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Register a new userMaximum likelihood estimation of cloud height from multi-angle satellite imagery
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Ethan Anderes
Publication date
2009
fields
Mathematical Statistics
and research's language is
English
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We develop a new estimation technique for recovering depth-of-field from multiple stereo images. Depth-of-field is estimated by determining the shift in image location resulting from different camera viewpoints. When this shift is not divisible by pixel width, the multiple stereo images can be combined to form a super-resolution image. By modeling this super-resolution image as a realization of a random field, one can view the recovery of depth as a likelihood estimation problem. We apply these modeling techniques to the recovery of cloud height from multiple viewing angles provided by the MISR instrument on the Terra Satellite. Our efforts are focused on a two layer cloud ensemble where both layers are relatively planar, the bottom layer is optically thick and textured, and the top layer is optically thin. Our results demonstrate that with relative ease, we get comparable estimates to the M2 stereo matcher which is the same algorithm used in the current MISR standard product (details can be found in [IEEE Transactions on Geoscience and Remote Sensing 40 (2002) 1547--1559]). Moreover, our techniques provide the possibility of modeling all of the MISR data in a unified way for cloud height estimation. Research is underway to extend this framework for fast, quality global estimates of cloud height.
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Unlike the commonly used parametric regression models such as mixed models, that can easily violate the required statistical assumptions and result in invalid statistical inference, target maximum likelihood estimation allows more realistic data-generative models and provides double-robust, semi-parametric and efficient estimators. Target maximum likelihood estimators (TMLEs) for the causal effect of a community-level static exposure were previously proposed by Balzer et al. In this manuscript, we build on this work and present identifiability results and develop two semi-parametric efficient TMLEs for the estimation of the causal effect of the single time-point community-level stochastic intervention whose assignment mechanism can depend on measured and unmeasured environmental factors and its individual-level covariates. The first community-level TMLE is developed under a general hierarchical non-parametric structural equation model, which can incorporate pooled individual-level regressions for estimating the outcome mechanism. The second individual-level TMLE is developed under a restricted hierarchical model in which the additional assumption of no covariate interference within communities holds. The proposed TMLEs have several crucial advantages. First, both TMLEs can make use of individual level data in the hierarchical setting, and potentially reduce finite sample bias and improve estimator efficiency. Second, the stochastic intervention framework provides a natural way for defining and estimating casual effects where the exposure variables are continuous or discrete with multiple levels, or even cannot be directly intervened on. Also, the positivity assumption needed for our proposed causal parameters can be weaker than the version of positivity required for other casual parameters.
Over the past years, many applications aim to assess the causal effect of treatments assigned at the community level, while data are still collected at the individual level among individuals of the community. In many cases, one wants to evaluate the effect of a stochastic intervention on the community, where all communities in the target population receive probabilistically assigned treatments based on a known specified mechanism (e.g., implementing a community-level intervention policy that target stochastic changes in the behavior of a target population of communities). The tmleCommunity package is recently developed to implement targeted minimum loss-based estimation (TMLE) of the effect of community-level intervention(s) at a single time point on an individual-based outcome of interest, including the average causal effect. Implementations of the inverse-probability-of-treatment-weighting (IPTW) and the G-computation formula (GCOMP) are also available. The package supports multivariate arbitrary (i.e., static, dynamic or stochastic) interventions with a binary or continuous outcome. Besides, it allows user-specified data-adaptive machine learning algorithms through SuperLearner, sl3 and h2oEnsemble packages. The usage of the tmleCommunity package, along with a few examples, will be described in this paper.
We consider the problem of estimating the direction of arrival of a signal embedded in $K$-distributed noise, when secondary data which contains noise only are assumed to be available. Based upon a recent formula of the Fisher information matrix (FIM) for complex elliptically distributed data, we provide a simple expression of the FIM with the two data sets framework. In the specific case of $K$-distributed noise, we show that, under certain conditions, the FIM for the deterministic part of the model can be unbounded, while the FIM for the covariance part of the model is always bounded. In the general case of elliptical distributions, we provide a sufficient condition for unboundedness of the FIM. Accurate approximations of the FIM for $K$-distributed noise are also derived when it is bounded. Additionally, the maximum likelihood estimator of the signal DoA and an approximated version are derived, assuming known covariance matrix: the latter is then estimated from secondary data using a conventional regularization technique. When the FIM is unbounded, an analysis of the estimators reveals a rate of convergence much faster than the usual $T^{-1}$. Simulations illustrate the different behaviors of the estimators, depending on the FIM being bounded or not.
Consider a setting with $N$ independent individuals, each with an unknown parameter, $p_i in [0, 1]$ drawn from some unknown distribution $P^star$. After observing the outcomes of $t$ independent Bernoulli trials, i.e., $X_i sim text{Binomial}(t, p_i)$ per individual, our objective is to accurately estimate $P^star$. This problem arises in numerous domains, including the social sciences, psychology, health-care, and biology, where the size of the population under study is usually large while the number of observations per individual is often limited. Our main result shows that, in the regime where $t ll N$, the maximum likelihood estimator (MLE) is both statistically minimax optimal and efficiently computable. Precisely, for sufficiently large $N$, the MLE achieves the information theoretic optimal error bound of $mathcal{O}(frac{1}{t})$ for $t < clog{N}$, with regards to the earth movers distance (between the estimated and true distributions). More generally, in an exponentially large interval of $t$ beyond $c log{N}$, the MLE achieves the minimax error bound of $mathcal{O}(frac{1}{sqrt{tlog N}})$. In contrast, regardless of how large $N$ is, the naive plug-in estimator for this problem only achieves the sub-optimal error of $Theta(frac{1}{sqrt{t}})$.
We present a novel technique for estimating disk parameters (the centre and the radius) from its 2D image. It is based on the maximal likelihood approach utilising both edge pixels coordinates and the image intensity gradients. We emphasise the following advantages of our likelihood model. It has closed-form formulae for parameter estimating, requiring less computational resources than iterative algorithms therefore. The likelihood model naturally distinguishes the outer and inner annulus edges. The proposed technique was evaluated on both synthetic and real data.
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