System and method for determining a probability distribution for a portfolio having a plurality of tasks

Abstract

A system and method for determining, from a portfolio having a plurality of tasks, possible values, for the portfolio, of one or more parameters shared across the plurality of tasks. A composite timeline is generated that encompasses each task timeline. Two or more probability distributions are received for each task, the probability distributions reflecting potential values of the one or more shared parameters at particular points on the composite timeline. The probability distributions for each task are used to calculate a bounded probability distribution for the portfolio.

1 . In a group of two or more objects, wherein the objects share one or more first parameters, a method of determining possible values, across the group of objects, of a selected one of the first parameters for one or more values of a second parameter, the method comprising:
 receiving two or more probability distributions for each object, each probability distribution reflecting potential values of the selected first parameter at a particular value of the second parameter;   selecting a value of the second parameter;   ascertaining, in a computing device and based on the probability distributions received for each object, a bounded probability distribution, for each object, of values of the selected first parameter at the selected value of the second parameter; and   determining, in a computing device, a composite bounded probability distribution for the selected first parameter across the group of objects at the selected value of the second parameter, wherein determining the composite bounded probability distribution includes performing a convolution on the bounded probability distribution of each object at the selected value of the second parameter,   wherein the composite bounded probability distribution defines, for the group of objects, a bounded probability distribution of values of the selected first parameter at the selected value of the second parameter, the composite bounded probability distribution representing likelihood for the group of objects of achieving particular values of the selected first parameter at the selected value of the second parameter.   
     
     
         2 . The method of  claim 1 , wherein the group of objects include a first object, and
 wherein ascertaining the bounded probability distribution for the first object at the selected value of the second parameter includes interpolating between two or more of the probability distributions received for the first object.   
     
     
         3 . The method of  claim 1 , wherein the objects include a first object, and
 wherein ascertaining the bounded probability distribution for the first object at the selected value of the second parameter includes extrapolating from two or more of the probability distributions received for the first object.   
     
     
         4 . The method of  claim 1 , wherein ascertaining includes applying rules to convert the received probability distributions to bounded probability distributions. 
     
     
         5 . The method of  claim 1 , wherein the group of objects includes a first object, and
 wherein determining the composite bounded probability distribution for the selected first parameter across the group of objects at the selected value of the second parameter further includes:
 modifying one or more of the probability distributions received for the first object under user control; and 
 displaying the determined composite bounded probability distribution, the composite bounded probability distribution based at least in part on the modified probability distributions. 
   
     
     
         6 . The method of  claim 5 , wherein modifying includes storing metadata annotating changes with a record of who made the changes. 
     
     
         7 . The method of  claim 1 , wherein determining the composite bounded probability distribution further includes:
 modifying the composite bounded probability distribution under user control; and   back propagating the modifications onto the probability distributions received for one or more of the objects.   
     
     
         8 . The method of  claim 1 , wherein each particular value of the second parameter is expressed as a probability distribution. 
     
     
         9 . The method of  claim 8 , wherein determining the composite bounded probability distribution further includes:
 applying rules to convert the probability distributions of the values of the second parameter to bounded probability distributions; and   performing a convolution over the bounded probability distributions of the values of the first and second parameter.   
     
     
         10 . The method of  claim 1 , wherein performing the convolution includes translating the bounded probability distributions of the objects, transforming the translated bounded probability distributions, multiplying the transformed bounded probability distributions to form a set of composite bounded probability distributions within a frequency domain, and performing an inverse transform on the set of composite bounded probability distributions. 
     
     
         11 . The method of  claim 1 , wherein the group of objects includes a first object, and
 wherein determining the composite bounded probability distribution for the selected first parameter across the group of objects at the selected value of the second parameter further includes:
 modifying one of the probability distributions received for the first object under user control; and 
 displaying the bounded probability distribution of the first object at the selected value of the second parameter, wherein the bounded probability distribution of the first object is a function of the modified probability distribution for the first object and of the one or more probability distributions received for the first object that were not modified. 
   
     
     
         12 . The method of  claim 1 , wherein the group of objects includes a first subgroup of objects and one or more second subgroups of objects, wherein each subgroup of objects includes two or more of the objects from the group of objects;
 wherein determining the composite bounded probability distribution for the group of objects further includes:
 determining a subgroup composite bounded probability distribution for each subgroup of objects, wherein determining the subgroup composite bounded probability distribution for each subgroup of objects includes performing a convolution based on one or more of the bounded probability distributions received for each object in the respective subgroup of objects; and 
   wherein performing the convolution on the bounded probability distribution of each object in the group of objects includes performing convolution on the subgroup composite bounded probability distributions such that the subgroup composite bounded probability distribution for the first subgroup of objects is given greater influence on the composite bounded probability distribution for the group of objects than the composite bounded probability distributions of the second subgroups of objects.   
     
     
         13 . The method of  claim 1 , wherein one or more of the bounded probability distributions received have 100% likelihood at a given scalar value of the first parameter,
 wherein performing the convolution on the bounded probability distribution of each object in the group of objects includes converting the bounded probability distribution for each object into a frequency domain using a transform only if the respective bounded probability distribution for the respective object does not have 100% likelihood at a given scalar value of the first parameter, and   wherein determining the composite bounded probability distribution further includes factoring the scalar value into the composite bounded probability distribution for the group of objects.   
     
     
         14 . The method of  claim 1 , wherein the group of objects further includes a parent object and two or more child objects, wherein each child object includes a bounded probability distribution of values of the first parameter, and
 wherein determining further includes determining a bounded probability distribution for the parent object as a composite bounded probability distribution of the bounded probability distributions of the child objects.   
     
     
         15 . The method of  claim 1 , wherein the composite bounded probability distribution has a shape, wherein performing the convolution includes:
 selecting a bounded probability distribution for each object;   determining a composite bounded probability distribution lower limit by summing lower limits of the selected bounded probability distributions;   determining a composite bounded probability distribution upper limit by summing upper limits of the selected bounded probability distributions;   calculating a span for each selected bounded probability distribution by subtracting the lower limit of the respective bounded probability distribution from the upper limit of the respective bounded probability distribution;   determining a maximum span from the calculated spans;   generating a periodic waveform for each selected bounded probability distribution, wherein generating the periodic waveform includes zero padding each of the selected bounded probability distributions out to a common wavelength greater than the maximum span;   transforming the periodic waveform generated for each of the selected bounded probability distributions into a frequency domain using a transform, wherein transforming the periodic waveform includes converting one wavelength of each periodic waveform into an array of points and transforming each array of points into the frequency domain;   performing complex multiplication of each transformed array of points to form an aggregate transformed array of points;   performing an inverse transform on the aggregate transformed array of points to form a periodic waveform result; and   converting one cycle of the periodic waveform result to an array of points defining the shape of the composite bounded probability distribution, and   wherein determining the composite bounded probability distribution further includes mapping the array of points defining the shape of the composite bounded probability distribution onto an interval defined by the composite bounded probability distribution lower limit and the composite bounded probability distribution upper limit.   
     
     
         16 . The method of  claim 15 , wherein mapping the array of points includes scaling the mapped array of points so than an integral across the mapped array of points is approximately equal to one. 
     
     
         17 . The method of  claim 15 , wherein each generated periodic waveform is translated along the first parameter axis such that the waveforms are in phase. 
     
     
         18 . The method of  claim 15 , wherein generating the periodic waveform includes zero padding to a common wavelength greater than or equal to approximately twice the maximum span. 
     
     
         19 . The method of  claim 15 , wherein selecting the bounded probability distribution for each object includes determining, for each object, a bounded probability distribution for the respective object. 
     
     
         20 . A system, comprising:
 a processor; and   a memory coupled to the processor, wherein the memory includes instructions that, when executed by the processor,
 define, for each object in a group of objects, two or more bounded probability distributions of values of a shared parameter, each probability distribution reflecting potential values of the shared parameter at a particular value of a second parameter; 
 select a value of the second parameter; 
 ascertain, based on the probability distributions received for each object, a bounded probability distribution, for each object, of values of the shared parameter at the selected value of the second parameter; and 
 determine, in a computing device, a composite bounded probability distribution for the selected first parameter across the group of objects at the selected value of the second parameter, wherein determining the composite bounded probability distribution includes performing a convolution on the bounded probability distribution of each object at the selected value of the second parameter, 
   wherein the composite bounded probability distribution defines, for the group of objects, a bounded probability distribution of values of the selected first parameter at the selected value of the second parameter, the composite bounded probability distribution representing likelihood for the group of objects of achieving particular values of the selected first parameter at the selected value of the second parameter.