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| | Poisson (const unsigned &n, const unsigned &num_dims) |
| | The constructor. More...
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| virtual void | NegLoglikelihood (double &objvalue, Eigen::VectorXd &Gradient) |
| | Negative loglikelihood of homogeneous Poisson process. More...
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| virtual double | Intensity (const double &t, const Sequence &data, Eigen::VectorXd &intensity_dim) |
| | The intensity of each dimension for a homogeneous Poisson process is a constant \(\lambda^0_n\). More...
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| virtual double | IntensityUpperBound (const double &t, const double &L, const Sequence &data, Eigen::VectorXd &intensity_upper_dim) |
| | Returns the upper bound of the summation of the intensity value on each dimension from time t to t + L given the history of past events in sequence data. Let \({\lambda_d^*(t)}\) be the conditional intensity function on the d-th dimension where \(d=1\dotso D\), and num_dims_ = D. This function returns
\begin{align} \lambda_0^D(t) \geq \sum_{d=1}^D\sup_{\tau\in[t, t + \tau(t)]}\lambda^*_d(\tau), \end{align}
where the returned value \(\lambda_0^D(t)\) will be used for Ogata's Thinning algorithm. More...
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| virtual double | IntensityIntegral (const double &lower, const double &upper, const Sequence &data) |
| | Returns the integral of the intensity function \(\int_{a}^b\lambda^*(\tau)d\tau\) where \(a = lower\) and \(b = upper\). More...
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| virtual void | Gradient (const unsigned &k, Eigen::VectorXd &gradient) |
| | Returns the gradient w.r.t. the model parameters on the k-th sequence. More...
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| virtual double | PredictNextEventTime (const Sequence &data, const unsigned &num_simulations) |
| | Predict the next event timing by the expectation \(\int_{t_n}^\infty tf^*(t)dt\). Currently, we use the sample average by simulations to approximate the expectation since the conditional density \(f^*(t)\) normally does not have an analytic form. More...
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| void | fit (const std::vector< Sequence > &data) |
| | Maximum likelihood estimation for the model parameters. More...
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| | IProcess (const unsigned &n, const unsigned &num_dims) |
| | The constructor. More...
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| const Eigen::VectorXd & | GetParameters () |
| | Return the column vector of model parameters. More...
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| unsigned | GetNumDims () |
| | Return the number of dimensions in the process. More...
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| void | SetParameters (const Eigen::VectorXd &v) |
| | Set the model parameters. More...
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| void | PlotIntensityFunction (const Sequence &data) |
| | Plots the intensity functions based on the given sequence. It plots the intensity function and the associated event points up of each dimension in the same figure. More...
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| void | PlotIntensityFunction (const Sequence &data, const unsigned &dim_id) |
| | Plots the intensity function and the associated event points of the dimension dim_id. More...
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Poisson implements the multivariate homogeneous process.
Definition at line 17 of file Poisson.h.
| double Poisson::IntensityUpperBound |
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const double & |
t, |
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const double & |
L, |
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const Sequence & |
data, |
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Eigen::VectorXd & |
intensity_upper_dim |
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Returns the upper bound of the summation of the intensity value on each dimension from time t to t + L given the history of past events in sequence data. Let \({\lambda_d^*(t)}\) be the conditional intensity function on the d-th dimension where \(d=1\dotso D\), and num_dims_ = D. This function returns
\begin{align} \lambda_0^D(t) \geq \sum_{d=1}^D\sup_{\tau\in[t, t + \tau(t)]}\lambda^*_d(\tau), \end{align}
where the returned value \(\lambda_0^D(t)\) will be used for Ogata's Thinning algorithm.
- Parameters
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| t | the starting time. |
| L | the duration. |
| data | the given sequence of the past events until time t. |
| intensity_upper_dim | a column vector of size num_dims_ storing the upper bound of the intensity function on each dimension from time t to t + L. |
- Returns
- the summation of the upper-bound of each intensity function from the respetive dimension within the interval [t, t + L].
Implements IProcess.
Definition at line 19 of file Poisson.cc.
Public Member Functions inherited from IProcess
1.8.11
