression model driven by a non-Gaussian stable Levy process, when the process is observed at high frequency over a fixed time period. The model depends on a covariate process and the finite-dimensional parameter: the stability index (activity index) and the scale in the noise term, and the (auto)regression coefficients in the trend term, all being unknown. The maximum-likelihood estimator is shown to be asymptotically mixed-normally distributed with maximum concentration property. In order to bypass possible multiple-root problem and heavy numerical optimization, we also consider some easily computable initial estimator with which the one-step improvement does work. The asymptotic properties hold true in a unified manner regardless of whether the model is stationary and/or ergodic, almost without taking care of character of the
covariate process. Also discussed will be model-selection issues and some possible model extensions.
[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
We will present some of recent developments in parametric inference for a linear regression model driven by a non-Gaussian stable Levy process, when the process is observed at high frequency over a fixed time period. The model depends on a covariate process and the finite-dimensional parameter: the stability index (activity index) and the scale in the noise term, and the (auto)regression coefficients in the trend term, all being unknown. The maximum-likelihood estimator is shown to be asymptotically mixed-normally distributed with maximum concentration property. In order to bypass possible multiple-root problem and heavy numerical optimization, we also consider some easily computable initial estimator with which the one-step improvement does work. The asymptotic properties hold true in a unified manner regardless of whether the model is stationary and/or ergodic, almost without taking care of character of the
covariate process. Also discussed will be model-selection issues and some possible model extensions.
https://docs.google.com/forms/d/e/1FAIpQLSfkHbmXT_3kHkBIUedzNSFqQ6QxuZzUQ9_qOgc8HqtZsKHTPQ/viewform
2021/05/19
14:30-16:00 Online
Register at least 3 days before at the reference URL. The URL for participation sent before the seminar.
Federico Camia (NYU Abu Dhabi)
Limit Theorems and Random Fractal Curves in Statistical Mechanics (ENGLISH)
https://docs.google.com/forms/d/e/1FAIpQLSe2ObhY3dsFUUU4EaRyslLiAwfuA6chMmiw5uyfa1bvKMdyfg/viewform
Register at least 3 days before at the reference URL. The URL for participation sent before the seminar.
Federico Camia (NYU Abu Dhabi)
Limit Theorems and Random Fractal Curves in Statistical Mechanics (ENGLISH)
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Statistical mechanics deals with systems that have a large number of components whose behavior can often be considered random. For this reason, probability theory plays an essential role in the mathematical analysis of the subject. After a gentle introduction to statistical mechanics, I will give a nontechnical overview of recent, exciting developments that combine in a beautiful and unexpected way discrete probability, stochastic processes and complex analysis. For concreteness, I will discuss two specific models, percolation and the Ising model, which have a long history, have played an important part in the development of statistical mechanics, and occupy a central place in modern probability theory.
[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Statistical mechanics deals with systems that have a large number of components whose behavior can often be considered random. For this reason, probability theory plays an essential role in the mathematical analysis of the subject. After a gentle introduction to statistical mechanics, I will give a nontechnical overview of recent, exciting developments that combine in a beautiful and unexpected way discrete probability, stochastic processes and complex analysis. For concreteness, I will discuss two specific models, percolation and the Ising model, which have a long history, have played an important part in the development of statistical mechanics, and occupy a central place in modern probability theory.
https://docs.google.com/forms/d/e/1FAIpQLSe2ObhY3dsFUUU4EaRyslLiAwfuA6chMmiw5uyfa1bvKMdyfg/viewform
2021/05/19
14:30-16:00 Room # (Graduate School of Math. Sci. Bldg.)
Federico Camia (NYU Abu Dhabi)
Limit Theorems and Random Fractal Curves in Statistical Mechanics
https://docs.google.com/forms/d/e/1FAIpQLSe2ObhY3dsFUUU4EaRyslLiAwfuA6chMmiw5uyfa1bvKMdyfg/viewform
Federico Camia (NYU Abu Dhabi)
Limit Theorems and Random Fractal Curves in Statistical Mechanics
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Statistical mechanics deals with systems that have a large number of components whose behavior can often be considered random. For this reason, probability theory plays an essential role in the mathematical analysis of the subject. After a gentle introduction to statistical mechanics, I will give a nontechnical overview of recent, exciting developments that combine in a beautiful and unexpected way discrete probability, stochastic processes and complex analysis. For concreteness, I will discuss two specific models, percolation and the Ising model, which have a long history, have played an important part in the development of statistical mechanics, and occupy a central place in modern probability theory.
[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Statistical mechanics deals with systems that have a large number of components whose behavior can often be considered random. For this reason, probability theory plays an essential role in the mathematical analysis of the subject. After a gentle introduction to statistical mechanics, I will give a nontechnical overview of recent, exciting developments that combine in a beautiful and unexpected way discrete probability, stochastic processes and complex analysis. For concreteness, I will discuss two specific models, percolation and the Ising model, which have a long history, have played an important part in the development of statistical mechanics, and occupy a central place in modern probability theory.
https://docs.google.com/forms/d/e/1FAIpQLSe2ObhY3dsFUUU4EaRyslLiAwfuA6chMmiw5uyfa1bvKMdyfg/viewform
2021/04/21
14:30-16:00 Room # (Graduate School of Math. Sci. Bldg.)
Han Liang Gan (University of Waikato)
Stationary distribution approximations for two-island and seed bank models (ENGLISH)
https://docs.google.com/forms/d/e/1FAIpQLSfLezQNquom7pjodIrc1suI0o5rsWg9AHNv7cix0A7h39tx-g/viewform
Han Liang Gan (University of Waikato)
Stationary distribution approximations for two-island and seed bank models (ENGLISH)
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Two-island Wright-Fisher models are used to model genetic frequencies and variability for subdivided populations. One of the key components of the model is the level of migration between the two
islands. We show that as the population size increases, the appropriate approximation and limit for the stationary distribution of a two-island Wright-Fisher Markov chain depends on the level of migration. In a seed bank model, individuals in one of the islands stay dormant rather than reproduce. We give analogous results for the seed bank model, compare and contrast the differences and examine the effect the seed bank has on genetic variability. Our results are derived from a new development of Stein's method for the two-island diffusion model and existing results for Stein's method for the Dirichlet distribution.
This talk is based on joint work with Adrian Röllin, Nathan Ross and Maite Wilke Berenguer.
[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Two-island Wright-Fisher models are used to model genetic frequencies and variability for subdivided populations. One of the key components of the model is the level of migration between the two
islands. We show that as the population size increases, the appropriate approximation and limit for the stationary distribution of a two-island Wright-Fisher Markov chain depends on the level of migration. In a seed bank model, individuals in one of the islands stay dormant rather than reproduce. We give analogous results for the seed bank model, compare and contrast the differences and examine the effect the seed bank has on genetic variability. Our results are derived from a new development of Stein's method for the two-island diffusion model and existing results for Stein's method for the Dirichlet distribution.
This talk is based on joint work with Adrian Röllin, Nathan Ross and Maite Wilke Berenguer.
https://docs.google.com/forms/d/e/1FAIpQLSfLezQNquom7pjodIrc1suI0o5rsWg9AHNv7cix0A7h39tx-g/viewform
2021/04/21
14:30-16:00 Room # (Graduate School of Math. Sci. Bldg.)
Han Liang Gan (University of Waikato)
Stationary distribution approximations for two-island and seed bank models
https://docs.google.com/forms/d/e/1FAIpQLSfLezQNquom7pjodIrc1suI0o5rsWg9AHNv7cix0A7h39tx-g/viewform
Han Liang Gan (University of Waikato)
Stationary distribution approximations for two-island and seed bank models
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Two-island Wright-Fisher models are used to model genetic frequencies and variability for subdivided populations. One of the key components of the model is the level of migration between the two islands. We show that as the population size increases, the appropriate approximation and limit for the stationary distribution of a two-island Wright-Fisher Markov chain depends on the level of migration. In a seed bank model, individuals in one of the islands stay dormant rather than reproduce. We give analogous results for the seed bank model, compare and contrast the differences and examine the effect the seed bank has on genetic variability. Our results are derived from a new development of Stein's method for the two-island diffusion model and existing results for
Stein's method for the Dirichlet distribution.
This talk is based on joint work with Adrian Röllin, Nathan Ross and Maite Wilke Berenguer.
[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Two-island Wright-Fisher models are used to model genetic frequencies and variability for subdivided populations. One of the key components of the model is the level of migration between the two islands. We show that as the population size increases, the appropriate approximation and limit for the stationary distribution of a two-island Wright-Fisher Markov chain depends on the level of migration. In a seed bank model, individuals in one of the islands stay dormant rather than reproduce. We give analogous results for the seed bank model, compare and contrast the differences and examine the effect the seed bank has on genetic variability. Our results are derived from a new development of Stein's method for the two-island diffusion model and existing results for
Stein's method for the Dirichlet distribution.
This talk is based on joint work with Adrian Röllin, Nathan Ross and Maite Wilke Berenguer.
https://docs.google.com/forms/d/e/1FAIpQLSfLezQNquom7pjodIrc1suI0o5rsWg9AHNv7cix0A7h39tx-g/viewform
2021/03/29
14:00-15:10 Online
Register at least 3 days before at the reference URL. The URL for participation sent before the seminar.
Masaaki Imaizumi (University of Tokyo)
On Gaussian Approximation for M-Estimator (JAPANESE)
https://docs.google.com/forms/d/e/1FAIpQLSfjQhmmZjWUllB6pQeEMGDRcLCe_0JPgVbEA05rHtcDYAZzqg/viewform
Register at least 3 days before at the reference URL. The URL for participation sent before the seminar.
Masaaki Imaizumi (University of Tokyo)
On Gaussian Approximation for M-Estimator (JAPANESE)
[ Abstract ]
This study develops a non-asymptotic Gaussian approximation theory for distributions of M-estimators, which are defined as maximizers of empirical criterion functions. In existing mathematical statistics literature, numerous studies have focused on approximating the distributions of the M-estimators for statistical inference. In contrast to the existing approaches, which mainly focus on limiting behaviors, this study employs a non-asymptotic approach, establishes abstract Gaussian approximation results for maximizers of empirical criteria, and proposes a Gaussian multiplier bootstrap approximation method. Our developments can be considered as extensions of the seminal works on the approximation theory for distributions of suprema of empirical processes toward their maximizers. Through this work, we shed new lights on the statistical theory of M-estimators. Our theory covers not only regular estimators, such as the least absolute deviations, but also some non-regular cases where it is difficult to derive or to approximate numerically the limiting distributions such as non-Donsker classes and cube root estimators.
[ Reference URL ]This study develops a non-asymptotic Gaussian approximation theory for distributions of M-estimators, which are defined as maximizers of empirical criterion functions. In existing mathematical statistics literature, numerous studies have focused on approximating the distributions of the M-estimators for statistical inference. In contrast to the existing approaches, which mainly focus on limiting behaviors, this study employs a non-asymptotic approach, establishes abstract Gaussian approximation results for maximizers of empirical criteria, and proposes a Gaussian multiplier bootstrap approximation method. Our developments can be considered as extensions of the seminal works on the approximation theory for distributions of suprema of empirical processes toward their maximizers. Through this work, we shed new lights on the statistical theory of M-estimators. Our theory covers not only regular estimators, such as the least absolute deviations, but also some non-regular cases where it is difficult to derive or to approximate numerically the limiting distributions such as non-Donsker classes and cube root estimators.
https://docs.google.com/forms/d/e/1FAIpQLSfjQhmmZjWUllB6pQeEMGDRcLCe_0JPgVbEA05rHtcDYAZzqg/viewform
2021/03/24
14:30-16:00 Online
Register at least 3 days before at the reference URL. The URL for participation sent before the seminar.
Rachel Fewster (University of Auckland)
Stochastic modelling in ecology: why is it interesting? (ENGLISH)
https://docs.google.com/forms/d/e/1FAIpQLSf05P9fCZ5Wkasc7clW1XBpkeONPSjPKuCkNYb3oIqnOAu5Mg/viewform
Register at least 3 days before at the reference URL. The URL for participation sent before the seminar.
Rachel Fewster (University of Auckland)
Stochastic modelling in ecology: why is it interesting? (ENGLISH)
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics https://sites.google.com/view/apsps/home
The ecological sciences offer rich pickings for stochastic modellers. There is currently an abundance of new technologies for monitoring wildlife and biodiversity, for which no practicable data-analysis methods exist. Often, modelling approaches that are motivated by a specific problem with relatively narrow focus can turn out to have surprisingly broad application elsewhere. As the generality of the problem structure becomes clear, this can also motivate new statistical theory.
I will describe some ecological modelling scenarios that have led to interesting developments from methodological and theoretical perspectives. As time allows, these will include: saddlepoint approximations for dealing with data corrupted by non-invertible linear transformations; information theory for assuring that it is a good idea to unite data from multiple sources; and methods for dealing with so-called 'enigmatic' data from remote sensors, involving a blend of ideas from point processes, queuing theory, and trigonometry. All scenarios will be generously illustrated with pictures of charismatic wildlife.
This talk covers joint work with numerous collaborators, especially Joey Wei Zhang, Mark Bravington, Peter Jupp, Jesse Goodman, Martin Hazelton, Godrick Oketch, Ben Stevenson, David Borchers, Paul van Dam-Bates, and Stephen Marsland.
[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics https://sites.google.com/view/apsps/home
The ecological sciences offer rich pickings for stochastic modellers. There is currently an abundance of new technologies for monitoring wildlife and biodiversity, for which no practicable data-analysis methods exist. Often, modelling approaches that are motivated by a specific problem with relatively narrow focus can turn out to have surprisingly broad application elsewhere. As the generality of the problem structure becomes clear, this can also motivate new statistical theory.
I will describe some ecological modelling scenarios that have led to interesting developments from methodological and theoretical perspectives. As time allows, these will include: saddlepoint approximations for dealing with data corrupted by non-invertible linear transformations; information theory for assuring that it is a good idea to unite data from multiple sources; and methods for dealing with so-called 'enigmatic' data from remote sensors, involving a blend of ideas from point processes, queuing theory, and trigonometry. All scenarios will be generously illustrated with pictures of charismatic wildlife.
This talk covers joint work with numerous collaborators, especially Joey Wei Zhang, Mark Bravington, Peter Jupp, Jesse Goodman, Martin Hazelton, Godrick Oketch, Ben Stevenson, David Borchers, Paul van Dam-Bates, and Stephen Marsland.
https://docs.google.com/forms/d/e/1FAIpQLSf05P9fCZ5Wkasc7clW1XBpkeONPSjPKuCkNYb3oIqnOAu5Mg/viewform
2021/02/17
14:30-15:30 Room #Zoom (Graduate School of Math. Sci. Bldg.)
Register at least 3 days before at the reference URL. The URL for participation sent before the seminar.
Nakahiro Yoshida (University of Tokyo)
Quasi-likelihood analysis for stochastic differential equations: volatility estimation and global jump filters (ENGLISH)
https://docs.google.com/forms/d/e/1FAIpQLSeLrq_Ifc4WvJC6uvwIpMyrAVM9v-0J3FOaZbsplbU9d21ALw/viewform
Register at least 3 days before at the reference URL. The URL for participation sent before the seminar.
Nakahiro Yoshida (University of Tokyo)
Quasi-likelihood analysis for stochastic differential equations: volatility estimation and global jump filters (ENGLISH)
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics https://sites.google.com/view/apsps/home
The quasi likelihood analysis (QLA) is a framework of statistical inference for stochastic processes, featuring the quasi-likelihood random field and the polynomial type large deviation inequality. The QLA enables us to systematically derive limit theorems and tail probability estimates for the associated QLA estimators (quasi-maximum likelihood estimator and quasi-Bayesian estimator) for various dependent models. The first half of the talk will be devoted to an introduction to the QLA for stochastic differential equations. The second half presents recent developments in a filtering problem to estimate volatility from the data contaminated with jumps. A QLA for volatility for a stochastic differential equation with jumps is constructed, based on a "global jump filter" that uses all the increments of the process to decide whether an increment has jumps.
Key words: stochastic differential equation, high frequency data, Le Cam-Hajek theory, Ibragimov-Has'minskii-Kutoyants program, polynomial type large deviation inequality, quasi-maximum likelihood estimator, quasi-Bayesian estimator, L^p-estimates of the error, non-ergodic statistics, asymptotic (mixed) normality.
[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics https://sites.google.com/view/apsps/home
The quasi likelihood analysis (QLA) is a framework of statistical inference for stochastic processes, featuring the quasi-likelihood random field and the polynomial type large deviation inequality. The QLA enables us to systematically derive limit theorems and tail probability estimates for the associated QLA estimators (quasi-maximum likelihood estimator and quasi-Bayesian estimator) for various dependent models. The first half of the talk will be devoted to an introduction to the QLA for stochastic differential equations. The second half presents recent developments in a filtering problem to estimate volatility from the data contaminated with jumps. A QLA for volatility for a stochastic differential equation with jumps is constructed, based on a "global jump filter" that uses all the increments of the process to decide whether an increment has jumps.
Key words: stochastic differential equation, high frequency data, Le Cam-Hajek theory, Ibragimov-Has'minskii-Kutoyants program, polynomial type large deviation inequality, quasi-maximum likelihood estimator, quasi-Bayesian estimator, L^p-estimates of the error, non-ergodic statistics, asymptotic (mixed) normality.
https://docs.google.com/forms/d/e/1FAIpQLSeLrq_Ifc4WvJC6uvwIpMyrAVM9v-0J3FOaZbsplbU9d21ALw/viewform
2021/01/13
14:30-15:30 Room #Zoom (Graduate School of Math. Sci. Bldg.)
Pierre Lafaye de Micheaux (UNSW)
Depth of Curve Data and Applications (ENGLISH)
https://sites.google.com/view/apsps/previous-speakers
Pierre Lafaye de Micheaux (UNSW)
Depth of Curve Data and Applications (ENGLISH)
[ Abstract ]
[ Reference URL ]https://sites.google.com/view/apsps/previous-speakers
