Iterated filtering algorithms are stochastic optimization procedures for latent variable models that recursively combine parameter perturbations with reconstruction. Previously, theoretical support these has been based on the use of conditional moments perturbed parameters to approximate derivatives log likelihood function. Here, a approach is introduced convergence an iterated Bayes map. An algorithm supported by this theory displays substantial numerical improvement computational challenge...

We present efficient methods for simulation, using the Fast Fourier Transform (FFT) algorithm, of two classes processes with symmetric α-stable (SαS) distributions. Namely, (i) linear fractional stable motion (LFSM) process and (ii) autoregressive moving average (FARIMA) time series SαS innovations. These types heavy-tailed have infinite variances long-range dependence they can be used in modeling traffic modern computer telecommunication networks. generate paths LFSM by Riemann-sum...

We develop classification results for max-stable processes, based on their spectral representations. The structure of max-linear isometries and minimal representations play important roles. propose a general strategy measurable processes the notion co-spectral functions. In particular, we discuss spectrally continuous-discrete, conservative-dissipative, positive-null decompositions. For stationary latter two decompositions arise from connections to nonsingular flows are closely related...

Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability general max-linear models, which include large class of max-stable fields. As consequence, we develop algorithm efficient and exact sampling from distributions. Our method provides computational solution to prediction problem spectrally discrete This work offers new tools perspective many statistical inference problems spatial extremes, arising,...

We study a family of locally self-similar stochastic processes Y = { ( t )} ∈ℝ with α-stable distributions, called linear multifractional stable motions. They have infinite variance and may possess skewed distributions. The motion include, in particular, the classical fractional processes, which stationary increments are self-similarity parameter H . process is obtained by replacing integral representation deterministic function ). Whereas always continuous probability, this not general case...

We establish characterization results for the ergodicity of stationary symmetric $\alpha$-stable ($\mathrm{S}\alpha\mathrm{S}$) and $\alpha$-Fréchet random fields. show that result Samorodnitsky [Ann. Probab. 33 (2005) 1782–1803] remains valid in multiparameter setting, is, a $\mathrm{S}\alpha\mathrm{S}$ ($0<\alpha<2$) field is ergodic (or, equivalently, weakly mixing) if only it generated by null group action. Similar are also established max-stable The key ingredient adaption positive/null...

In this paper, a novel approach to the problem of estimating heavy-tail exponent α >; 0 distribution is proposed. It based on fact that block-maxima size m scale at rate <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/α</sup> for independent, as well number dependent data. This scaling can be captured by max-spectrum plot data leads regression estimators α. Consistency and asymptotic normality these established independent under mild...

The statistical modeling of spatial extremes has been an active area recent research with a growing domain applications. Much the existing methodology, however, focuses on magnitudes extreme events rather than their timing. To address this gap, article investigates notion extremal concurrence. Suppose that daily temperatures are measured at several synoptic stations. We say concurrent if record maximum occur simultaneously, is, same day for all It is important to be able understand,...

The Internet, as a global system of interconnected networks, carries an extensive array information resources and services. Key requirements include good quality-of-service protection the infrastructure from nefarious activity [e.g., distributed denial service (DDoS) attacks]. Network monitoring is essential to network engineering, capacity planning, prevention/mitigation threats. We develop open-source architecture, All-packet MONitor (AMON), for online analysis multi-gigabit streams. It...

ABSTRACT The prediction of extreme events in time series is a fundamental problem arising many financial, scientific, engineering, and other applications. We begin by establishing general Neyman–Pearson‐type characterization optimal event predictors terms density ratios. This yields new insights several closed‐form for additive models. These results naturally extend to series, where we study both light‐ heavy‐tailed autoregressive moving average Using uniform law large numbers ergodic...

The workshop brought together researchers contributing to various recent topics in Extreme Value Theory. Discussions and talks included probabilistic development the theory of regular variation, advances multivariate representations compatible with sparsity structures, statistical inference both high dimensional time series frameworks, novel applications emerging directions that leverage deep learning.

The linear multifractional stable motion (LMSM) processes Y = {Y(t)} t∈ℝ is an α-stable (0 &lt; α 2) stochastic process, which exhibits local self-similarity, has heavy tails and can have skewed distributions. process obtained from the well-known class of fractional (LFSM) by replacing their self-similarity parameter H a function time H(t). We show that paths Y(t) are bounded on intervals only if 1/α ≤ H(t) 1, t ∈ ℝ. In particular, 0 then everywhere discontinuous paths, with probability one....

Introduced is the notion of minimality for spectral representations sum- and max-infinitely divisible processes it shown that minimal representation on a Borel space exists unique. This fact used to show stationary, stochastically continuous, or max-i.d. random process $\mathbb{R}^d$ can be generated by measure-preserving flow $\sigma$-finite measure this development makes possible extend classification program Rosi\'{n}ski (Ann. Probab. 23 (1995) 1163-1187) with unified treatment both...

Abstract. Methods for parameter estimation in the presence of long‐range dependence and heavy tails are scarce. Fractional autoregressive integrated moving average (FARIMA) time series positive values fractional differencing exponent d can be used to model case heavy‐tailed distributions. In this paper, we focus on Hurst H = + 1/ α dependent FARIMA with symmetric ‐stable (1 &lt; 2) innovations. We establish consistency asymptotic normality two types wavelet estimators . do so by exploiting...

The extremal index parameter θ characterizes the degree of local dependence in extremes a stationary time series and has important applications number areas, such as hydrology, telecommunications, finance, environmental studies. In this study, novel estimator for based on asymptotic scaling block-maxima resampling is introduced. It shown to be consistent asymptotically normal large class m-dependent series. Further, procedure automatic selection its tuning developed different types...