https://github.com/vaithak/univariate-truncated-sampling

Sampling from univariate truncated distributions for GeomScale's tests for GSoC 2021
https://github.com/vaithak/univariate-truncated-sampling

Last synced: 4 months ago
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Sampling from univariate truncated distributions for GeomScale's tests for GSoC 2021

• Host: GitHub
• URL: https://github.com/vaithak/univariate-truncated-sampling
• Owner: vaithak
• Created: 2021-03-25T11:22:15.000Z (over 4 years ago)
• Default Branch: main
• Last Pushed: 2021-03-26T02:06:46.000Z (over 4 years ago)
• Last Synced: 2025-05-31T13:05:10.117Z (4 months ago)
• Language: C++
• Size: 3.63 MB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

          
### Univariate-Truncated-Sampling for the project: "Sampling from a parametric polynomial curve"

*Sampling from univariate truncated distributions for GeomScale's tests for GSoC 2021*

## Easy

- Generated a 100 dimensional cube and sampled points using three different random walks:

  - ["Ball Walk", "Random Direction Hit and Run", "Change Direction Hit and Run"]

- Plots of sampled points projected along the first two dimensions: 

![Easy/Combined_Walks.png](Easy/Combined_Walks.png)  

## Medium: Accept-Reject Sampling

* The code is written such that it also works for unnormalized pdf, maximum value **M** of **F(x)/G(x)** is calculated by evaluating the ratio over random uniform samples over the support.  

* The samples points were written into `data_1.txt` and `data_2.txt` and plotted using python file `plot.py`.  

* The pdfs are chosen with form similar to the density functions that can be obtained by norm of velocity vector of a parametric polynomial curve.  

1) **Target pdf (Unnormalized) (F) :**  sqrt(x + x2 - x3 + 2)

    - **Suppport :** (-2, 2)  

    - **Proposal pdf (G) :** Uniform (-2, 2)  

    - **Plots:** 
  

    ![Medium/Histogram_1.png](Medium/Histogram_1.png)  

2) **Target pdf (Unnormalized) (F) :**  sqrt(4.5(x-1) + (x-1)2 - 4(x-1)3 - (x-1)4 + 3)

    - **Suppport :** (-3.0, 2.2)  

    - **Proposal pdf (G) :** Uniform (-3.0, 2.2)  

    - **Plots:** 
  

    ![Medium/Histogram_2.png](Medium/Histogram_2.png)  

## Hard: Metropolis-Hastings algorithm

* The samples points were written into `data_1.txt` and `data_2.txt` and plotted using python file `plot.py`.  

* The pdfs are chosen with form similar to the density functions that can be obtained by norm of velocity vector of a parametric polynomial curve.  

1) **Target pdf (Unnormalized) (F) :**  sqrt(x + x2 - x3 + 2)

    - **Suppport :** (-2, 2)  

    - **Transition kernel pdf (G) :** Gaussian Distribution with standard deviation = 0.25  

    - **Plots:** 
  

      - ![Hard/Histogram_1.png](Hard/Histogram_1.png)  

      - ![Hard/Trace_Plot_1.png](Hard/Trace_Plot_1.png)  

2) **Target pdf (Unnormalized) (F) :**  sqrt(4.5(x-1) + (x-1)2 - 4(x-1)3 - (x-1)4 + 3)

    - **Suppport :** (-3.0, 2.2)  

    - **Transition kernel pdf (G) :** Gaussian Distribution with standard deviation = 0.65  

    - **Plots:** 
  

      - ![Hard/Histogram_2.png](Hard/Histogram_2.png)  

      - ![Hard/Trace_Plot_2.png](Hard/Trace_Plot_2.png)