2019年 演習II．第１章 ベイズ推論の考え方 Part 3
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This document discusses Bayesian modeling and inference using PyMC3. It introduces a Poisson switching model where the rate parameter switches between two exponential distributions before and after a change point. The model is defined using PyMC3 with Exponential and DiscreteUniform priors over the rate parameters and change point. The model is sampled to obtain the posterior distribution which can then be analyzed using traceplots and summary statistics.
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( ) 1 Part 3 July 2, 2019 9 / 17](https://image.slidesharecdn.com/ch01-message-slide2-190702072553/85/2019-II-Part-3-9-320.jpg)
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Shifting Focus on AI: How it Can Make a Positive Difference1508 A/S
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This morgenbooster will share how to find the positive impact of AI and how to integrate it into your own digital process. Prescriptive Process Monitoring Under Uncertainty and Resource Constraints: A...
Prescriptive Process Monitoring Under Uncertainty and Resource Constraints: A...Mahmoud Shoush
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We introduced Black-Box Prescriptive Process Monitoring (BB-PrPM) – a reinforcement learning approach that learns when, whether, and how to intervene in business processes to boost performance under real-world constraints.
This work is presented at the International Conference on Advanced Information Systems Engineering CAiSE Conference #CAiSE2025
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2019年 演習II．第１章 ベイズ推論の考え方 Part 3
- 1. 1 Part 3 July 2, 2019 : https://courses.wshito.com/semi2/2019-bayes-AI ( ) 1 Part 3 July 2, 2019 1 / 17
- 2. Python pp.15–24 : ? PyMC3 ( ) 1 Part 3 July 2, 2019 2 / 17
- 3. : ? : ? Figure: ( ) 1 Part 3 July 2, 2019 3 / 17
- 4. : ? ? ( ) 1 Part 3 July 2, 2019 4 / 17
- 5. : ? X P ({X = k}) = λke?λ k! λ > 0 intensity E[X] = λ V ar[X] = λ ( ) 1 Part 3 July 2, 2019 5 / 17
- 6. : ? xt ～ Poisson(λ) where λ = ? ? ? λ1 for t < τ λ2 for t ≥ τ ( ) 1 Part 3 July 2, 2019 6 / 17
- 7. : ? P r(H|D) = P r(D|H)P r(H) P r(D) ∝ P r(D|H)P r(H) f(θ|x) ∝ f(x|θ)f(θ) ? f(λ|x) ∝ f(x|λ)f(λ), x ( ) 1 Part 3 July 2, 2019 7 / 17
- 8. : ? λ λ1, λ2, τ f(λ|x) ∝ f(x|λ)f(λ) ? f({λ1, λ2, τ}|x) ∝ f(x|{λ1, λ2, τ})f({λ1, λ2, τ}) = f(x|{λ1, λ2, τ})f(λ1)f(λ2)f(τ) ( ) 1 Part 3 July 2, 2019 8 / 17
- 9. : ? f({λ1, λ2, τ}|x) ∝ f(x|{λ1, λ2, τ})f(λ1)f(λ2)f(τ) : f(xt|{λ1, λ2, τ}) = λxt e?λ xt! , where ? ? ? λ1 for t < τ λ2 for t ≥ τ : f(τ) = DiscreteUniform(1, 70) : f(λi) = eα for i = 1, 2 α = ( xt/N)?1 E[λ] = 1/α λ ( ) 1 Part 3 July 2, 2019 9 / 17
- 10. : ? Stan PyMC3 ( ) 1 Part 3 July 2, 2019 10 / 17
- 11. : ? PyMC3 General API Quickstart: https://docs.pymc.io/notebooks/api_quickstart.html with pm.Model() observed pm.Deterministic() ( ) 1 Part 3 July 2, 2019 11 / 17
- 12. : ? PyMC3 1 1 import numpy as np 2 import pymc3 as pm 3 4 count_data = np.loadtxt("data/txtdata.csv") 5 6 n_count_data = len(count_data) 7 alpha = 1.0 / count_data.mean() 8 idx = np.arange(n_count_data) # 0 n_count_data-1 index 9 10 with pm.Model() as model: # 11 lambda_1 = pm.Exponential("lambda_1", alpha) 12 lambda_2 = pm.Exponential("lambda_2", alpha) 13 tau = pm.DiscreteUniform("tau", lower=0, upper=n_count_data) 14 lambda_ = pm.math.switch(tau >= idx, lambda_1, lambda_2) 15 obs = pm.Poisson("obs", lambda_, observed=count_data) 16 17 with model: 18 trace = pm.sample(40000) # ( ) 1 Part 3 July 2, 2019 12 / 17
- 13. : ? 2 with pm.Model() as model: # lambda_1 = pm.Exponential("lambda_1", alpha) lambda_2 = pm.Exponential("lambda_2", alpha) tau = pm.DiscreteUniform("tau", lower=0, upper=n_count_data) # idx lambda lambda_ = pm.math.switch(tau >= idx, lambda_1, lambda_2) # obs = pm.Poisson("obs", lambda_, observed=count_data) ( ) 1 Part 3 July 2, 2019 13 / 17
- 14. : ? pm.model_to_graphviz(model) 74 tau ~ DiscreteUniform obs ~ Poisson lambda_2 ~ Exponential lambda_1 ~ Exponential ( ) 1 Part 3 July 2, 2019 14 / 17
- 15. : ? pm.traceplot(trace) ( ) 1 Part 3 July 2, 2019 15 / 17
- 16. : ? pm.plot_posterior(trace) ( ) 1 Part 3 July 2, 2019 16 / 17
- 17. : ? pm.summary(trace) ( ) 1 Part 3 July 2, 2019 17 / 17