Astronomical energy spectrum fitting method based on Bayesian inference

Abstract

The invention relates to a Bayesian inference-based astronomical energy spectrum fitting method, which comprises the following steps of: firstly, constructing a photon time sequence energy spectrum fitting model for describing a celestial body source photon time sequence energy spectrum by applying an astronomical spectrometer, and then, constructing a photon time sequence energy spectrum fitting model for describing a celestial body source photon time sequence energy spectrum on the basis of iteration of a parameter group under Bayesian inference; and forming an optimal photon time sequence energy spectrum fitting model by taking the calculated value of the photon time sequence energy spectrum fitting model of the observation energy channels of each group of detectors under each wave band under single iteration at a specific moment, combining the observed value and the sum of fitting statistics representing the goodness of fit between the calculated value and the observed value in a statistical manner and taking convergence of the sum of fitting statistics as a target, so that the optimal photon time sequence energy spectrum fitting model is obtained. According to the scheme design, an energy spectrum fitting framework and a Bayesian inference algorithm are fused, and through improvement of algorithm performance and combination of a more universal energy spectrum fitting framework, the working efficiency of the energy spectrum fitting algorithm is optimized and improved, and the astronomical energy spectrum fitting accuracy is improved.

Description

Technical Field

[0001] The invention relates to an astronomical energy spectrum fitting method based on Bayesian inference, belonging to the technical field of astronomical band fitting. Background Art

[0002] Xspec is currently one of the most widely used technologies in the field of high-energy astronomical spectrum analysis and fitting. Xspec provides a rich physical model library that can fit and analyze various astronomical X-ray and gamma-ray spectrum data. Its main technical features include:

[0003] (1) Parameter estimation algorithm

[0004] 1) Xspec uses the Levenberg-Marquardt algorithm by default. The Levenberg-Marquardt algorithm is an iterative optimization algorithm commonly used for nonlinear least squares problems. It is a combination of the Gauss-Newton method and the gradient descent method. Its advantage is that it is applicable to linear and nonlinear models and does not require analytical calculations. Instead, it gradually approaches the optimal parameters through iterative optimization. Its disadvantage is that it is sensitive to the initial values ​​of the parameters and may fall into a local optimal solution.

[0005] 2) Xspec supports parameter exploration using the MCMC (Markov Chain Monte Carlo) sampling algorithm.

[0006] (2) Energy spectrum fitting architecture.

[0007] 1) Xspec supports joint analysis of multi-band (X-ray and gamma-ray) energy spectra.

[0008] 2) Xspec has built-in a large number of commonly used single-dimensional (frequency domain) astronomical spectrum models.

[0009] Although Xspec is currently a very widely used tool in the field of astronomical spectrum analysis, it still has many limitations.

[0010] (1) Limitations of parameter estimation algorithms.

[0011] 1) The Levenberg-Marquardt algorithm is a local algorithm. The fitting process may fall into the local minimum and fail to find the global best fit. Moreover, the fitting effect depends on the setting of the initial model parameters. This leads to the poor reliability of Xspec and the lack of sufficient stability and repeatability of its fitting results.

[0012] 2) The MCMC sampling algorithm in Xspec converges slowly and is not efficient for fitting complex multidimensional parameter spaces.

[0013] (2) Limitations of the energy spectrum fitting architecture.

[0014] 1) Xspec only supports the traditional single-dimensional model, that is, the model Just energy However, the energy spectra of many astronomical sources have time evolution phenomena, so the model fitting architecture needs to support multi-dimensional models. , thereby modeling the evolution of astronomical phenomena over time.

[0015] 2) Although Xspec supports user-defined models, it is difficult to integrate and use, resulting in weak scalability. Summary of the invention

[0016] The technical problem to be solved by the present invention is to provide an astronomical energy spectrum fitting method based on Bayesian inference, which adopts a more advanced Bayesian inference algorithm and a more general energy spectrum fitting architecture to significantly improve key indicators and better meet the needs of astronomical data analysis.

[0017] In order to solve the above technical problems, the present invention adopts the following technical solution: the present invention designs an astronomical energy spectrum fitting method based on Bayesian inference, uses an astronomical spectrometer, and according to the following steps A to B, fits the astronomical spectrum observation data to obtain the photon time series energy spectrum of the celestial source; Step A. Build including parameter groups , and a photon time series energy spectrum fitting model used to describe the photon time series energy spectrum of the celestial source, and then proceed to step B; Step B. Based on parameter group Iterations under Bayesian inference, with parameter sets in a single iteration The corresponding photon time series energy spectrum fitting model is used to calculate the calculated value of the photon time series energy spectrum fitting model of each group of detectors in each band at a specific moment, and the sum of the fitting statistics of the degree of fit between the calculated value and the observed value of each group of detectors in each band is calculated by combining the observed value of the photon time series energy spectrum of each group of detectors in each band at a specific moment. The optimal parameter group is obtained with the convergence of the sum of fitting statistics as the goal. , forming the best photon time series energy spectrum fitting model, that is, fitting the photon time series energy spectrum of the celestial source.

[0018] As a preferred technical solution of the present invention: in step A, constructing a parameter group , and used to describe the photon time series energy spectrum fitting model of astronomical source photon time series energy spectrum ,in, Indicates energy, Indicates time.

[0019] As a preferred technical solution of the present invention, the step B includes the following steps B1 to B4; Step B1. Based on parameter group The preset initial values ​​of each parameter in the update photon time series energy spectrum fitting model in all bands , and proceed to step B2; Step B2. For each group of detectors in each band, use the following formula: Calculate the observation energy of each group of detectors in each band at a specific time Calculated value of photon time series energy spectrum fitting model ,in, , Indicates the number of bands, , Indicates the number of detector groups, Indicates The photon time series spectrum fitting model in each band, Indicates Band The incident energy channel of the detector The corresponding energy range is Indicates Band The observation energy of the detector group is Indicates Band The observation energy of the detector At a specific moment The calculated value of the photon time series energy spectrum fitting model, Indicates Band The instrument response of the detector group, i.e. Band The effective detection area of ​​the group detector; then enter step B3; Step B3. Based on the observations of the astronomical spectrometer, the observation energy of each group of detectors in each band is obtained at a specific time. Observed values ​​of photon time series energy spectrum , according to the following formula: The sum of the fitting statistics of the degree of agreement between the calculated values ​​and the observed values ​​of each group of detectors in each band is calculated. ,in, Indicates Band The observation energy of the detector At a specific moment The observed value of the photon time series energy spectrum, Indicates Band Group detector characterization calculation value With observed value The fitting statistics of the goodness of fit between them; then proceed to step B4; Step B4. Judgment Whether it converges, if so, the sum of the minimum fitting statistics under multiple iterations is obtained The corresponding parameter group , that is, the optimal parameter group, constitutes the best photon time series energy spectrum fitting model; otherwise, based on Bayesian inference, update the parameter group The value of each parameter in and return to step B2.

[0020] As a preferred technical solution of the present invention: Based on Bayesian inference, in step B1, based on the parameter group The preset prior distribution of , set the initial values ​​of various parameters and update the photon time series energy spectrum fitting model, where: Represents the photon time series spectrum fitting model in all bands ; In step B3, based on the sum of the fitting statistics ,according to , calculate the likelihood function ,in, Represents the observed value of the photon time series energy spectrum of all detectors in all bands , Represents the photon time series energy spectrum fitting model In the parameter group The observed value of the photon time series energy spectrum can be obtained under The probability of In step B4, a Bayesian inference sampler is applied based on Not converged, the sampler is based on the prior distribution and the likelihood function Update parameter group The values ​​of the parameters in and return to step B2; based on Convergence, the sampler is based on the prior distribution under multiple iterations , likelihood function , combined with Bayesian evidence , that is, the photon time series energy spectrum fitting model In the prior distribution The observed value of the photon time series energy spectrum is obtained under The total probability is as follows: Get the posterior distribution , Represents the observed value based on the photon time series energy spectrum , the photon time series energy spectrum fitting model Parameter group The current knowledge of the parameters in the posterior distribution The sum of the corresponding minimum fitting statistics Parameter group is the optimal parameter set.

[0021] As a preferred technical solution of the present invention: the sampler of Bayesian inference is a tool for implementing Bayesian inference using computer language, which is based on the Markov chain-Monte Carlo algorithm or the nested sampling algorithm.

[0022] As a preferred technical solution of the present invention: in step B3, if the statistical distribution of the observed values ​​of the photon time series energy spectrum conforms to the chi-square ( ) distribution, then the sum of the fitting statistics The calculation formula is updated as follows: in, Indicates Band The observation energy of the detector At the moment Observation error of photon time series energy spectrum.

[0023] As a preferred technical solution of the present invention: in step B4, based on the optimal photon time series energy spectrum fitting model, , the goodness of fit is calculated, which characterizes the degree of explanation of the observed values ​​of the photon time series energy spectrum by the best photon time series energy spectrum fitting model, where, Indicates the total number of observation channels and parameter groups of all detectors in all bands The difference in the total number of parameters in .

[0024] The astronomical energy spectrum fitting method based on Bayesian inference described in the present invention adopts the above technical solution and has the following technical effects compared with the prior art: The present invention designs an astronomical energy spectrum fitting method based on Bayesian inference. The astronomical spectrometer is used to first construct a photon time series energy spectrum fitting model for describing the time series energy spectrum of celestial source photons. Then, based on the parameter group In the iteration under Bayesian inference, the calculated value of the photon time series energy spectrum fitting model of each group of detectors in each band at a specific moment in a single iteration is combined with the observed value, and the sum of the fitting statistics that statistically characterizes the degree of agreement between the calculated value and the observed value is statistically characterized. With the convergence of the sum of the fitting statistics as the goal, the optimal photon time series energy spectrum fitting model is constructed to fit the photon time series energy spectrum of the celestial source. The scheme design integrates the energy spectrum fitting architecture and the Bayesian inference algorithm. By improving the algorithm performance and combining it with a more general energy spectrum fitting architecture, the working efficiency of the energy spectrum fitting algorithm is optimized and improved, and the accuracy of astronomical energy spectrum fitting is improved; The astronomical energy spectrum fitting method based on Bayesian inference designed in the present invention provides sufficient stability and accuracy for the implementation of the solution by improving the algorithm performance; and the general model architecture involved can easily be compatible with multi-dimensional models, multi-band models and user-defined models. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a schematic diagram of the framework of the astronomical energy spectrum fitting method designed by the present invention based on Bayesian inference. DETAILED DESCRIPTION

[0026] The specific implementation modes of the present invention will be further described in detail below in conjunction with the accompanying drawings.

[0027] Regarding the detection of astronomical energy spectra, although spectrometers are used in astronomy to measure the energy spectra of astronomical sources, what the spectrometer actually obtains is not the true photon energy spectrum. , but the detector observes the energy channel Photon count in the energy channel , the detector response Characterizes the effective area of ​​the detector, which is proportional to the observed energy The incident energy channel The probability of a photon is and Corresponding to energy range and , the formula is described as follows: It is worth noting that in time-domain astrophysical processes, the true spectrum of celestial sources is a function that depends on time, but the existing traditional astronomical energy spectrum fitting technology does not take into account the time dependence of celestial energy spectra.

[0028] In applications, regarding the principle of spectrum fitting, the most important purpose of astronomical spectrum detection is to deduce the true photon spectrum of the astronomical source. Ideally, given the known observed spectrum and the detector response In the case of , the true energy spectrum can be derived by inversely solving formula (1) Unfortunately, this is not possible in general, since such inversions are often non-unique and unstable.

[0029] Regarding the above analysis, the present invention designs an astronomical spectrum fitting method based on Bayesian inference, using an astronomical spectrometer, specifically as follows Figure 1 As shown, the following steps A to B are performed to fit the astronomical spectrum observation data to obtain the photon time-series energy spectrum of the celestial source.

[0030] Step A. Build including parameter groups , and used to describe the photon time series energy spectrum fitting model of astronomical source photon time series energy spectrum , and proceed to step B; wherein, Indicates energy, Indicates time.

[0031] Step B. Based on parameter group Iterations under Bayesian inference, with parameter sets in a single iteration The corresponding photon time series energy spectrum fitting model is used to calculate the calculated value of the photon time series energy spectrum fitting model of each group of detectors in each band at a specific moment, and the sum of the fitting statistics of the degree of fit between the calculated value and the observed value of each group of detectors in each band is calculated by combining the observed value of the photon time series energy spectrum of each group of detectors in each band at a specific moment. The optimal parameter group is obtained with the convergence of the sum of fitting statistics as the goal. , forming the best photon time series energy spectrum fitting model, that is, fitting the photon time series energy spectrum of the celestial source.

[0032] In practical application, the above step B is specifically designed to execute the following steps B1 to B4.

[0033] Step B1. Based on Bayesian inference, according to the parameter set The preset prior distribution of , set the initial values ​​of each parameter, and update the photon time series energy spectrum fitting model in all bands , and proceed to step B2; wherein, Represents the photon time series spectrum fitting model in all bands .

[0034] Step B2. For each group of detectors in each band, use the following formula: Calculate the observation energy of each group of detectors in each band at a specific time Calculated value of photon time series energy spectrum fitting model ,in, , Indicates the number of bands, , Indicates the number of detector groups, Indicates The photon time series spectrum fitting model in each band, Indicates Band The incident energy channel of the detector The corresponding energy range is Indicates Band The observation energy of the detector group is Indicates Band The observation energy of the detector At a specific moment The calculated value of the photon time series energy spectrum fitting model, Indicates Band The instrument response of the detector group, i.e. Band The effective detection area of ​​the group detector; then enter step B3.

[0035] Step B3. Based on the observations of the astronomical spectrometer, the observation energy of each group of detectors in each band is obtained at a specific time. Observed values ​​of photon time series energy spectrum , according to the following formula: The sum of the fitting statistics of the degree of agreement between the calculated values ​​and the observed values ​​of each group of detectors in each band is calculated. ;in, Indicates Band The observation energy of the detector At a specific moment The observed value of the photon time series energy spectrum, Indicates Band Group detector characterization calculation value With observed value The fit statistic of the goodness of fit between the two.

[0036] In application, if the statistical distribution of the observed values ​​of the photon time series energy spectrum conforms to the chi-square ( ) distribution, then the sum of the fitting statistics The calculation formula is updated as follows: in, Indicates Band The observation energy of the detector At the moment Observation error of photon time series energy spectrum.

[0037] Based on the sum of fit statistics To obtain, press , calculate the likelihood function ,in, Represents the observed value of the photon time series energy spectrum of all detectors in all bands , Represents the photon time series energy spectrum fitting model In the parameter group The observed value of the photon time series energy spectrum can be obtained under The probability of ; then go to step B4.

[0038] Step B4. Judgment Is it convergent? If Convergence, then apply the Bayesian inference sampler, which is based on the prior distribution under multiple iterations , likelihood function , combined with Bayesian evidence , that is, the photon time series energy spectrum fitting model In the prior distribution The observed value of the photon time series energy spectrum is obtained under The total probability is as follows: Get the posterior distribution , Represents the observed value based on the photon time series energy spectrum , the photon time series energy spectrum fitting model Parameter group The current knowledge of the parameters in the posterior distribution The sum of the corresponding minimum fitting statistics Parameter group The optimal parameter group constitutes the optimal photon time series energy spectrum fitting model, that is, in further applications, the photon time series energy spectrum of the celestial source can be fitted through the optimal photon time series energy spectrum fitting model.

[0039] And in further analysis, based on the optimal photon time series energy spectrum fitting model, , calculate the goodness of fit, and use the goodness of fit to characterize the degree of explanation of the observed values ​​of the photon time series energy spectrum by the best photon time series energy spectrum fitting model, where, Indicates the total number of observation channels and parameter groups of all detectors in all bands The difference in the total number of parameters in .

[0040] like Not converged, apply Bayesian inference sampler, based on Bayesian inference, the sampler is based on the prior distribution and the likelihood function , update the parameter group The value of each parameter in and return to step B2.

[0041] In practical applications, the Bayesian inference sampler here is a tool that uses computer language to implement Bayesian inference, which is based on the Markov chain-Monte Carlo algorithm or the nested sampling algorithm.

[0042] In order to solve the limitations of Xspec in the spectrum fitting architecture, the above design scheme innovates the fitting architecture and achieves the following two points in the technical solution of the spectrum fitting architecture: In the field of time-domain astrophysics, the energy spectra of many celestial sources have time evolution phenomena. Therefore, the energy spectrum fitting architecture of the present invention takes into account the multi-dimensional (frequency domain and time domain) characteristics of the energy spectrum of celestial sources, and supports multi-dimensional models. , so that the time evolution characteristics of the energy spectrum of astronomical sources can be modeled; Many celestial sources have different characteristics in the radiation energy spectra of different bands. Therefore, when performing joint fitting of multi-band energy spectra, different theoretical models need to be adopted for energy spectra of different bands. Based on the above requirements, the present invention expands the formula as follows: It supports the joint fitting of multiple energy spectra and multiple models, and the energy spectrum fitting architecture is more general.

[0043] The present invention relates to Bayesian inference and the application of the Bayesian inference downsampler in the design. In particular, regarding Bayesian inference, in the process of energy spectrum fitting, how to obtain the best fit by minimizing the fitting statistic is the most important and also the most difficult step. Ideally, the minimum fitting statistic can be found by traversing each point in the multidimensional parameter space. Unfortunately, however, this is generally undesirable because this method greatly wastes computing resources, especially when the number of parameters is large, the required computing resources are extremely expensive. Therefore, people have developed a variety of fitting algorithms, such as the Levenberg-Marquardt algorithm used by Xspec, but this iterative optimization algorithm is sensitive to initial values ​​and is easily trapped in a local optimal solution.

[0044] In view of the high dimensionality and high complexity of physical models in astronomy, the above shortcomings will be further amplified. The present invention adopts the Bayesian inference algorithm for astronomical spectrum fitting. Bayesian inference is based on the Bayesian theorem, which updates the posterior distribution of parameters by combining the prior distribution of parameters, observation data and likelihood probability. That is, the Bayesian theorem is as follows: Application of Bayesian inference in energy spectrum fitting: In order to embed Bayesian inference into the above energy spectrum fitting framework, the following three elements are involved: Sampler: Sampler is a tool that implements Bayesian theorem using computer language. It is the most core element. Currently, samplers can be divided into two categories: one is based on Markov chain Monte Carlo algorithm, such as Python module emcee. Markov chain Monte Carlo algorithm constructs a Markov chain to make its stable distribution the posterior distribution of the parameter to be estimated, then selects the initial state, and migrates from one state to the next state through the transition probability of the Markov chain until the sample of the Markov chain converges to a stable distribution. The other is based on nested sampling algorithm, such as Fortran module Multinest. The nested sampling algorithm generates a set of initial samples, then selects samples according to the likelihood value threshold and regenerates samples under new restrictions, gradually compresses the sampling space and increases the likelihood value threshold. When the increase in likelihood value or the compression of sampling space reaches the predetermined convergence condition, the iteration is terminated. Finally, the samples of each iteration are used to calculate model evidence and posterior analysis. Both samplers only need prior functions and likelihood functions, and generate parameter posterior samples, so they can be used without distinction in energy spectrum fitting applications.

[0045] Prior function: The prior function is used to define the prior distribution of all parameters to be estimated and return the current parameter value The parameter prior distribution is generally uniform distribution, normal distribution, etc.

[0046] Likelihood function: The likelihood function defines and returns the model In the parameters Observed data The relationship between the probability, likelihood and fitting statistic is The fitting statistics generally use chi-square (assuming that the observed data is Gaussian distributed), cstat (assuming that the observed data and noise are both Poisson distributed), pgstat (assuming that the observed data is Poisson distributed and the noise is Gaussian distributed), etc.

[0047] The application of Bayesian inference has the following advantages: (1) Correctly handle the noise and uncertainty of astronomical observation data; (2) Integration of prior knowledge, which can incorporate astronomers’ prior knowledge into the parameter estimation process; (3) High flexibility, applicable to various complex models and high-dimensional parameter spaces; (4) Quantification of parameter uncertainty: the posterior distribution provides uncertainty information about parameter estimation; (5) Model evidence quantification, which allows easy model comparison.

[0048] The astronomical spectrum fitting method designed by the present invention based on Bayesian inference uses an astronomical spectrometer to first construct a photon time series spectrum fitting model for describing the time series spectrum of celestial source photons, and then based on the parameter group In the iteration under Bayesian inference, the calculated values ​​of the photon time series energy spectrum fitting model of each group of detectors in each band at a specific moment in a single iteration are combined with the observed values, and the sum of the fitting statistics that statistically characterizes the degree of fit between the calculated values ​​and the observed values ​​is taken. With the convergence of the sum of fitting statistics as the goal, the optimal photon time series energy spectrum fitting model is constructed, and the photon time series energy spectrum of the celestial source is obtained by fitting. The scheme design integrates the energy spectrum fitting architecture and the Bayesian inference algorithm. By improving the algorithm performance and combining it with a more general energy spectrum fitting architecture, the working efficiency of the energy spectrum fitting algorithm is optimized and improved, and the accuracy of astronomical energy spectrum fitting is improved.

[0049] The design improves the performance of the algorithm to provide sufficient stability and accuracy for the implementation of the solution; and the general model architecture involved can easily be compatible with multi-dimensional models, multi-band models and user-defined models; among them, the general form of the energy spectrum fitting architecture is proposed and implemented, namely , which supports the joint fitting of multiple energy spectra and multiple models at the same time, and can better characterize the multi-band characteristics of celestial sources. In addition, the energy spectrum fitting architecture proposed in this invention also supports multi-dimensional (time domain + frequency domain) models , which makes it possible to model the time evolution characteristics of the energy spectrum of celestial sources.

[0050] In addition, regarding the designed spectrum fitting algorithm, the Levenberg-Marquardt algorithm used by Xspec is a local algorithm. The fitting process may fall into the local minimum and fail to find the global best fit, and the fitting effect depends on the setting of the initial model parameters. The present invention adopts the Bayesian inference algorithm, which does not depend on the initial parameters, can obtain a global steady-state solution, is applicable to various complex models and high-dimensional parameter spaces, and provides richer statistical characteristics, such as parameter uncertainty and model evidence.

[0051] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. An astronomical energy spectrum fitting method based on Bayesian inference, characterized in that: Using an astronomical spectrometer, according to the following steps A to B, the astronomical spectrum observation data is fitted to obtain the photon time series energy spectrum of the celestial source; Step A. Build including parameter groups , and a photon time series energy spectrum fitting model used to describe the photon time series energy spectrum of the celestial source, and then proceed to step B; Step B. Based on parameter group Iterations under Bayesian inference, with parameter sets in a single iteration The corresponding photon time series energy spectrum fitting model is used to calculate the calculated value of the photon time series energy spectrum fitting model of each group of detectors in each band at a specific moment, and the sum of the fitting statistics of the degree of fit between the calculated value and the observed value of each group of detectors in each band is calculated by combining the observed value of the photon time series energy spectrum of each group of detectors in each band at a specific moment. The optimal parameter group is obtained with the convergence of the sum of fitting statistics as the goal. , forming the best photon time series energy spectrum fitting model, that is, fitting the photon time series energy spectrum of the celestial source.

2. The astronomical energy spectrum fitting method based on Bayesian inference according to claim 1, characterized in that: In step A, construct a parameter group , and used to describe the photon time series energy spectrum fitting model of astronomical source photon time series energy spectrum ,in, Indicates energy, Indicates time.

3. The astronomical energy spectrum fitting method based on Bayesian inference according to claim 2, characterized in that: The step B includes the following steps B1 to B4; Step B1. Based on parameter group The preset initial values ​​of each parameter in the update photon time series energy spectrum fitting model in all bands , and proceed to step B2; Step B2. For each group of detectors in each band, use the following formula: Calculate the observation energy of each group of detectors in each band at a specific time Calculated value of photon time series energy spectrum fitting model ,in, , Indicates the number of bands, , Indicates the number of detector groups, Indicates The photon time series spectrum fitting model in each band, Indicates Band The incident energy channel of the detector The corresponding energy range is Indicates Band The observation energy of the detector group is Indicates Band The observation energy of the detector At a specific moment The calculated value of the photon time series energy spectrum fitting model, Indicates Band The instrument response of the detector group, i.e. Band The effective detection area of ​​the group detector; then enter step B3; Step B3. Based on the observations of the astronomical spectrometer, the observation energy of each group of detectors in each band is obtained at a specific time. Observed values ​​of photon time series energy spectrum , according to the following formula: The sum of the fitting statistics of the degree of agreement between the calculated values ​​and the observed values ​​of each group of detectors in each band is calculated. ,in, Indicates Band The observation energy of the detector At a specific moment The observed value of the photon time series energy spectrum, Indicates Band Group detector characterization calculation value With observed value The fitting statistics of the goodness of fit between them; then proceed to step B4; Step B4. Judgment Whether it converges, if so, the sum of the minimum fitting statistics under multiple iterations is obtained The corresponding parameter group , that is, the optimal parameter group, constitutes the best photon time series energy spectrum fitting model; otherwise, based on Bayesian inference, update the parameter group The value of each parameter in and return to step B2.

4. The astronomical energy spectrum fitting method based on Bayesian inference according to claim 3, characterized in that: Based on Bayesian inference, in step B1, based on the parameter set The preset prior distribution of , set the initial values ​​of various parameters and update the photon time series energy spectrum fitting model, where: Represents the photon time series spectrum fitting model in all bands ; In step B3, based on the sum of the fitting statistics ,according to , calculate the likelihood function ,in, Represents the observed value of the photon time series energy spectrum of all detectors in all bands , Represents the photon time series spectrum fitting model In the parameter group The observed value of the photon time series energy spectrum can be obtained under The probability of In step B4, a Bayesian inference sampler is applied based on Not converged, the sampler is based on the prior distribution and the likelihood function Update parameter group The values ​​of the parameters in and return to step B2; based on Convergence, the sampler is based on the prior distribution under multiple iterations , likelihood function , combined with Bayesian evidence , that is, the photon time series energy spectrum fitting model In the prior distribution The observed value of the photon time series energy spectrum is obtained under The total probability is as follows: Get the posterior distribution , Represents the observed value based on the photon time series energy spectrum , the photon time series energy spectrum fitting model Parameter group The current knowledge of the parameters in the posterior distribution The sum of the corresponding minimum fitting statistics Parameter group is the optimal parameter set.

5. The astronomical energy spectrum fitting method based on Bayesian inference according to claim 4, characterized in that: The Bayesian inference sampler is a tool that implements Bayesian inference using computer language, which is based on the Markov Chain-Monte Carlo algorithm or the nested sampling algorithm.

6. The astronomical energy spectrum fitting method based on Bayesian inference according to claim 3, characterized in that: In step B3, if the statistical distribution of the observed values ​​of the photon time series energy spectrum conforms to the chi-square ( ) distribution, then the sum of the fitting statistics The calculation formula is updated as follows: in, Indicates Band The observation energy of the detector At the moment Observation error of photon time series energy spectrum.

7. The astronomical energy spectrum fitting method based on Bayesian inference according to claim 3, characterized in that: In step B4, based on the optimal photon time series energy spectrum fitting model, , the goodness of fit is calculated, which characterizes the degree of explanation of the observed values ​​of the photon time series energy spectrum by the best photon time series energy spectrum fitting model, where, Indicates the total number of observation channels and parameter groups of all detectors in all bands The difference in the total number of parameters in .

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