scholarly journals Uncertainty Evaluation in Hydrological Frequency Analysis Based on Confidence Interval and Prediction Interval

Water ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 2554 ◽  
Author(s):  
Keita Shimizu ◽  
Tadashi Yamada ◽  
Tomohito J. Yamada
Keyword(s):  
Confidence Interval ◽  
Prediction Interval ◽  
Probability Distributions ◽  
Extreme Rainfall ◽  
Critical Values ◽  
Function Form ◽  
Acceptance Region ◽  
Probability Limit ◽  
Torrential Rainfall ◽  
Substantial Uncertainty

The shortage of extreme rainfall data gives substantial uncertainty to design rainfalls and causes predictions for torrential rainfall to deviate strongly from adopted probability distributions used in river planning. These torrential rainfalls are treated as outliers which existing studies do not evaluate. However, probability limit method test which its acceptance region expresses with high accuracy the range where observed ith order statistics could realize. Confidence interval which quantifies uncertainty of adopted distributions can be constructed by assuming that these critical values in both sides of the adopted region follow the same function form applied to actual observed data. Furthermore, its validity is proved through comparison of confidence interval derived from ensemble downscaling calculations. In addition, these critical values are almost in accordance with outliers in samples from the ensemble downscaling calculations. Therefore, prediction interval which expresses the range that an unknown observed datum can take is constructed by extrapolating the critical values for limit estimation of a future datum. In this paper, quantification method of uncertainty of design rainfall and occurrence risk of outliers in the traditional framework, using the proposed confidence interval and prediction interval, is shown. Moreover, their application to future climate by using Bayesian statistics is explained.

Time-average optimal constrained semi-Markov decision processes

1986 ◽  
Vol 18 (2) ◽  
pp. 341-359 ◽  
Author(s):  
Frederick J. Beutler ◽  
Keith W. Ross
Keyword(s):  
Transition Probabilities ◽  
Decision Processes ◽  
The State ◽  
Death Process ◽  
Birth And Death Process ◽  
Average Reward ◽  
Acceptance Region ◽  
Dynamic Programming Equation ◽  
Markov Decision ◽  
Time Average

Optimal causal policies maximizing the time-average reward over a semi-Markov decision process (SMDP), subject to a hard constraint on a time-average cost, are considered. Rewards and costs depend on the state and action, and contain running as well as switching components. It is supposed that the state space of the SMDP is finite, and the action space compact metric. The policy determines an action at each transition point of the SMDP.Under an accessibility hypothesis, several notions of time average are equivalent. A Lagrange multiplier formulation involving a dynamic programming equation is utilized to relate the constrained optimization to an unconstrained optimization parametrized by the multiplier. This approach leads to a proof for the existence of a semi-simple optimal constrained policy. That is, there is at most one state for which the action is randomized between two possibilities; at all other states, an action is uniquely chosen for each state. Affine forms for the rewards, costs and transition probabilities further reduce the optimal constrained policy to ‘almost bang-bang’ form, in which the optimal policy is not randomized, and is bang-bang except perhaps at one state. Under the same assumptions, one can alternatively find an optimal constrained policy that is strictly bang-bang, but may be randomized at one state. Application is made to flow control of a birth-and-death process (e.g., an M/M/s queue); under certain monotonicity restrictions on the reward and cost structure the preceding results apply, and in addition there is a simple acceptance region.

scholarly journals Gluten free pasta with natural ingredient of color and carotene source

2021 ◽  
Vol 10 (4) ◽  
pp. e21310413959
Author(s):  
Michele Scarton ◽  
Tatiane Ribeiro ◽  
Helena Teixeira Godoy ◽  
Jorge Herman Behrens ◽  
Pedro Henrique Campelo ◽  
...  
Keyword(s):  
Nutritional Value ◽  
Visual Analysis ◽  
Rice Flour ◽  
Gluten Free ◽  
Color Analysis ◽  
Acceptance Region ◽  
Instrumental Color ◽  
Technological Characteristics ◽  
Central Composite ◽  
Β Carotene

The gluten-free pasta (GFP) has a higher cost and is often brittle, pale, and poorly balanced in macro and micronutrients when compared to wheat-based pasta. This study aimed to use the biofortified sweet potato flour, a natural source of color and provitamin A ingredient, with rice flour, hydrolyzed soy protein concentrate, and carboxymethyl cellulose gum to produce GFP, using a central composite rotatable design with three factors (23) and the central point. The GFP were evaluated by instrumental color analysis, and visual analysis of technological characteristics (presence of cracks, defect, and shape aspect), used for selection. Three GFP were selected: E1, E2 and E12, which showed absence of breaks or defects and an intermediate aspect after cooking, which were submitted to nutritional, functional and sensory evaluations. These GFPs presented levels of β-carotene of 135.22, 292.04 and 147.54 µg/g (dry basis), respectively, and showed sensory overall liking means in the acceptance region (>4.5) with no significant differences among them. According to the penalty analysis, the parameters color and consistency penalized these averages. Therefore, optimizing the ingredients’ concentrations improved the nutritional value and the sensory acceptability of GFP.

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