Dynamic Markov Assumption

Crop phenology is dynamic as it changes with times of the year. Such biophysical processes also look spectrally different to remote sensing satellites. Some crops may depict similar spectral properties if their phenology coincide, but differ later when their phenology diverge. Thus, conventional approaches that select only images from phenological stages where crops are distinguishable for classification, have low discrimination. In contrast, stacking images within a cropping season limits discrimination to a single feature space that can suffer from overlapping classes. Since crop backscatter varies with time, it can aid discrimination. Therefore, our main objective is to develop a crop sequence classification method using multitemporal TerraSAR-X images. We adopt first order markov assumption in undirected temporal graph sequence. This property is exploited to implement Dynamic Conditional Random Fields (DCRFs). Our DCRFs model has a repeated structure of temporally connected Conditional Random Fields (CRFs). Each node in the sequence is connected to its predecessor via conditional probability matrix. The matrix is computed using posterior class probabilities from association potential. This way, there is a mutual temporal exchange of phenological information observed in TerraSAR-X images. When compared to independent epoch classification, the designed DCRF model improved crop discrimination at each epoch in the sequence. However, government, insurers, agricultural market traders and other stakeholders are interested in the quantity of a certain crop in a season. Therefore, we further develop a DCRF ensemble classifier. The ensemble produces an optimal crop map by maximizing over posterior class probabilities selected from the sequence based on maximum F1-score and weighted by correctness. Our ensemble technique is compared to standard approach of stacking all images as bands for classification using Maximum Likelihood Classifier (MLC) and standard CRFs. It outperforms MLC and CRFs by 7.70% and 6.42% in overall accuracy, respectively.

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A hybrid landmark Aalen-Johansen estimator for transition probabilities in partially non-Markov multi-state models

Lifetime Data Analysis ◽

10.1007/s10985-021-09534-4 ◽

2021 ◽

Author(s):

Niklas Maltzahn ◽

Rune Hoff ◽

Odd O. Aalen ◽

Ingrid S. Mehlum ◽

Hein Putter ◽

...

Keyword(s):

Statistical Power ◽

Transition Probabilities ◽

Real Data ◽

Testing Procedure ◽

Data Application ◽

Stratification Method ◽

Model Complex ◽

Markov Assumption ◽

State Models ◽

Disability Education

AbstractMulti-state models are increasingly being used to model complex epidemiological and clinical outcomes over time. It is common to assume that the models are Markov, but the assumption can often be unrealistic. The Markov assumption is seldomly checked and violations can lead to biased estimation of many parameters of interest. This is a well known problem for the standard Aalen-Johansen estimator of transition probabilities and several alternative estimators, not relying on the Markov assumption, have been suggested. A particularly simple approach known as landmarking have resulted in the Landmark-Aalen-Johansen estimator. Since landmarking is a stratification method a disadvantage of landmarking is data reduction, leading to a loss of power. This is problematic for “less traveled” transitions, and undesirable when such transitions indeed exhibit Markov behaviour. Introducing the concept of partially non-Markov multi-state models, we suggest a hybrid landmark Aalen-Johansen estimator for transition probabilities. We also show how non-Markov transitions can be identified using a testing procedure. The proposed estimator is a compromise between regular Aalen-Johansen and landmark estimation, using transition specific landmarking, and can drastically improve statistical power. We show that the proposed estimator is consistent, but that the traditional variance estimator can underestimate the variance of both the hybrid and landmark estimator. Bootstrapping is therefore recommended. The methods are compared in a simulation study and in a real data application using registry data to model individual transitions for a birth cohort of 184 951 Norwegian men between states of sick leave, disability, education, work and unemployment.

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Almost Markovian processes from closed dynamics

Quantum ◽

10.22331/q-2019-04-30-136 ◽

2019 ◽

Vol 3 ◽

pp. 136 ◽

Cited By ~ 7

Author(s):

Pedro Figueroa-Romero ◽

Kavan Modi ◽

Felix A. Pollock

Keyword(s):

Systems Theory ◽

Closed System ◽

Weak Coupling ◽

Open Systems ◽

System Size ◽

Quantum Processes ◽

Global System ◽

Open Systems Theory ◽

Markovian Processes ◽

Markov Assumption

It is common, when dealing with quantum processes involving a subsystem of a much larger composite closed system, to treat them as effectively memory-less (Markovian). While open systems theory tells us that non-Markovian processes should be the norm, the ubiquity of Markovian processes is undeniable. Here, without resorting to the Born-Markov assumption of weak coupling or making any approximations, we formally prove that processes are close to Markovian ones, when the subsystem is sufficiently small compared to the remainder of the composite, with a probability that tends to unity exponentially in the size of the latter. We also show that, for a fixed global system size, it may not be possible to neglect non-Markovian effects when the process is allowed to continue for long enough. However, detecting non-Markovianity for such processes would usually require non-trivial entangling resources. Our results have foundational importance, as they give birth to almost Markovian processes from composite closed dynamics, and to obtain them we introduce a new notion of equilibration that is far stronger than the conventional one and show that this stronger equilibration is attained.

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A GENERIC PROBABILISTIC MODEL AND A HIERARCHICAL SOLUTION FOR SENSOR LOCALIZATION IN NOISY AND RESTRICTED CONDITIONS

ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences ◽

10.5194/isprs-archives-xli-b1-193-2016 ◽

2016 ◽

Vol XLI-B1 ◽

pp. 193-198

Author(s):

S. Ji ◽

X. Yuan

Keyword(s):

Kalman Filtering ◽

Optical Sensors ◽

Probabilistic Model ◽

Particle Filtering ◽

Bundle Adjustment ◽

Stochastic Errors ◽

Localization Model ◽

Markov Assumption ◽

Integrated Processing ◽

And Control

A generic probabilistic model, under fundamental Bayes’ rule and Markov assumption, is introduced to integrate the process of mobile platform localization with optical sensors. And based on it, three relative independent solutions, bundle adjustment, Kalman filtering and particle filtering are deduced under different and additional restrictions. We want to prove that first, Kalman filtering, may be a better initial-value supplier for bundle adjustment than traditional relative orientation in irregular strips and networks or failed tie-point extraction. Second, in high noisy conditions, particle filtering can act as a bridge for gap binding when a large number of gross errors fail a Kalman filtering or a bundle adjustment. Third, both filtering methods, which help reduce the error propagation and eliminate gross errors, guarantee a global and static bundle adjustment, who requires the strictest initial values and control conditions. The main innovation is about the integrated processing of stochastic errors and gross errors in sensor observations, and the integration of the three most used solutions, bundle adjustment, Kalman filtering and particle filtering into a generic probabilistic localization model. The tests in noisy and restricted situations are designed and examined to prove them.

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