Conditional Probability Density Distribution Research Articles

Are basic actors brainbound agents? Narrowing down solutions to the problem of probabilistic content for predictive perceivers

Clark (Journal of Consciousness Studies, 25(3–4), 71–87, 2018) worries that predictive processing (PP) accounts of perception introduce a puzzling disconnect between the content of personal-level perceptual states and their underlying subpersonal representations. According to PP, in perception, the brain encodes information about the environment in conditional probability density distributions over causes of sensory input. But it seems perceptual experience only presents us with one way the world is at a time. If perception is at bottom probabilistic, shouldn’t this aspect of subpersonally represented content show up in consciousness? To address this worry, Clark argues that representations underlying personal-level content are constrained by the need to provide a single action-guiding take on the environment. However, this proposal rests a conception of the nature of agency, famously articulated by Davidson (1980a, b), that is inconsistent with a view of the mind as embodied-extended. Since Clark and other enactivist PP theorists present the extended mind as an important consequence of the predictive framework, the proposal is in tension with his complete view. I claim that this inconsistency could be resolved either by retaining the Davidsonian view of action and abandoning the extended-embodied approach, or by adopting a more processual, world-involving account of agency and perceptual experience than Clark currently endorses. To solve the puzzle he raises, Clark must become a radical enactivist or a consistent internalist.

Improved Cubature Kalman Filter for High-Dimensional Systems with Multiplicative Noises

It is a challenging mission to estimate accurately the state of a non-cooperative spacecraft with multiplicative noises. In this paper, an improved cubature Kalman filter for nonlinear systems with multiplicative noises (ICKF_M) is proposed. First, based on the assumption that multiplicative noise satisfies the Gaussian distribution, the conditional mean variance of multiplicative noise is considered in the prediction and updating process. According to the Bayesian estimation theory, the conditional probability density distribution of multiplicative noise is added to the prediction and update functions to adapt the multiplicative noise. Then, to solve the defect of cubature Kalman filter (CKF), a new method for generating sigma points is designed instead of the classical methods, which has transformed the posterior sigma-points error matrix from prediction phase to the posterior domain of update. Finally, a binocular visual method is used to measure the state of the spacecraft. Compared with the previous methods, the simulation results indicate that the average norm of estimation error has nearly decreased by 20% in comparison with the similar filters in the reference. Moreover, the convergence rate of the proposed algorithm is obviously faster than that of the previous algorithm.

Uncertainty Analysis of Multi-Model Flood Forecasts

This paper demonstrates, by means of a systematic uncertainty analysis, that the use of outputs from more than one model can significantly improve conditional forecasts of discharges or water stages, provided the models are structurally different. Discharge forecasts from two models and the actual forecasted discharge are assumed to form a three-dimensional joint probability density distribution (jpdf), calibrated on long time series of data. The jpdf is decomposed into conditional probability density distributions (cpdf) by means of Bayes formula, as suggested and explored by Krzysztofowicz in a series of papers. In this paper his approach is simplified to optimize conditional forecasts for any set of two forecast models. Its application is demonstrated by means of models developed in a study of flood forecasting for station Stung Treng on the middle reach of the Mekong River in South-East Asia. Four different forecast models were used and pairwise combined: forecast with no model, with persistence model, with a regression model, and with a rainfall-runoff model. Working with cpdfs requires determination of dependency among variables, for which linear regressions are required, as was done by Krzysztofowicz. His Bayesian approach based on transforming observed probability distributions of discharges and forecasts into normal distributions is also explored. Results obtained with his method for normal prior and likelihood distributions are identical to results from direct multiple regressions. Furthermore, it is shown that in the present case forecast accuracy is only marginally improved, if Weibull distributed basic data were converted into normally distributed variables.

A Novel Conditional Probability Density Distribution Surface for the Analysis of the Drop Life of Solder Joints Under Board Level Drop Impact

The scattering of fatigue life data is a common problem and usually described using the normal distribution or Weibull distribution. For solder joints under drop impact, due to the complicated stress distribution, the relationship between the stress and the drop life is so far unknown. Furthermore, it is important to establish a function describing the change in standard deviation for solder joints under different drop impact levels. Therefore, in this study, a novel conditional probability density distribution surface (CPDDS) was established for the analysis of the drop life of solder joints. The relationship between the drop impact acceleration and the drop life is proposed, which comprehensively considers the stress distribution. A novel exponential model was adopted for describing the change of the standard deviation with the impact acceleration (0 → +∞). To validate the model, the drop life of Sn-3.0Ag-0.5Cu solder joints was analyzed. The probability density curve of the logarithm of the fatigue life distribution can be easily obtained for a certain acceleration level fixed on the acceleration level axis of the CPDDS. The P–A–N curve was also obtained using the functions μ(A) and σ(A), which can reflect the regularity of the life data for an overall reliability P.

Inversion Theorem Based Kernel Density Estimation for the Ordinary Least Squares Estimator of a Regression Coefficient

The traditional confidence interval associated with the ordinary least squares estimator of linear regression coefficient is sensitive to non-normality of the underlying distribution. In this article, we develop a novel kernel density estimator for the ordinary least squares estimator via utilizing well-defined inversion based kernel smoothing techniques in order to estimate the conditional probability density distribution of the dependent random variable. Simulation results show that given a small sample size, our method significantly increases the power as compared with Wald-type CIs. The proposed approach is illustrated via an application to a classic small data set originally from Graybill (1961).

A New Method to Determine the Fatigue Limit and the p-S-N Curve

The performances of material fatigue can be illustrated by the S-N curve, the p-S-N curve and the fatigue limit, which are very important to engineering and the mechanical design. Recently, the author proposed a new method to determine a conditional probability density distribution surface(CPDDS) of the material, and the surface can reflects most properties of the material’s fatigue. Methods to obtain the theoretical fatigue limit and the p-S-N curve are introduced in this paper on the basis of previous study. The methods are applied on the fatigue test data of C45 steel, and the p-S-N curves that obtained by various methods are compared in this paper.

A methodology to determine a conditional probability density distribution surface from S–N data

A conditional probability density distribution surface (CPDDS) is constructed by two functions in this paper. One is the function of population mean and the stress level; the other is the function of standard deviation and the stress level. The surface represents the probability density curve of fatigue life changing with the stress level. A new definition of fatigue limit as well as the determination method is given in this paper according to the small probability event of CPDDS. The proposed method can save considerable cost and time in the determination of fatigue limit.

Estimate of the error in monitoring the energy release distribution on the basis of a conditional probability distribution density

It is shown by means of calculations and experiments that the generally accepted practice of using an unconditional instead of a conditional probability density distribution when estimating the error in monitoring the power in the fuel channels with the highest power density in the cores of a wide class of reactors with standard power monitoring error greater than 1.5% results in a systematic underestimation of the margin up to the limits for safe operation by up to approximately 5 and 10% for regimes with and without real-time optimization of the energy release distributions, respectively. This underestimation decreases to zero monotonically when the average power is used instead of the maximum power.

Fidelity of quantum interferometers

For a generic interferometer, the conditional probability density distribution, $p(\phi|m)$, for the phase $\phi$ given measurement outcome $m$, will generally have multiple peaks. Therefore, the phase sensitivity of an interferometer cannot be adequately characterized by the standard deviation, such as $\Delta\phi\sim 1/\sqrt{N}$ (the standard limit), or $\Delta\phi\sim 1/N$ (the Heisenberg limit). We propose an alternative measure of phase sensitivity--the fidelity of an interferometer--defined as the Shannon mutual information between the phase shift $\phi$\ and the measurement outcomes $m$. As an example application of interferometer fidelity, we consider a generic optical Mach-Zehnder interferometer, used as a sensor of a classical field. We find the surprising result that an entangled {\it N00N} state input leads to a lower fidelity than a Fock state input, for the same photon number.

Application of Heston model and its solution to German DAX data

We compare two well-known examples of stochastic volatility models, the Heston model and the Hull–White model. We derive the stationary probability density distribution of the variance. In addition, we apply this stationary solution to the probability density distribution of the logarithmic returns by using the conditional probability density distribution. Furthermore, we compare the received solutions of the logarithmic returns with empirical high-frequency data of DAX and its stocks.

Streaky Structures in a Turbulent Square-Duct Flow. Identification of Streaky Structures by Combined Flow Visualization-Velocity Measurement Techniques.

Streaky structures have been studied in a fully developed turbulent square-duct flow by using combined dye flow visualization-LDV velocity measurement techniques. Transverse distributions of low-speed streaks and mean streak spacing are shown in the near-wall region, i.e., yuτ/v < 25. At z/H < 0.16, the transverse distribution of the low-speed streaks is homogeneous and their spacing is about 90v/uτ, which suggests that the streaky structures near the wall bisector may be similar to those in turbulent boundary layers. In addition, the transverse distance between the visually identified low-speed streak and the velocity-measurement point was measured for each set of visual data. Conditioning the velocity fluctuations on this transverse distance, conditional probability density distributions of the axial, wall-normal and spanwise velocity fluctuations are shown. These distributions suggest the existence of quasi-streamwise vortical motions associated with the visualized streaky structures, their wall-normal dimension and the intermittency of their appearance.

GREEN'S FUNCTION FORMALISM IN GENERALIZED TAYLOR DISPERSION THEORY†

Green's function formalism is applied to obtain the asymptotically long-time solution of the multidimensional, phase-space, convective-diffusion equation governing transport and temporal evolution of the conditional probability density P of a Brownian tracer particle. In the long-time limit, P (as well as its infinite sequence of polyadic moments) is shown to be derivable from a pair of time-independent scalar fields characterizing the local-space transport process. These two functions are employed to obtain the global phenomenological coefficients occurring in the physical-space (global) equation governing the asymptotically long-time, locally-averaged, conditional probability density distribution

A Monte Carlo technique using a fast repetitive analog computer for determining lowest eigenvalues of partial differential equations for various boundaries, with applications

This paper describes a Monte Carlo technique for estimating the lowest eigenvalues of certain elliptic and hyperbolic partial differential equations with Dirichlet boundary conditions. (2) A stochastic process whose output conditional probability density distribution satisfies a partial differential equation similar to the partial differential equation under consideration is, along with the boundary conditions, implemented on ASTRAC II, a fast repetitive analog computer. Eight different boundaries on the scalar Helmholtz equation in one, two, and three-dimensional space were implemented. Each of the resulting eight lowest-eigenvalue estimates is then compared to its corresponding and expected true lowest eigenvalue. Computer hardware errors, along with the error resulting from the mathematical approximation employed in deriving the estimate, are indicated. Corrective measures are included when necessary. Applications result from a presentation of analogies relating the partial differential equations under consideration to partial differential equations modeling physical processes.

Statistical Studies on the Level Fluctuations of Random Noise (III) : Explicit Representation of the Conditional Probability Density Distribution of Randon Noise

Statistical Studies on the Level Fluctuations of Random Noise (III) : Explicit Representation of the Conditional Probability Density Distribution of Randon Noise

不規則Energy動揺に対する条件付確率分布関数の測定

We need, very often, to measure the joint probability distribution of many correlative random physical quantities in case when we observe simultaneously one or more waves having random phases (like random noise) at two or more different observation points that are different in time, position, frequency or propagation constant. If we call our particular attention to the effect of general correlations among their random physical quantities, it would be well to measure directly the conditional probability distribution rather than the joint probability distribution.This paper proposes a new method for obtaining sample points of the conditional probability distribution by using the combination of Schmitt trigger circuit and phantastron. We can vary the trigger level in Schmitt trigger circuit and the delay time by use of variable condensers at will. And then, this paper gives a series of photographs prepared to illustrate directly the effect of delay time τ on the wave form of output fluctuation by intensity modulation. Three explicit expressions of conditional probability density distribution for white noise, after passing a mean squaring circuit and an audio band-pass filter of arbitrary width, are experimentally derived in connection with an autocorrelation function of input noise. These are reasonably expressed in terms of Bessel-, Biased Γ-, and Γ-types of distribution.In this case, the conditional probability distribution for the above output fluctuation is theoretically treated as a probability problem of “distance” in an N-dimensional function space with N=2TW (W: frequency interval, T: time interval), where dsitance is taken as the mean squared fluctuation.The experimental and theoretical results described in this paper are also applicable to the other fields of measurement on random phenomena, since the mean energy is a universal physical quantity.