Dynamical Mechanism of Sampling-Based Probabilistic Inference under Probabilistic Population Codes

2022 ◽  
pp. 1-24
Author(s):  
Kohei Ichikawa ◽  
Asaki Kataoka
Keyword(s):  
Dynamical Systems ◽  
Probability Distributions ◽  
Probabilistic Inference ◽  
Point Estimation ◽  
Accurate Estimation ◽  
Neural Basis ◽  
Optimal Point ◽  
Dynamical Mechanism ◽  
Noisy Information ◽  
Population Codes

Abstract Animals make efficient probabilistic inferences based on uncertain and noisy information from the outside environment. It is known that probabilistic population codes, which have been proposed as a neural basis for encoding probability distributions, allow general neural networks (NNs) to perform near-optimal point estimation. However, the mechanism of sampling-based probabilistic inference has not been clarified. In this study, we trained two types of artificial NNs, feedforward NN (FFNN) and recurrent NN (RNN), to perform sampling-based probabilistic inference. Then we analyzed and compared their mechanisms of sampling. We found that sampling in RNN was performed by a mechanism that efficiently uses the properties of dynamical systems, unlike FFNN. In addition, we found that sampling in RNNs acted as an inductive bias, enabling a more accurate estimation than in maximum a posteriori estimation. These results provide important arguments for discussing the relationship between dynamical systems and information processing in NNs.

scholarly journals Probability distributions for explaining hydrological losses in South Australian catchments

2013 ◽  
Vol 10 (4) ◽  
pp. 4597-4626
Author(s):  
S. H. P. W. Gamage ◽  
G. A. Hewa ◽  
S. Beecham
Keyword(s):  
Goodness Of Fit ◽  
Probability Distributions ◽  
Joint Probability ◽  
Accurate Estimation ◽  
Rainfall Runoff ◽  
Design Flood ◽  
Wide Variability ◽  
Multiple Variables ◽  
Two Parameter ◽  
Non Parametric

Abstract. The wide variability of hydrological losses in catchments is due to multiple variables that affect the rainfall-runoff process. Accurate estimation of hydrological losses is required for making vital decisions in design applications that are based on design rainfall models and rainfall-runoff models. Using representative single values of losses, despite their wide variability, is common practice, especially in Australian studies. This practice leads to issues such as over or under estimation of design floods. Probability distributions can be used as a better representation of losses. In particular, using joint probability approaches (JPA), probability distributions can be incorporated into hydrological loss parameters in design models. However, lack of understanding of loss distributions limits the benefit of using JPA. The aim of this paper is to identify a probability distribution function that can successfully describe hydrological losses in South Australian (SA) catchments. This paper describes suitable parametric and non-parametric distributions that can successfully describe observed loss data. The goodness-of-fit of the fitted distributions and quantification of the errors associated with quantile estimation are also discussed a two-parameter Gamma distribution was identified as one that successfully described initial loss (IL) data of the selected catchments. Also, a non-parametric standardised distribution of losses that describes both IL and continuing loss (CL) data were identified. The results obtained for the non-parametric methods were compared with similar studies carried out in other parts of Australia and a remarkable degree of consistency was observed. The results will be helpful in improving design flood applications.

Variation analysis driven by small-sample data for compliant aero-structure assembly

2019 ◽  
Vol 39 (1) ◽  
pp. 101-112 ◽  
Author(s):  
Biao Mei ◽  
Weidong Zhu ◽  
Yinglin Ke ◽  
Pengyu Zheng
Keyword(s):  
Probability Distributions ◽  
Small Sample ◽  
Accurate Estimation ◽  
Production Volume ◽  
Analysis Method ◽  
Variation Analysis ◽  
Content Type ◽  
Aircraft Manufacturing ◽  
Sample Data ◽  
Structure Assembly

Purpose Assembly variation analysis generally demands probability distributions of variation sources. However, due to small production volume in aircraft manufacturing, especially prototype manufacturing, the probability distributions are hard to obtain, and only the small-sample data of variation sources can be consulted. Thus, this paper aims to propose a variation analysis method driven by small-sample data for compliant aero-structure assembly. Design/methodology/approach First, a hybrid assembly variation model, integrating rigid effects with flexibility, is constructed based on the homogeneous transformation and elasticity mechanics. Then, the bootstrap approach is introduced to estimate a variation source based on small-sample data. The influences of bootstrap parameters on the estimation accuracy are analyzed to select suitable parameters for acceptable estimation performance. Finally, the process of assembly variation analysis driven by small-sample data is demonstrated. Findings A variation analysis method driven by small-sample data, considering both rigid effects and flexibility, is proposed for aero-structure assembly. The method provides a good complement to traditional variation analysis methods based on probability distributions of variation sources. Practical implications With the proposed method, even if probability distribution information of variation sources cannot be obtained, accurate estimation of the assembly variation could be achieved. The method is well suited for aircraft assembly, especially in the stage of prototype manufacturing. Originality/value A variation analysis method driven by small-sample data is proposed for aero-structure assembly, which can be extended to deal with other similar applications.

Resonance Analysis of Train–Track–Bridge Interaction Systems with Correlated Uncertainties

2019 ◽  
Vol 20 (01) ◽  
pp. 2050008 ◽  
Author(s):  
Lifeng Xin ◽  
Xiaozhen Li ◽  
Jiaxin Zhang ◽  
Yan Zhu ◽  
Lin Xiao
Keyword(s):  
Probability Distributions ◽  
Three Dimensional ◽  
Estimation Method ◽  
Interaction Model ◽  
Point Estimation ◽  
Statistical Characteristics ◽  
Resonance Analysis ◽  
Track Bridge ◽  
Point Estimation Method ◽  
Nataf Transformation

Over the last decades, the resonance-related dynamics for bridge systems subjected to a moving train has been researched and discussed from mechanics, physics and mathematics. In the current work, new perspectives of train-induced resonance analysis are investigated through introducing random propagation process into the train–bridge dynamic interactions. Besides, the Nataf-transformation-based point estimation method is applied to generate pseudorandom variables following arbitrarily correlated probability distributions. A three-dimensional (3D) nonlinear train-ballasted track–bridge interaction model founded on fundamental physical and mechanical principles is employed to convey and depict train–bridge interactions with random properties considered. After that, extensive applications are illustrated in detail for revealing the statistical characteristics of the so-called “random resonance”. Numerical results show that the critical train speeds associated with resonance and cancelation are random in essence owing to the variability of system parameters; the correlation between parameters exerts obvious influences on system dynamic behaviors; the last vehicle of a train will be in more violent vibrations compared to the front vehicles; the influences of track irregularities on the wheel–rail interactions are significantly greater than those of resonance.

A Simple Technique for the Rapid Estimation of the Optimal Support Locations for a Vibrating Plate

1992 ◽  
Vol 114 (1) ◽  
pp. 112-118 ◽  
Author(s):  
J. M. Pitarresi ◽  
R. J. Kunz
Keyword(s):  
Simple Technique ◽  
Optimization Theory ◽  
Nonlinear Least Squares ◽  
Response Surfaces ◽  
Accurate Estimation ◽  
Optimal Point ◽  
Spreadsheet Program ◽  
Rapid Estimation ◽  
Least Squares Fit ◽  
Vibrating Plates

This paper is aimed at presenting a simple technique for the rapid estimation of the optimal point support locations of vibrating plates. Using a two-dimensional nonlinear least-squares fit of natural frequency versus support location data, along with the concept of response surfaces, a difficult design optimization problem involving changing boundary conditions is transformed to a much simpler, approximate form. By using classical optimization theory, the estimated optimal location of the support can then be readily found. The computations for the formation of the response function and its optimum can be readily carried out on a personal computer using a spreadsheet program. The validity of this approach is demonstrated through a number of examples using analytical, computational, and experimental data. The technique is well suited to preliminary design investigations where a rapid but accurate estimation of the support location is required. Finally, a key advantage of the proposed method is that it can be used with data from any analytical, computational, or experimental effort, including any combination of the above.

scholarly journals Dynamic population coding and its relationship to working memory

2018 ◽  
Vol 120 (5) ◽  
pp. 2260-2268 ◽  
Author(s):  
Ethan M. Meyers
Keyword(s):  
Working Memory ◽  
Population Coding ◽  
Future Research ◽  
Neural Basis ◽  
Firing Rates ◽  
Sustained Activity ◽  
Early Results ◽  
Population Codes ◽  
Dynamic Population ◽  
Insight Into

For over 45 years, neuroscientists have conducted experiments aimed at understanding the neural basis of working memory. Early results examining individual neurons highlighted that information is stored in working memory in persistent sustained activity where neurons maintained elevated firing rates over extended periods of time. However, more recent work has emphasized that information is often stored in working memory in dynamic population codes, where different neurons contain information at different periods in time. In this paper, I review findings that show that both sustained activity as well as dynamic codes are present in the prefrontal cortex and other regions during memory delay periods. I also review work showing that dynamic codes are capable of supporting working memory and that such dynamic codes could easily be “readout” by downstream regions. Finally, I discuss why dynamic codes could be useful for enabling animals to solve tasks that involve working memory. Although additional work is still needed to know definitively whether dynamic coding is critical for working memory, the findings reviewed here give insight into how different codes could contribute to working memory, which should be useful for guiding future research.

Determining the Information Flow of Dynamical Systems from Continuous Probability Distributions

1997 ◽  
Vol 78 (12) ◽  
pp. 2345-2348 ◽  
Author(s):  
Gustavo Deco ◽  
Christian Schittenkopf ◽  
Bernd Schürmann
Keyword(s):  
Dynamical Systems ◽  
Information Flow ◽  
Probability Distributions

The joint probability distribution function of structure factors with rational indices. IV. The P1 case

1999 ◽  
Vol 55 (3) ◽  
pp. 512-524
Author(s):  
Carmelo Giacovazzo ◽  
Dritan Siliqi ◽  
Cristina Fernández-Castaño
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Probabilistic Approach ◽  
Joint Probability ◽  
Distribution Functions ◽  
Accurate Estimation ◽  
Joint Probability Distribution ◽  
Structure Factors ◽  
Joint Probability Distributions ◽  
The Hilbert Transform

The method of the joint probability distribution functions of structure factors has been extended to reflections with rational indices. The most general case, space group P1, has been considered. The positional parameters are the primitive random variables of our probabilistic approach, while the reflection indices are kept fixed. Quite general joint probability distributions have been considered from which conditional distributions have been derived: these proved applicable to the accurate estimation of the real and imaginary parts of a structure factor, given prior information on other structure factors. The method is also discussed in relation to the Hilbert-transform techniques.

Seismic inversion of a carbonate buildup: A case study

2017 ◽  
Vol 5 (4) ◽  
pp. T641-T652 ◽  
Author(s):  
Mark Sams ◽  
Paul Begg ◽  
Timur Manapov
Keyword(s):  
Seismic Data ◽  
Probability Distributions ◽  
Low Frequency ◽  
Rock Physics ◽  
Seismic Inversion ◽  
Accurate Estimation ◽  
Amplitude Analysis ◽  
Simultaneous Inversion ◽  
Band Limited ◽  
Using Data

The information within seismic data is band limited and angle limited. Together with the particular physics and geology of carbonate rocks, this imposes limitations on how accurately we can predict the presence of hydrocarbons in carbonates, map the top carbonate, and characterize the porosity distribution through seismic amplitude analysis. Using data for a carbonate reef from the Nam Con Son Basin, Vietnam, the expectations based on rock-physics analysis are that the presence of gas can be predicted only when the porosity at the top of the carbonate is extremely high ([Formula: see text]), but that a fluid contact is unlikely to be observed in the background of significant porosity variations. Mapping the top of the carbonate (except when the top carbonate porosities are low) or a fluid contact requires accurate estimates of changes in [Formula: see text]. The seismic data do not independently support such an accurate estimation of sharp changes in [Formula: see text]. The standard approach of introducing low-frequency models and applying rock-physics constraints during a simultaneous inversion does not resolve the problems: The results are heavily biased by the well control and the initial interpretation of the top carbonate and fluid contact. A facies-based inversion in which the elastic properties are restricted to values consistent with the facies predicted to be present removes the well bias, but it does not completely obviate the need for a reasonably accurate initial interpretation in terms of prior facies probability distributions. Prestack inversion improves the quality of the facies predictions compared with a poststack inversion.

scholarly journals Bayesian Change Point Estimation Based on Masked Data in Exponential Distribution Parallel System

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Exponential Distribution ◽  
Gibbs Sampling ◽  
Change Point ◽  
Latent Variables ◽  
Likelihood Function ◽  
Probability Distributions ◽  
Qualitative Change ◽  
Parallel System ◽  
Point Estimation ◽  
Unknown Parameters

Change point reflects a qualitative change in things. It has gained some applications in the field of reliability. In order to estimate the position parameters of the change point, a Bayesian change point model based on masked data and Gibbs sampling was proposed. By filling in missing lifetime data and introducing latent variables, the simple likelihood function is obtained for exponential distribution parallel system under censored data. This paper describes the probability distributions and random generation methods of the missing lifetime variables and latent variables, and obtains the full conditional distributions of the change point position parameters and other unknown parameters. By Gibbs sampling and estimation of unknown parameters, the estimates of the mean, median, and quantile of the parameter posterior distribution are obtained. The specific steps of Gibbs sampling are introduced in detail. The convergence of Gibbs sampling is also diagnosed. Random simulation results show that the estimations are fairly accurate.

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