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| + | In addition to the [[table view of a result]] and the [[graph view of a result]], the [[Result window]] also offers seven '''''uncertainty views''''' for displaying various [[Evaluation Modes|probabilistic]] values. These uncertainty views can be selected from the icon in the top-left corner of a [[Result window]]. |
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| | + | Each probability value is associated with a characteristic icon, e.g. the miniature probability distribution [[File:Chapter 1.20.png]] indicates that '''''Probability Density''''' is selected: |
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| − | Every variable has a certain or deterministic value, which we term its [[mid]] value. Some variables, notably chance variables and variables that depend on chance variables, can also have an uncertain or probabilistic value, which we term its [[Evaluation Modes|prob]] value. A mid value is computed using the mid value of each variable it depends on or the median of any probability distribution. The mid value of a result is not necessarily the median of its probability distribution, but usually close.
| + | :[[File:Chapter 1.19.png]] |
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| − | The [[Result window]] offers seven '''''uncertainty views''''', including the mid value (which is not uncertain) and six ways to display a prob value. You can select the uncertainty views from a menu in the top-left corner of a [[Result window]]. Or you can select a variable, and select an uncertainty view option from the [[Result menu]].
| + | Clicking on the icon opens up a popup menu where the probability views can be changed: |
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| − | :[[File:Chapter2 17.png]] | + | :[[File:Chapter 1.21.png]] |
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| − | The checkmark indicates the currently selected view.
| + | Depending on the chosen probability mode, the [[Result window]] will display different probability curves: |
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| − | Here we illustrate each uncertainty view using the chance variable, <code>Rate_of_inflation</code>, defined as a normal distribution with a mean of 2.5 and a standard deviation of 1:
| + | :[[File:Chapter 1.22.png]] |
| − | :<code>Chance Rate_of_inflation := Normal(2.5, 1)</code> | |
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| − | ==Mid value==
| + | All uncertainty view options are explained in detail in the [[Uncertainty views]] chapter in the [[User Guide]] and in the [[Tutorial]] [[Tutorial: Open a model to browse#Displaying_alternative_uncertain_views|Displaying alternative uncertain views]]. |
| − | The [[mid]] value is the deterministic value, computed by using the median instead of any input probability distribution. It is computed very quickly compared to uncertain values. It is the only option available for a variable that is not probabilistic.
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| − | :[[File:Chapter2 18.png]]
| + | The probability options are also available in the [[Result menu]], so alternatively, you can select a variable, and then select an uncertainty view option from the [[Result menu]]. |
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| − | <tip title="Tip">A [[mid]] value is much faster to compute than a prob(abilistic) value, since it doesn’t use Monte Carlo simulation to compute a probabilistic sample. It is often useful to look first at the mid value of a variable as a quick sanity check. Then you might select an uncertainty view, which causes its prob value to be computed if it has not already been cached.</tip>
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| − | ==Mean value==
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| − | An estimate of the [[mean]] (or expected value) of the uncertain value, based on the random (Monte Carlo) sample.
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| − | :[[File:Chapter2 19.png]]
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| − | <tip title="Tip">The mean and the other uncertainty views below are estimates based on the Monte Carlo (or Latin hypercube) sample. The precision of these estimates depends on the sample size and the sampling method. A larger sample size gives higher precision and takes more time and memory to compute. You can '''modify the sample size ''' and sampling method in the [[Uncertainty Setup dialog]] from the [[Result menu]].</tip>
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| − | ==Statistics==
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| − | A table of statistics of the uncertain value, usually, the minimum, median, mean, maximum, and standard deviation, estimated from the random sample. You can select which statistics to show in the '''Statistics tab''' of the [[Uncertainty Setup dialog]] from the [[Result menu]].
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| − | :[[File:Chapter2 20.png]]
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| − | '''Probability bands''': An array of percentiles ([[fractiles]]) estimated from the random sample, by default the 5%, 25%, 50%, 75%, and 95%iles. You can select which percentiles to show in the '''Probability Bands tab''' of the [[Uncertainty Setup dialog]] from the '''Result '''menu.
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| − | :[[File:Chapter2 21.png]]
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| − | ==Probability density==
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| − | Select '''probability density '''to display the uncertain distribution as a probability density function (PDF).
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| − | For a probability density function, it plots values of the quantity over the '''X''' (usually horizontal) axis, and probability density on the '''Y''' (vertical axis). Probability density shows the relative probability of different values. High values show probable regions; low values show less probable regions. The peak is the mode, the most probable value. If the density is zero, it is certain that the quantity will not have values in that range.
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| − | :[[File:Chapter2 22.png]]
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| − | ==Probability mass function==
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| − | If you select '''Probability density '''for a discrete variable, it displays the variable as a '''probability mass '''function (PMF) in a bar graph with the height of each bar indicating the probability of that value.
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| − | :[[File:Chapter2 23.png]]
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| − | Usually, it figures out whether to use a probability density or mass function. Very rarely, you might need to tell it the domain is discrete. See [[The domain attribute and discrete variables]] [[Choosing an appropriate distribution|Is the quantity discrete or continuous?]], and [[Probability density and mass graphs]] for more.
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| − | <div id="Cumulative_Probability">'''Cumulative probability''': The cumulative probability distribution ([[CDF]]) plots the possible values of the uncertain quantity along the '''X''' (usually horizontal) axis. The '''Y''' value (usually height) of the graph at each value of '''X''' shows the probability that the quantity is less than or equal to that '''X''' value. The CDF must start at a probability of 0 on the extreme left and increase to a probability of 1 on the extreme right, never decreasing.</div><br/>
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| − | The steeper the curve, the more likely the quantity will have a value in that region. The [[PDF]] is the slope (first derivative) of the [[CDF]]. Conversely, the [[CDF]] is the cumulative integral of the [[PDF]].
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| − | :[[File:Chapter2 24.png]]
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| − | ==Sample==
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| − | A [[sample]] is an array of the random values from the distribution generated by the Monte Carlo sampling process. The sample is the underlying form used to represent each uncertain quantity. All the other uncertainty views use statistics estimated from the sample. The sample view gives more detail than you usually want. You will likely want to view it mainly when verifying or debugging a model.
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| − | :[[File:Chapter2 25.png]]
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| − | Like any other graph, you can display a sample as a table by clicking [[File:Chapter2 4.png]] to see the underlying numerical values.
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| − | :[[File:Chapter2 26.png]]
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| | ==See Also== | | ==See Also== |
| | <div style="column-count:2;-moz-column-count:2;-webkit-column-count:2"> | | <div style="column-count:2;-moz-column-count:2;-webkit-column-count:2"> |
| | + | * [[Result window]] |
| | * [[Result menu]] | | * [[Result menu]] |
| − | * [[Result window]] | + | * [[Uncertainty views]] |
| | * [[Expressing Uncertainty]] | | * [[Expressing Uncertainty]] |
| | * Tutorial: [[Tutorial: Open a model to browse#Examining_and_changing_uncertain_input|Examining and changing uncertain input]] | | * Tutorial: [[Tutorial: Open a model to browse#Examining_and_changing_uncertain_input|Examining and changing uncertain input]] |
indicates that Probability Density is selected:
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