A comparison of automatic histogram constructions

Davies, Laurie; Gather, Ursula; Nordman, Dan; Weinert, Henrike

doi:10.1051/ps:2008005

Cited by 15 publications

(22 citation statements)

References 38 publications

(53 reference statements)

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“…Stochastic complexity is found using the normalized maximum likelihood distribution. In [28], the performance of 11 different bin selection criteria were analyzed, among them variants of AIC, BIC and MDL. Here, all the criteria were used to calculate the optimal number of bins for 19 different density shapes and real data.…”

Section: Related Workmentioning

confidence: 99%

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Spherical Minimum Description Length

Herntier

Ihou

Smith

et al. 2018

Entropy

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We consider the problem of model selection using the Minimum Description Length (MDL) criterion for distributions with parameters on the hypersphere. Model selection algorithms aim to find a compromise between goodness of fit and model complexity. Variables often considered for complexity penalties involve number of parameters, sample size and shape of the parameter space, with the penalty term often referred to as stochastic complexity. Current model selection criteria either ignore the shape of the parameter space or incorrectly penalize the complexity of the model, largely because typical Laplace approximation techniques yield inaccurate results for curved spaces. We demonstrate how the use of a constrained Laplace approximation on the hypersphere yields a novel complexity measure that more accurately reflects the geometry of these spherical parameters spaces. We refer to this modified model selection criterion as spherical MDL. As proof of concept, spherical MDL is used for bin selection in histogram density estimation, performing favorably against other model selection criteria.

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Section: Related Workmentioning

confidence: 99%

“…Probably because of its prominence, approaches to bin selection for histograms are very popular, with many of the schemes deeply rooted in model selection theory [28,44]. Here, we consider histograms with equal bin width, also known as regular histograms.…”

Section: Case Study: Spherical MDL For Histogramsmentioning

confidence: 99%

Spherical Minimum Description Length

Herntier

Ihou

Smith

et al. 2018

Entropy

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“…the bin width δω can be found by applying an adequate algorithm that optimizes a given criterion (see e.g. Davies et al (2009)). This means that δω has an optimal value which depends on the MC data only.…”

Section: Discussionmentioning

confidence: 99%

The photo-electric current in laser-Doppler flowmetry by Monte Carlo simulations

2009

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Monte Carlo (MC) simulations significantly contributed to a better understanding of laser-Doppler flowmetry (LDF). Here it is shown that the data obtained from standard MC simulations can be reinterpreted and used to extract more information such as the photo-electric current (i(t)). This is important because i(t) is the starting point for evaluating any existing or new algorithm to be used in LDF instrumentation. This circumvents the tedious procedure of generating a specific model (often approximated if possible at all) each time a different algorithm is considered. By a series of tutorial examples, the influence of various parameters is investigated, e.g. sampling rate, total acquisition time and dc filtering. These cases also demonstrate the fundamental role played by the photons' random phase in the shaping of the LDF signal. In particular, it is demonstrated by MC simulation that when the number of photon-moving red blood cell interactions is too low, then the Siegert relation that exists between the field and photo-electric current autocorrelation functions does not hold. This is an important point because the validity of the Siegert relation is implicitly admitted in the majority of the classical analytical models for the autocorrelation function in LDF (the classical MC approach does not allow one to study this problem). The proposed method and examples could stimulate new ideas and help the scientific community develop, test and validate new approaches in LDF.

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“…Choosing M , in fact, corresponds to the well-studied, but nevertheless difficult, problem of choosing the number of bins in a regular histogram given a sample of data. Numerous approaches for solving this problem exist, see for example [20] and references therein.…”

Section: Parameter Choicesmentioning

confidence: 99%

Data-driven and adaptive statistical residual evaluation for fault detection with an automotive application

Svärd

Nyberg

Frisk

et al. 2014

Mechanical Systems and Signal Processing

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An important step in model-based fault detection is residual evaluation, where residuals are evaluated with the aim to detect changes in their behavior caused by faults. To handle residuals subject to time-varying uncertainties and disturbances, which indeed are present in practice, a novel statistical residual evaluation approach is presented. The main contribution is to base the residual evaluation on an explicit comparison of the probability distribution of the residual, estimated online using current data, with a no-fault residual distribution. The no-fault distribution is based on a set of a-priori known no-fault residual distributions, and is continuously adapted to the current situation. As a second contribution, a method is proposed for estimating the required set of no-fault residual distributions off-line from no-fault training data. The proposed residual evaluation approach is evaluated with measurement data on a residual for fault detection in the gas-flow system of a Scania truck diesel engine. Results show that small faults can be reliable detected with the proposed approach in cases where regular methods fail.

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A comparison of automatic histogram constructions

Cited by 15 publications

References 38 publications

Spherical Minimum Description Length

Spherical Minimum Description Length

The photo-electric current in laser-Doppler flowmetry by Monte Carlo simulations

Data-driven and adaptive statistical residual evaluation for fault detection with an automotive application

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