An Introduction to Probability, Statistics, and Uncertainty

Loucks, Daniel P.; Beek, Eelco van

doi:10.1007/978-3-319-44234-1_6

Cited by 17 publications

(13 citation statements)

References 122 publications

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“…To handle wind's speed uncertainty, Bayesian network is one of the effective models [25]. Bayesian statistics apply probability to a statistical approach, and thus results in probability distribution rather than point estimates [10]. Machine learning-based Bayesian inference is implemented using PyMC3 & ArViZ from python library to deal with wind speed uncertainty through posterior distribution sampling.…”

Section: Bayesian Inference Statisticsmentioning

confidence: 99%

“…This necessitates a computationally competitive and efficient model to handle RE uncertainty. Owing to the development of the Markov chain Monte Carlo (MCMC) method, Bayesian inference statistics has become computationally effective and feasible to handle parameter uncertainty [9,10]. Bayesian inference, unlike other frequentist models, updates the priors' belief with new data and leads to the posterior distribution.…”

Section: Introductionmentioning

confidence: 99%

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PFR constrained energy storage and interruptible load scheduling under high RE penetration

Kushwaha¹,

Prakash

Bhakar³

et al. 2020

IET Generation, Transmission & Distribution

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Section: Bayesian Inference Statisticsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

PFR constrained energy storage and interruptible load scheduling under high RE penetration

Kushwaha¹,

Prakash

Bhakar³

et al. 2020

IET Generation, Transmission & Distribution

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“…is the critical value (1 − γ percent) of the central chi-squared distribution with N − 1 degrees of freedom and noncentrality parameter δ = 0, i.e., ( ) 2 shows an example chi-squared distribution with N − 1 = 3. The probability of having a value greater for any given γ and N can be found in(Loucks and van Beek 2017). Some commonly used critical values of chisquare distribution are listed inTable 2.…”

mentioning

confidence: 99%

Quantifying and Qualifying Alloys Based on Level of Homogenization: A U–10 wt% Mo Alloy Case Study

Wang

Fagan

et al. 2019

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“…"Processes that are not fully understood and, whose outcomes cannot be precisely predicted, are often call uncertain" (Loucks and van Beek, 2017). Most uncertainly rainfall is the key factor that determines the effectiveness of rain-fed agriculture.…”

Section: Incorporating Risk In Benefit-cost Analysismentioning

confidence: 99%

“…Probability distributions can be used to account for uncertainty (World Meteorological Organization, 2010). Randomness of a variable is a basic concept in probability theory and rainfall volume in the next month is a random variable of which the certain value cannot be predicted (Loucks and van Beek, 2017). The value is realised only after the event occurred, or expost.…”

Section: Incorporating Risk In Benefit-cost Analysismentioning

confidence: 99%

Weather variability and coconut production in Sri Lanka: state-contingent analysis

Jayalath¹

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Weather variability presents an external impediment that increases the uncertainty in crop production potential specially for perennial crops under rain-fed cultivation. In particular, increasing rainfall variability that has accompany climate change in the tropics is increasing production uncertainty exposing farmers to a range of risks. Producer behavior under uncertainty is theoretically advanced in Chambers and Quiggin (2000) with the development of the state-contingent approach. This theory advocates farmers manage uncertainty by allocating inputs into different states of nature. This will enhance farmers' capacity to choose variable production technologies to manage uncertainty associated with unexpected events as state-contingent production technologies are naturally more flexible. This thesis examines the application of a state-contingent model for coconut production to assess the impact of a changing climate on coconut production with a view to assess adaptation options for a production system involving long-lived crops. The analysis of production of perennial crops encounters the treatment of long gestation periods, gradual increase in yield over an extended maturation period and yield stabilization following maturity. In considering optimal resource allocation from an agricultural production system perspective, a) the nature of resource constraints, b) the appropriateness of production technology and c) decision makers managerial behaviour needs to be considered together. The analysis in this thesis integrates these three aspects, with a special focus on managing uncertainty in coconut production in Sri Lanka. Climate is a primary determinant of crop choice and weather variability is the major factor influencing agricultural productivity and uncertainty in production outcomes. To examine the impact of changes in climatological variables, rainfall and temperature, on coconut production, a production time series over 1950-2014 was used to identify variations and trends over time and their statistical significance. The graphical and statistical analyses undertaken proved useful in gaining a more complete understanding of how the production environment is changing in the short run as well as over the long run. It offered a sound basis to further consider effective adaptation options in agricultural production, especially long-lived assets such as coconuts, in response to changing states of climate, representing the natural environment in which production takes place. It was revealed that while climate change impacts are observable over longer time horizons, understanding the nature of such changes may allow farmers to adapt to more observable variations in weather over narrow time periods.

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An Introduction to Probability, Statistics, and Uncertainty

Cited by 17 publications

References 122 publications

PFR constrained energy storage and interruptible load scheduling under high RE penetration

PFR constrained energy storage and interruptible load scheduling under high RE penetration

Quantifying and Qualifying Alloys Based on Level of Homogenization: A U–10 wt% Mo Alloy Case Study

Weather variability and coconut production in Sri Lanka: state-contingent analysis

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