On the Distinction Between the Conditional Probability and the Joint Probability Approaches in the Specification of Nearest-Neighbour Systems

Biometrika ◽  
1964 ◽  
Vol 51 (3/4) ◽  
pp. 481 ◽  
Author(s):  
D. Brook
Keyword(s):  
Conditional Probability ◽  
Joint Probability ◽  
Nearest Neighbour

scholarly journals Prediction suppression in monkey inferotemporal cortex depends on the conditional probability between images

2016 ◽  
Vol 115 (1) ◽  
pp. 355-362 ◽  
Author(s):  
Suchitra Ramachandran ◽  
Travis Meyer ◽  
Carl R. Olson
Keyword(s):  
Conditional Probability ◽  
Joint Probability ◽  
Inferotemporal Cortex ◽  
Fixed Sequence ◽  
Weak Response ◽  
Predictive Relations ◽  
Area Te

When monkeys view two images in fixed sequence repeatedly over days and weeks, neurons in area TE of the inferotemporal cortex come to exhibit prediction suppression. The trailing image elicits only a weak response when presented following the leading image that preceded it during training. Induction of prediction suppression might depend either on the contiguity of the images, as determined by their co-occurrence and captured in the measure of joint probability P( A, B), or on their contingency, as determined by their correlation and as captured in the measures of conditional probability P( A| B) and P( B| A). To distinguish between these possibilities, we measured prediction suppression after imposing training regimens that held P( A, B) constant but varied P( A| B) and P( B| A). We found that reducing either P( A| B) or P( B| A) during training attenuated prediction suppression as measured during subsequent testing. We conclude that prediction suppression depends on contingency, as embodied in the predictive relations between the images, and not just on contiguity, as embodied in their co-occurrence.

Study on the joint probability distribution of irrigation water volume and irrigation water efficiency

2015 ◽  
Vol 15 (4) ◽  
pp. 802-809
Author(s):  
Yong Zhao ◽  
Jinping Zhang ◽  
Weihua Xiao
Keyword(s):  
Probability Distribution ◽  
Conditional Probability ◽  
Irrigation Water ◽  
Joint Probability ◽  
Water Volume ◽  
Joint Probability Distribution ◽  
Water Efficiency ◽  
Copula Method ◽  
Joint Return ◽  
Water Volumes

Using the copula method, the joint probability distribution of irrigation water volume and efficiency is constructed, and their joint return period is also described to reveal the encounter probability of irrigation water volume and efficiency. Furthermore, the conditional probability of irrigation water efficiency with different water volumes is built to show the quantitative effects of flow on irrigation water efficiency. The results show that the copula-based function can present the encounter risk and conditional probability of irrigation water volume and efficiency at their different magnitudes.

New models for Markov random fields

1992 ◽  
Vol 29 (04) ◽  
pp. 877-884 ◽  
Author(s):  
Noel Cressie ◽  
Subhash Lele
Keyword(s):  
Random Field ◽  
Conditional Probability ◽  
Markov Random Field ◽  
Random Fields ◽  
Markov Random Fields ◽  
Sufficient Conditions ◽  
Joint Probability ◽  
Probability Models ◽  
Markov Random ◽  
New Models

The Hammersley–Clifford theorem gives the form that the joint probability density (or mass) function of a Markov random field must take. Its exponent must be a sum of functions of variables, where each function in the summand involves only those variables whose sites form a clique. From a statistical modeling point of view, it is important to establish the converse result, namely, to give the conditional probability specifications that yield a Markov random field. Besag (1974) addressed this question by developing a one-parameter exponential family of conditional probability models. In this article, we develop new models for Markov random fields by establishing sufficient conditions for the conditional probability specifications to yield a Markov random field.

Pseudo Independent Models

2011 ◽  
pp. 935-940
Author(s):  
Yang Xiang
Keyword(s):  
Probability Distribution ◽  
Computer System ◽  
Conditional Probability ◽  
Graphical Models ◽  
Intelligent Systems ◽  
Probabilistic Reasoning ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Conditional Probability Distribution ◽  
Binary Variables

Graphical models such as Bayesian networks (BNs) (Pearl, 1988) and decomposable Markov networks (DMNs) (Xiang, Wong & Cercone, 1997) have been applied widely to probabilistic reasoning in intelligent systems. Figure1 illustrates a BN and a DMN on a trivial uncertain domain: A virus can damage computer files, and so can a power glitch. A power glitch also causes a VCR to reset. The BN in (a) has four nodes, corresponding to four binary variables taking values from {true, false}. The graph structure encodes a set of dependence and independence assumptions (e.g., that f is directly dependent on v, and p but is independent of r, once the value of p is known). Each node is associated with a conditional probability distribution conditioned on its parent nodes (e.g., P(f | v, p)). The joint probability distribution is the product P(v, p, f, r) = P(f | v, p) P(r | p) P(v) P(p). The DMN in (b) has two groups of nodes that are maximally pair-wise connected, called cliques. Each clique is associated with a probability distribution (e.g., clique {v, p, f} is assigned P(v, p, f)). The joint probability distribution is P(v, p, f, r) = P(v, p, f) P(r, p) / P(p), where P(p) can be derived from one of the clique distributions. The networks, for instance, can be used to reason about whether there are viruses in the computer system, after observations on f and r are made.

New models for Markov random fields

1992 ◽  
Vol 29 (4) ◽  
pp. 877-884 ◽  
Author(s):  
Noel Cressie ◽  
Subhash Lele
Keyword(s):  
Random Field ◽  
Conditional Probability ◽  
Markov Random Field ◽  
Random Fields ◽  
Markov Random Fields ◽  
Sufficient Conditions ◽  
Joint Probability ◽  
Probability Models ◽  
Markov Random ◽  
New Models

The Hammersley–Clifford theorem gives the form that the joint probability density (or mass) function of a Markov random field must take. Its exponent must be a sum of functions of variables, where each function in the summand involves only those variables whose sites form a clique. From a statistical modeling point of view, it is important to establish the converse result, namely, to give the conditional probability specifications that yield a Markov random field. Besag (1974) addressed this question by developing a one-parameter exponential family of conditional probability models. In this article, we develop new models for Markov random fields by establishing sufficient conditions for the conditional probability specifications to yield a Markov random field.

scholarly journals Risk Analysis for Cascade Reservoirs Collapse Based on Bayesian Networks under the Combined Action of Flood and Landslide Surge

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Ping Li ◽  
Chuan Liang
Keyword(s):  
Monte Carlo ◽  
Conditional Probability ◽  
Normal Level ◽  
Joint Probability ◽  
Risk Calculation ◽  
Cascade Reservoirs ◽  
Dadu River ◽  
Combined Action ◽  
Mc Simulation ◽  
Dam Overtopping

A method based on a Bayesian network (BN) combined with stochastic Monte Carlo (MC) simulation is used in this research to calculate the probability and analyze the risk of a single reservoir dam overtopping and two reservoirs collapsing under the combined action of flood and landslide surge. Two adjacent cascade reservoirs on the Dadu River are selected for risk calculation and analysis. The results show that the conditional probability of a dam overtopping due to flooding in a single reservoir is relatively small; the conditional probability of a dam overtopping due to landslide surge in a single reservoir is relatively large; a combination of flooding and landslide surge greatly increases the risk of the dam overtopping. The conditional probability that the dam in (downstream) Changheba reservoir overtops as a result of a dam-break flood from (upstream) Houziyan reservoir is greater than 0.8 when the water in Changheba reservoir is at its normal level. Under the combined action of flooding and landslide surges, the joint probability that the two cascade reservoirs collapse in a variety of typical situations is very small.

scholarly journals Penerapan Metode Bayesian Network Model Untuk Menghitung Probabilitas Penyakit Sesak Nafas Bayi

2018 ◽  
Vol 2 (1) ◽  
pp. 62
Author(s):  
Hasniati Hasniati ◽  
Arianti Arianti ◽  
William Philip
Keyword(s):  
Probability Distribution ◽  
Bayesian Network ◽  
Conditional Probability ◽  
Network Model ◽  
Posterior Probability ◽  
Prior Probability ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Bayesian Network Model

Bayesian Network dapat digunakan untuk menghitung probabilitas dari kehadiran berbagai gejala penyakit. Dalam tulisan ini, penulis menerapkan bayesian network model untuk menghitung probabilitas penyakit sesak nafas pada bayi. Bayesian network diterapkan berdasar pada data yang diperoleh melalui wawancara kepada dokter spesialis anak yaitu data nama penyakit, penyebab, dan gejala penyakit sesak nafas pada bayi. Struktur Bayesian Network penyakit sesak nafas bayi dibuat berdasarkan ada tidaknya keterkaitan antara gejala terhadap penyakit sesak nafas. Untuk setiap gejala yang direpresentasikan pada struktur bayesian network mempunyai estimasi parameter yang didapat dari data yang telah ada atau pengetahuan dari dokter spesialis. Data estimasi ini disebut nilai prior probaility atau nilai kepercayaan dari gejala penyakit sesak nafas bayi. Setelah diketahui prior probability, langkah berikutnya adalah menentukan Conditional probability (peluang bersyarat) antara jenis penyakit sesak nafas dengan masing-masing gejalanya. Pada langkah akhir, nilai posterior probability dihitung dengan mengambil nilai hasil joint probability distribution (JPD) yang telah diperoleh, kemudian nilai inilah yang digunakan untuk menghitung probabilitas kemunculan suatu gejala. Dengan mengambil satu contoh kasus bahwa bayi memiliki gejala sesak, lemah, gelisah dan demam, disimpulkan bahwa bayi menderita penyakit sesak nafas Pneumoni Neonatal sebesar 0,1688812743.

Exact joint distribution of E h , E k and E h+k , and the probability for the positive sign of the triple product in the space group P\overline{1}

1986 ◽  
Vol 42 (4) ◽  
pp. 240-246 ◽  
Author(s):  
U. Shmueli ◽  
G. H. Weiss
Keyword(s):  
Conditional Probability ◽  
Joint Probability ◽  
Convergent Series ◽  
Exact Expression ◽  
Triple Product ◽  
Positive Sign ◽  
Hyperbolic Tangent ◽  
Space Group ◽  
Heterogeneous Models ◽  
Approximate Probability

A recently formulated method of deriving exact Fourier-series representations of joint probability density functions (p.d.f.'s) of several normalized structure factors is applied to the derivation of an exact expression for the conditional probability that the sign of the triple product E h E k E h + k is positive. The relevant joint and conditional probabilities are derived for the space group P\bar 1. The Fourier coefficients of the p.d.f. are given by rapidly convergent series of Bessel functions, and the convergence properties of the Fourier summations are also found to be favourable. The exact conditional probability is compared with the currently employed approximate one, well known as the hyperbolic tangent formula, for several hypothetical structures. The examples illustrate the effects of the number of atoms in the unit cell, the magnitude of the E values and the atomic composition on the exact and approximate probabilities. It is found, in agreement with previous studies, that the hyperbolic tangent formula may indeed significantly underestimate the probability when the number of equal atoms is small and the E values are only moderately large, and when the structure contains outstandingly heavy atoms. The opposite behaviour, i.e. the approximate probability overestimating the exact one, was not observed in the present calculations. For large values of the triple product in equal-atom and heterogeneous models, the agreement between the approximate and exact probabilities is usually good.

Joint, Marginal, and Conditional Probability

2019 ◽  
pp. 11-26
Author(s):  
Therese M. Donovan ◽  
Ruth M. Mickey
Keyword(s):  
Conditional Probability ◽  
Human Population ◽  
Joint Probability ◽  
Marginal Probability ◽  
Venn Diagrams ◽  
First Metatarsal ◽  
Eye Dominance ◽  
Independent Events ◽  
Second Metatarsal

This chapter introduces additional terms and concepts used in the study of probability, including Venn diagrams, independent events, and dependent events. The chapter focuses on two characteristics observed at the same time. In the example given in the chapter, the characteristics are eye dominance (i.e., left eye dominance or right eye dominance) and the presence or absence of “Morton’s toe” (Morton’s toe is a large second metatarsal which is longer than that the first metatarsal, or big toe; less than 20% of the human population has this condition). The chapter then analyses the distribution of these characteristics, both separately and simultaneously. In doing so, the chapter introduce the important concepts of joint probability, marginal probability, and conditional probability.

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