Search results for "uncertainty."

Frequentist and Bayesian approaches for a joint model for prostate cancer risk and longitudinal prostate-specific antigen data

2015

The paper describes the use of frequentist and Bayesian shared-parameter joint models of longitudinal measurements of prostate-specific antigen (PSA) and the risk of prostate cancer (PCa). The motivating dataset corresponds to the screening arm of the Spanish branch of the European Randomized Screening for Prostate Cancer study. The results show that PSA is highly associated with the risk of being diagnosed with PCa and that there is an age-varying effect of PSA on PCa risk. Both the frequentist and Bayesian paradigms produced very close parameter estimates and subsequent 95% confidence and credibility intervals. Dynamic estimations of disease-free probabilities obtained using Bayesian infe…

Non-parametric Estimation of the Death Rate in Branching Diffusions

2002

We consider finite systems of diffusing particles in R with branching and immigration. Branching of particles occurs at position dependent rate. Under ergodicity assumptions, we estimate the position-dependent branching rate based on the observation of the particle process over a time interval [0, t]. Asymptotics are taken as t → ∞. We introduce a kernel-type procedure and discuss its asymptotic properties with the help of the local time for the particle configuration. We compute the minimax rate of convergence in squared-error loss over a range of Holder classes and show that our estimator is asymptotically optimal.

Designing and pricing guarantee options in defined contribution pension plans

2015

Abstract The shift from defined benefit (DB) to defined contribution (DC) is pervasive among pension funds, due to demographic changes and macroeconomic pressures. In DB all risks are borne by the provider, while in plain vanilla DC all risks are borne by the beneficiary. However, for DC to provide income security some kind of guarantee is required. A minimum guarantee clause can be modeled as a put option written on some underlying reference portfolio and we develop a discrete model that selects the reference portfolio to minimize the cost of a guarantee. While the relation DB–DC is typically viewed as a binary one, the model shows how to price a wide range of guarantees creating a continu…

Haldane Model at finite temperature

2019

We consider the Haldane model, a 2D topological insulator whose phase is defined by the Chern number. We study its phases as temperature varies by means of the Uhlmann number, a finite temperature generalization of the Chern number. Because of the relation between the Uhlmann number and the dynamical transverse conductivity of the system, we evaluate also the conductivity of the model. This analysis does not show any sign of a phase transition induced by the temperature, nonetheless it gives a better understanding of the fate of the topological phase with the increase of the temperature, and it provides another example of the usefulness of the Uhlmann number as a novel tool to study topolog…

Fisher Renormalization for Logarithmic Corrections

2008

For continuous phase transitions characterized by power-law divergences, Fisher renormalization prescribes how to obtain the critical exponents for a system under constraint from their ideal counterparts. In statistical mechanics, such ideal behaviour at phase transitions is frequently modified by multiplicative logarithmic corrections. Here, Fisher renormalization for the exponents of these logarithms is developed in a general manner. As for the leading exponents, Fisher renormalization at the logarithmic level is seen to be involutory and the renormalized exponents obey the same scaling relations as their ideal analogs. The scheme is tested in lattice animals and the Yang-Lee problem at t…

Bayesian Essentials with R, 2nd edn. J.-M. Marin and C. P. Robert (2014). New York: Springer/Springer Texts in Statistics. 296 pages, ISBN: 978-1-461…

2015

El que de la Probabilidad

1985

The concept of probability is studied under its mathematical and philosophical aspects; special emphasis is laid on its ontological status.

Quantum jump statistics with a shifted jump operator in a chiral waveguide

2019

Resonance fluorescence, consisting of light emission from an atom driven by a classical oscillating field, is well-known to yield a sub-Poissonian photon counting statistics. This occurs when only emitted light is detected, which corresponds to a master equation (ME) unraveling in terms of the canonical jump operator describing spontaneous decay. Formally, an alternative ME unraveling is possible in terms of a shifted jump operator. We show that this shift can result in sub-Poissonian, Poissonian or super-Poissonian quantum jump statistics. This is shown in terms of the Mandel Q parameter in the limit of long counting times, which is computed through large deviation theory. We present a wav…

On the empirical spectral distribution for certain models related to sample covariance matrices with different correlations

2021

Given [Formula: see text], we study two classes of large random matrices of the form [Formula: see text] where for every [Formula: see text], [Formula: see text] are iid copies of a random variable [Formula: see text], [Formula: see text], [Formula: see text] are two (not necessarily independent) sets of independent random vectors having different covariance matrices and generating well concentrated bilinear forms. We consider two main asymptotic regimes as [Formula: see text]: a standard one, where [Formula: see text], and a slightly modified one, where [Formula: see text] and [Formula: see text] while [Formula: see text] for some [Formula: see text]. Assuming that vectors [Formula: see t…

Mode-coupling theory for multiple decay channels

2013

We investigate the properties of a class of mode-coupling equations for the glass transition where the density mode decays into multiple relaxation channels. We prove the existence and uniqueness of the solutions for Newtonian as well as Brownian dynamics and demonstrate that they fulfill the requirements of correlation functions, in the latter case the solutions are purely relaxational. Furthermore, we construct an effective mode-coupling functional which allows to map the theory to the case of a single decay channel, such that the covariance principle found for the mode-coupling theory for simple liquids is properly generalized. This in turn allows establishing the maximum theorem stating…