Related papers: Financial Probabilities from Fisher Information
We show how preparation uncertainty relations that are formulated as sums of variances may be tightened by using the quantum Fisher information to quantify quantum fluctuations. We apply this to derive stronger angular momentum uncertainty…
An approach based on the Fisher information (FI) is developed to quantify the maximum information gain and optimal experimental design in neutron reflectometry experiments. In these experiments, the FI can be analytically calculated and…
When estimating quantities and fields that are difficult to measure directly, such as the fluidity of ice, from point data sources, such as satellite altimetry, it is important to solve a numerical inverse problem that is formulated with…
The quantum Fisher information (QFI) is a fundamental quantity of interest in many areas from quantum metrology to quantum information theory. It can in particular be used as a witness to establish the degree of multi-particle entanglement…
A simple proof is given for the monotonicity of entropy and Fisher information associated to sums of i.i.d. random variables. The proof relies on a characterization of maximal correlation for partial sums due to Dembo, Kagan and Shepp.
In this paper, a new three-parameter lifetime distribution is introduced and many of its standard properties are discussed. These include shape of the probability density function, hazard rate function and its shape, quantile function,…
This paper extends quantile factor analysis to a probabilistic variant that incorporates regularization and computationally efficient variational approximations. We establish through synthetic and real data experiments that the proposed…
We show how to verify the metrological usefulness of quantum states based on the expectation values of an arbitrarily chosen set of observables. In particular, we estimate the quantum Fisher information as a figure of merit of metrological…
Fair representation learning is an attractive approach that promises fairness of downstream predictors by encoding sensitive data. Unfortunately, recent work has shown that strong adversarial predictors can still exhibit unfairness by…
The implied volatility is a crucial element of any financial toolbox, since it is used for quoting and the hedging of options as well as for model calibration. In contrast to the Black-Scholes formula its inverse, the implied volatility, is…
Simulators often provide the best description of real-world phenomena. However, they also lead to challenging inverse problems because the density they implicitly define is often intractable. We present a new suite of simulation-based…
The problem of determining the achievable sensitivity with digitization exhibiting minimal complexity is addressed. In this case, measurements are exclusively available in hard-limited form. Assessing the achievable sensitivity via the…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
The method of maximum entropy has proven to be a rather powerful way to solve the inverse problem consisting of determining a probability density $f_S(s)$ on $[0,\infty)$ from the knowledge of the expected value of a few generalized…
Integral equations frequently arise in surface science, and in some cases, they must be treated as inverse problems. In our previous work on optical tweezers, atomic force microscopy, and surface force measurement apparatus, we performed…
Theoretical studies in gravitational wave astronomy often require the calculation of Fisher Information Matrices and Likelihood functions, which in a direct approach entail the costly step of computing gravitational waveforms. Here I…
We propose a Bayesian framework of Gaussian process in order to extend Fisher's discriminant to classify functional data such as spectra and images. The probability structure for our extended Fisher's discriminant is explicitly formulated,…
We introduce an event based framework of directional changes and overshoots to map continuous financial data into the so-called Intrinsic Network - a state based discretisation of intrinsically dissected time series. Defining a method for…
We describe the pricing and hedging of financial options without the use of probability using rough paths. By encoding the volatility of assets in an enhancement of the price trajectory, we give a pathwise presentation of the replication of…
A principled procedure to infer a hierarchy of statistical distributions possessing ill-conditioned eigenstructures, from incomplete constraints, is presented. The inference process of the \textit{pdf}'s employs the Fisher information as…