Compact representation of multivariate posterior probability distribution from simulated samples
First Claim
1. A computer-program product tangibly embodied in a non-transitory machine-readable storage medium, the computer-program product including, instructions operable to cause a computing device to perform operations including:
- order a plurality of un-normalized probability density functions (PDFs) by an un-normalized PDF value of each un-normalized PDF, wherein the plurality of un-normalized PDFs provides an approximation of a chain of draws of a set of simulated samples that have been generated from and provide an approximate representation of a probability distribution, wherein each draw comprises multiple parameters, and wherein the un-normalized PDF values of the plurality of un-normalized PDFs proportionally map to parameter values of the multiple parameters of the draws within the chain of draws;
select a subset of the plurality of un-normalized PDFs based on the subset of the plurality of un-normalized PDFs having un-normalized PDF values that correspond to specified iso-probability surfaces which map to a subset of the parameter values that are to be included in a subset of the set of simulated samples; and
transmit to another computing device an indication of at least one draw within the chain of draws comprising parameters having parameter values to include in the subset of the set of simulated samples, wherein the indication identifies the at least one draw by referring, to at least one un-normalized PDF of the plurality of un-normalized PDFs associated with the at least one draw.
1 Assignment
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Accused Products
Abstract
Various embodiments are directed to techniques for selecting a subset of a set of simulated samples. A computer-program product including instructions to cause a computing device to order a plurality of UPDFs by UPDF value, wherein the plurality of UPDFs is associated with a chain of draws of a set of simulated samples, wherein each draw comprises multiple parameters and the UPDF values map to parameter values of the parameters; select a subset of the plurality of UPDFs based on the subset of the plurality of UPDFs having UPDF values within a range corresponding to a range of parameter values to include in a subset of the set of simulated samples; and transmit an indication of a draw comprising parameters having parameter values to include in the subset of the set of simulated samples, wherein the indication identifies the draw by associated UPDF. Other embodiments are described and claimed.
12 Citations
28 Claims
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1. A computer-program product tangibly embodied in a non-transitory machine-readable storage medium, the computer-program product including, instructions operable to cause a computing device to perform operations including:
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order a plurality of un-normalized probability density functions (PDFs) by an un-normalized PDF value of each un-normalized PDF, wherein the plurality of un-normalized PDFs provides an approximation of a chain of draws of a set of simulated samples that have been generated from and provide an approximate representation of a probability distribution, wherein each draw comprises multiple parameters, and wherein the un-normalized PDF values of the plurality of un-normalized PDFs proportionally map to parameter values of the multiple parameters of the draws within the chain of draws; select a subset of the plurality of un-normalized PDFs based on the subset of the plurality of un-normalized PDFs having un-normalized PDF values that correspond to specified iso-probability surfaces which map to a subset of the parameter values that are to be included in a subset of the set of simulated samples; and transmit to another computing device an indication of at least one draw within the chain of draws comprising parameters having parameter values to include in the subset of the set of simulated samples, wherein the indication identifies the at least one draw by referring, to at least one un-normalized PDF of the plurality of un-normalized PDFs associated with the at least one draw. - View Dependent Claims (2, 3, 4)
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5. The computer-program product of claim the computing device caused to perform operations including:
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generate a portion of the chain and a portion of the plurality of un-normalized PDFs from a posterior probability distribution derived by a Bayesian analysis; and select parameter values of parameters of a draw of the portion of the chain to include in the subset of the set of simulated samples based on an association of the draw with an un-normalized PDF of the subset of the plurality of un-normalized PDFs.
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6. A computer-implemented method comprising:
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ordering, on a computing device, a plurality of un-normalized probability density functions (PDFs) by an un-normalized PDF value of each un-normalized PDF, wherein the plurality of un-normalized PDFs provides an approximation of a chain of draws of a set of simulated samples that have been generated from and provide an approximate representation of a probability distribution, wherein each draw comprises multiple parameters, and wherein the un-normalized PDF values of the plurality of un-normalized PDFs proportionally map to multivariate parameter values of the multiple parameters of the draws within the chain of draws; selecting, on the computing device, a subset of the plurality of un-normalized PDFs based on the subset of the plurality of un-normalized PDFs having un-normalized PDF values that correspond to specified iso-probability surfaces which map to a subset of the parameter values that are to be included in a subset of the set of simulated samples; and transmitting, from the computing device, to another computing device an indication of at least one draw within the chain of draws comprising parameters having parameter values to include in the subset of the set of simulated samples, wherein the indication identifies the at least one draw by referring to at least one un-normalized PDF of the plurality of un-normalized PDFs associated with the at least one draw. - View Dependent Claims (7, 8, 9, 10)
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11. A computer-program product tangibly embodied in a non-transitory machine-readable storage medium, the computer-program product including instructions operable to cause a computing device to perform operations including:
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generate a portion of a set of simulated samples from a posterior probability distribution, wherein the set of simulated samples comprises a chain of draws of parameters that provides an approximate representation of the posterior probability distribution; generate a portion of a set of un-normalized probability density functions (PDFs), wherein each un-normalized PDF of the set of un-normalized PDFs is associated with one of the draws of the chain of draws, wherein the set of un-normalized PDFs provides an approximation of the chain of draws, and wherein un-normalized PDF values of the set of un-normalized PDFs proportionally map to parameter values of the parameters of the draws within the chain of draws; transmit the portion of the set of un-normalized PDFs to a requesting device; select at least one draw of the chain to include in a subset of the set of simulated samples based on an indication from the requesting device of the at least one chain as included in the subset, wherein the indication specifies the at least one draw by at least one un-normalized PDF of the set of un-normalized PDFs, and wherein the at least one un-normalized PDF is associated with the at least one draw; and transmit parameter values of the at least one draw to the requesting device based on the indication. - View Dependent Claims (12, 13, 14, 15, 16)
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17. A computer-implemented method comprising:
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generating, at a computing device, a portion of a set of simulated samples from a posterior probability distribution, wherein the set of simulated samples comprises a chain of draws of parameters that provides an approximate representation of the posterior probability distribution; generating, at the computing device, a portion of a set of un-normalized probability density functions (PDFs), wherein each un-normalized PDF of the set of un-normalized PDFs is associated with one of the draws of the chain of draws, wherein the set of un-normalized PDFs provides an approximation of the chain of draws, and wherein un-normalized PDF values of the set of un-normalized PDFs proportionally map to parameter values of the parameters of the draws within the chain of draws; transmitting, from the computing device, the portion of the set of un-normalized PDFs to a requesting device; selecting, at the computing device, at least one draw of the chain to include in a subset of the set of simulated samples based on an indication from the requesting device of the at least one chain as included in the subset, wherein the indication specifies the at least one draw by at least one un-normalized PDF of the set of un-normalized PDFs, and wherein the at least one un-normalized PDF is associated with the at least one draw; and transmitting, from the computing device, parameter values of the at least one draw to the requesting device based on the indication. - View Dependent Claims (18, 19, 20, 21, 22)
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23. An apparatus comprising a processor and a storage to store instructions that, when executed by the processor, cause the processor to perform operations comprising:
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order a plurality of un-normalized probability density functions (PDFs) by an un-normalized PDF value of each un-normalized PDF, wherein the plurality of un-normalized PDFs provides an approximation of a chain of draws of a set of simulated samples that have been generated from and provide an approximate representation of a probability distribution, wherein each draw comprises multiple parameters, and wherein the un-normalized PDF values of the plurality of un-normalized PDFs proportionally map to multivariate parameter values of the multiple parameters of the draws within the chain of draws; select a subset of the plurality of un-normalized PDFs based on the subset of the plurality of un-normalized PDFs having un-normalized PDF values that correspond to specified iso-probability surfaces which map to a subset of the parameter values that are to be included in a subset of the set of simulated samples; and transmit to a computing device an indication of at least one draw within the chain of draws comprising parameters having parameter values to include in the subset of the set of simulated samples, wherein the indication identifies the at least one draw by referring to at least one un-normalized PDF of the plurality of un-normalized PDFs associated with the at least one draw. - View Dependent Claims (24, 25, 26, 27, 28)
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Specification