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IMP Reference Guide
2.10.0
The Integrative Modeling Platform
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Joint Student's t-distribution of Function. More...
#include <IMP/isd/FStudentT.h>
Inheritance diagram for IMP::isd::FStudentT:Joint Student's t-distribution of Function.
If a vector of values \(F(X)\) is jointly distributed according to the t distribution with shared center \(F(M)\), scale \(\sigma\), and degrees of freedom \(\nu\), then the vector \(X\) is distributed according to the F-t distribution, where \(F\) is a one-to-one (strictly monotonic) function.
For a vector \(X=\{x_1,...,x_N\}\) containing \(N\) observations, the joint F-t density is given by
\[ p(X \mid M, \sigma, \nu) = \frac{ \Gamma[(N + \nu) / 2]}{\Gamma[\nu / 2]} (\pi \nu)^{-N / 2} \sigma^{-N} J(X) \left[1 + \frac{t(X, M, \sigma)^2}{\nu} \right]^{-(N + \nu)/2}, \]
where
\[ J(X) = \left| \prod_{i=1}^N F'(x_i) \right|, \]
is a normalization factor according to the change of variables technique.
\[ t(X, M, \sigma)^2 = \frac{S_2(X) - 2 F(M) S_1(X) + N F(M)^2}{\sigma^2}, \]
and the minimally sufficient statistics are
\begin{align*} S_1(X) &= \sum_{i=1}^N F(x_i) \ S_2(X) &= \sum_{i=1}^N F(x_i)^2. \end{align*}
The degrees of freedom \(\nu\) controls the heaviness of the tails. When \(\nu = 1\), the F-t distribution becomes the F-Cauchy distribution. For very large \(\nu\), the F-t distribution approaches the F-Normal distribution. Set \(J(X)\) values to 1 for the joint t distribution.
Definition at line 61 of file FStudentT.h.
Public Member Functions | |
| FStudentT (Floats FXs, Floats JXs, double FM, double sigma, double nu, std::string name="FStudentT %1%") | |
| Create from observations vectors. More... | |
| FStudentT (double sumFX, double sumFX2, unsigned N, double LogJX, double FM, double sigma, double nu, std::string name="FStudentT %1%") | |
| Create from sufficient statistics. More... | |
| virtual double | evaluate_derivative_FM () const |
| Evaluate derivative of negative log-density wrt \(F(M)\). More... | |
| virtual double | evaluate_derivative_Fx (double Fx) const |
| Evaluate derivative of negative log-density wrt single \(F(x_i)\). More... | |
| Floats | evaluate_derivative_FX (const Floats FXs) const |
| Evaluate derivative of negative log-density wrt elements of \(F(X)\). More... | |
| virtual double | evaluate_derivative_LogJX () const |
| Evaluate derivative of negative log-density wrt \(\log J(X)\). More... | |
| virtual double | evaluate_derivative_nu () const |
| Evaluate derivative of negative log-density wrt \(\nu\). More... | |
| virtual double | evaluate_derivative_sigma () const |
| Evaluate derivative of negative log-density wrt \(\sigma\). More... | |
| double | get_FM () |
| double | get_LogJX () |
| unsigned | get_N () |
| double | get_nu () |
| double | get_sigma () |
| double | get_sumFX () |
| Get sufficient statistic for passed \(J(X)\) values. More... | |
| double | get_sumFX2 () |
| virtual std::string | get_type_name () const |
| virtual ::IMP::VersionInfo | get_version_info () const |
| Get information about the module and version of the object. More... | |
| void | set_FM (double v) |
| void | set_LogJX (double v) |
| void | set_N (unsigned v) |
| void | set_nu (double v) |
| void | set_sigma (double v) |
| void | set_sumFX (double v) |
| void | set_sumFX2 (double v) |
| void | update_cached_values () const |
| Update cached intermediate values. More... | |
| void | update_sufficient_statistics (Floats FXs, Floats JXs) |
| Update sufficient statistics with values and derivatives. More... | |
| Public Member Functions inherited from IMP::isd::OneDimensionalSufficientDistribution | |
| OneDimensionalSufficientDistribution (std::string name="OneDimensionalSufficientDistribution %1%") | |
| Constructor. More... | |
| double | evaluate () const |
| Get negative log-density using cached sufficient statistics. More... | |
| double | get_density () const |
| Get probability density using cached sufficient statistics. More... | |
| Floats | get_sufficient_statistics () const |
| void | update_sufficient_statistics (Floats vs) |
| Update cached sufficient statistics from data. More... | |
| Public Member Functions inherited from IMP::isd::Distribution | |
| Distribution (std::string name="Distribution %1%") | |
| Public Member Functions inherited from IMP::Object | |
| virtual void | clear_caches () |
| CheckLevel | get_check_level () const |
| LogLevel | get_log_level () const |
| void | set_check_level (CheckLevel l) |
| void | set_log_level (LogLevel l) |
| Set the logging level used in this object. More... | |
| void | set_was_used (bool tf) const |
| void | show (std::ostream &out=std::cout) const |
| const std::string & | get_name () const |
| void | set_name (std::string name) |
Protected Member Functions | |
| virtual double | do_evaluate () const |
| virtual Floats | do_get_sufficient_statistics () const |
| virtual void | do_update_sufficient_statistics (Floats FXs) |
| virtual void | do_update_sufficient_statistics (Floats FXs, Floats JXs) |
| Protected Member Functions inherited from IMP::isd::OneDimensionalSufficientDistribution | |
| virtual double | do_get_density () const |
| Protected Member Functions inherited from IMP::Object | |
| Object (std::string name) | |
| Construct an object with the given name. More... | |
| virtual void | do_destroy () |
| IMP::isd::FStudentT::FStudentT | ( | Floats | FXs, |
| Floats | JXs, | ||
| double | FM, | ||
| double | sigma, | ||
| double | nu, | ||
| std::string | name = "FStudentT %1%" |
||
| ) |
Create from observations vectors.
| [in] | FXs | Vector of N \(F(x)\) observations drawn independently from the same F-t distribution. |
| [in] | JXs | Vector of N derivatives of \(F(x)\) with respect to \(X\) vector. |
| [in] | FM | Center of F-Student t with respect to \(F(x)\). |
| [in] | sigma | Scale of F-Student t with respect to \(F(x)\). |
| [in] | nu | Degrees of freedom of Student t distribution. |
| [in] | name | Name. |
| IMP::isd::FStudentT::FStudentT | ( | double | sumFX, |
| double | sumFX2, | ||
| unsigned | N, | ||
| double | LogJX, | ||
| double | FM, | ||
| double | sigma, | ||
| double | nu, | ||
| std::string | name = "FStudentT %1%" |
||
| ) |
Create from sufficient statistics.
| [in] | sumFX | Sum of observations of \(F(x)\). |
| [in] | sumFX2 | Sum of observations of \(F(x)^2\). |
| [in] | N | Number of observations. |
| [in] | LogJX | Log of \(J(X)\). |
| [in] | FM | Center of F-t with respect to \(F(x)\). |
| [in] | sigma | Scale of F-t with respect to \(F(x)\). |
| [in] | nu | Degrees of freedom of Student t distribution. |
| [in] | name | Name. |
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virtual |
Evaluate derivative of negative log-density wrt \(F(M)\).
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virtual |
Evaluate derivative of negative log-density wrt single \(F(x_i)\).
\(F(x_i)\) represents an element of \(F(X)\). Since only the sufficient statistics are stored, this value must be provided.
Evaluate derivative of negative log-density wrt elements of \(F(X)\).
This is equivalent to though faster than running evaluate_derivative_Fx() on every element of \(F(X)\).
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virtual |
Evaluate derivative of negative log-density wrt \(\log J(X)\).
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virtual |
Evaluate derivative of negative log-density wrt \(\nu\).
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virtual |
Evaluate derivative of negative log-density wrt \(\sigma\).
| double IMP::isd::FStudentT::get_sumFX | ( | ) |
Get sufficient statistic for passed \(J(X)\) values.
Definition at line 141 of file FStudentT.h.
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virtual |
Get information about the module and version of the object.
Reimplemented from IMP::isd::OneDimensionalSufficientDistribution.
Definition at line 149 of file FStudentT.h.
| void IMP::isd::FStudentT::update_cached_values | ( | ) | const |
Update cached intermediate values.
This method is automatically called during evaluation. If evaluating derivatives after modifying parameters but before evaluation, this method must be manually called.
Update sufficient statistics with values and derivatives.
Definition at line 97 of file FStudentT.h.
