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https://github.com/sadmanca/mermaid-test


https://github.com/sadmanca/mermaid-test

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## `figure_1.1-1.txt`
```mermaid
flowchart TD
A[Markov Chains] --> B[State]
A --> C[Transition Probability]
A --> D[Transition Matrix]
B --> B1[Represents a specific condition]
B --> B2[Tracks progress or transitions]
C --> C1[Likelihood of moving between states]
C --> C2[Single time-step transition]
D --> D1[Matrix format]
D --> D2[Sum of probabilities = 1 for each state]

```

---

## `figure_1.1-2.txt`
```mermaid
graph TD
M[Markov Chains] --> S[State]
M --> TP[Transition Probability]
M --> TM[Transition Matrix]
S --> |Describes condition| SC1[Tracks system status]
TP --> |Governs movement| TPC1[Probability between states]
TM --> |Defines probabilities| TMC1[Matrix structure]
TMC1 --> |Each row sums to 1| TMC2[Valid probability distribution]

```

---

## `figure_1.1-3.txt`
```mermaid
sequenceDiagram
participant System
participant StateA
participant StateB
participant TransitionMatrix
System->>StateA: Begin in State A
StateA->>TransitionMatrix: Reference probabilities
TransitionMatrix-->>StateB: Transition Probability to State B
StateB->>TransitionMatrix: Lookup next transition

```

---

## `figure_2.1-1.txt`
```mermaid
flowchart TD
A[Bayesian Networks] --> B[Risk Analysis]
B --> C[Probabilistic Relationships]
C --> D[Model Dependencies and Uncertainties]
D --> E[Assess and Analyze Risks]

```

---

## `figure_2.1-2.txt`
```mermaid
graph TD
A[Bayesian Network]
A --> B[Node: Variable Representation]
A --> C[Edge: Conditional Dependencies]
B --> D[Probabilistic Relationships]
C --> D

```

---

## `figure_2.1-3.txt`
```mermaid
graph TD
Weather((Weather))
Season((Season))
Rain((Rain))
Sprinkler((Sprinkler))
WetGrass((Wet Grass))
Traffic((Traffic))
Accident((Accident))

Season --> Weather
Weather --> Rain
Weather --> Sprinkler
Rain --> WetGrass
Sprinkler --> WetGrass
Rain --> Traffic
Traffic --> Accident
WetGrass --> Accident
```

---

## `figure_3.1-1.txt`
```mermaid
flowchart TD
A[Time Series Forecasting] --> B[Univariate Forecasting]
A --> C[Multivariate Forecasting]
A --> D[Long-Term Forecasting]

B --> B1[Single Variable Analysis for Economic Indicators]
B --> B2[Weather Forecasting Based on Specific Parameters]
B --> B3[Sales Predictions Using Historical Sales Data]

C --> C1[Market Basket Analysis in Retail]
C --> C2[Economic Forecasting Using Multiple Indicators]
C --> C3[Predicting Stock Prices with Influencing Factors]

D --> D1[Climate Change Studies]
D --> D2[Economic Growth Projections]
D --> D3[Population Growth Predictions]

```

---

## `figure_3.1-2.txt`
```mermaid
graph TD
TS[Time Series Forecasting] --> UV[Univariate Forecasting]
TS --> MV[Multivariate Forecasting]
TS --> LT[Long-Term Forecasting]

UV --> UV1[Examples]
UV1 --> UV2[Single Variable for Economic Indicators]
UV1 --> UV3[Weather Forecasting on Specific Parameters]
UV1 --> UV4[Sales Predictions Using Historical Data]

MV --> MV1[Examples]
MV1 --> MV2[Market Basket Analysis in Retail]
MV1 --> MV3[Economic Forecasting with Multiple Indicators]
MV1 --> MV4[Stock Price Predictions]

LT --> LT1[Examples]
LT1 --> LT2[Climate Change Studies]
LT1 --> LT3[Economic Growth Projections]
LT1 --> LT4[Population Growth Predictions]

```

---

## `figure_3.1-3.txt`
```mermaid
sequenceDiagram
participant User as User
participant System as Forecasting System
participant Data as Historical Data

User->>System: Request Forecast
System->>Data: Retrieve Historical Data
Data-->>System: Provide Data
System->>System: Analyze Trends, Patterns, Seasonality
System-->>User: Provide Forecast
Note over User,System: Types of Forecasting
User->>System: Choose Univariate, Multivariate, or Long-Term

```

---

## `figure_3.2-1.txt`
```mermaid
flowchart TD
A[Time Series Forecasting] --> B[Analyze Historical Data]
B --> C[Identify Trends]
B --> D[Analyze Seasonality]
B --> E[Residuals Analysis]
C --> C1[Increasing, Decreasing, or Constant Trends]
C --> C2[Smoothing Techniques]
C --> C3[Detrending Techniques]
D --> D1[Daily, Weekly, Monthly Patterns]
D --> D2[Seasonal Decomposition]
D --> D3[Seasonal Adjustment]
E --> E1[Analyze Residuals for Randomness]
E --> E2[ACF & PACF Analysis]
E --> E3[Model Diagnostics and Validation]

```

---

## `figure_3.2-2.txt`
```mermaid
graph TB
A[Time Series Forecasting] --> B[Trend Analysis]
A --> C[Seasonality Analysis]
A --> D[Residuals Analysis]

B --> B1[Identifies Trends]
B1 --> B2[Uses Smoothing Techniques]
B1 --> B3[Uses Detrending Techniques]

C --> C1[Detects Regular Patterns]
C1 --> C2[Seasonal Decomposition]
C1 --> C3[Seasonal Adjustment]

D --> D1[Assesses Model Fit]
D1 --> D2[ACF & PACF Analysis]
D1 --> D3[Diagnostics and Validation]

```

---

## `figure_3.2-3.txt`
```mermaid
sequenceDiagram
participant User
participant Data
participant ForecastModel

User->>Data: Obtain Historical Data
Data->>ForecastModel: Feed Data for Analysis
ForecastModel->>User: Trend Analysis
ForecastModel->>User: Identifies Seasonality
ForecastModel->>User: Residuals Analysis
User->>ForecastModel: Validate with Diagnostics
ForecastModel->>User: Provides Final Forecast

```

---

## `figure_4-1.txt`
```mermaid
flowchart TD
A[Big Data Analytics & Machine Learning] --> B[Risk Analysis]
A --> C[Benefits]
A --> D[Challenges]

B --> E[Analyze historical data]
B --> F[Identify risk factors]
B --> G[Predict future trends]
B --> H[Optimize risk management]

C --> I[Accurate risk assessments]
C --> J[Faster decision-making]
C --> K[Automation of tasks]

D --> L[Data quality issues]
D --> M[Interpretability challenges]
D --> N[Need for domain expertise]

E --> O{Algorithms}
O --> P[Random Forest]
O --> Q[Gradient Boosting]
O --> R[Neural Networks]

```

---

## `figure_4-2.txt`
```mermaid
sequenceDiagram
participant BigDataAnalytics as Big Data Analytics
participant MLAlgorithms as Machine Learning Algorithms
participant RiskAnalysis as Risk Analysis
participant Benefits as Benefits
participant Challenges as Challenges

BigDataAnalytics ->> MLAlgorithms: Provide large datasets
MLAlgorithms ->> RiskAnalysis: Use algorithms (Random Forest, Gradient Boosting, Neural Networks)
RiskAnalysis ->> Benefits: Improved accuracy, faster decisions, automation
RiskAnalysis ->> Challenges: Data quality, model interpretability, domain expertise

```

---

## `figure_4-3.txt`
```mermaid
stateDiagram-v2
[*] --> BigDataAnalytics
BigDataAnalytics --> MLAlgorithms
MLAlgorithms --> RiskAnalysis
RiskAnalysis --> Benefits
RiskAnalysis --> Challenges

state Benefits {
Accurate_Risk_Assessments
Faster_Decision_Making
Automation_of_Tasks
}

state Challenges {
Data_Quality_Issues
Model_Interpretability
Domain_Expertise
}

state MLAlgorithms {
Random_Forest
Gradient_Boosting
Neural_Networks
}

```