decision-tree-analyzer

Business

Decision tree analysis skill with expected value, risk analysis, and utility theory.

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decision-tree-analyzer

You are decision-tree-analyzer - a specialized skill for decision tree analysis including expected value calculations, risk analysis, and utility theory applications.

Overview

This skill enables AI-powered decision tree analysis including:

Decision tree construction
Expected Monetary Value (EMV) calculation
Expected Value of Perfect Information (EVPI)
Expected Value of Sample Information (EVSI)
Risk profiles and sensitivity
Utility function application
Decision rollback analysis
Multi-stage sequential decisions

Capabilities

1. Decision Tree Construction

import numpy as np
from dataclasses import dataclass
from typing import List, Dict, Optional
from enum import Enum

class NodeType(Enum):
    DECISION = "decision"
    CHANCE = "chance"
    TERMINAL = "terminal"

@dataclass
class TreeNode:
    node_id: str
    node_type: NodeType
    name: str
    value: float = 0  # For terminal nodes
    probability: float = 1.0  # For chance branches
    children: List['TreeNode'] = None
    parent: Optional['TreeNode'] = None

    def __post_init__(self):
        if self.children is None:
            self.children = []

def build_decision_tree(structure: dict):
    """
    Build decision tree from structure definition

    structure: nested dict defining tree
    {
        'type': 'decision',
        'name': 'Initial Decision',
        'branches': [
            {
                'name': 'Option A',
                'type': 'chance',
                'branches': [
                    {'name': 'High', 'probability': 0.3, 'value': 100},
                    {'name': 'Low', 'probability': 0.7, 'value': 50}
                ]
            }
        ]
    }
    """
    def build_node(data, parent=None, node_id='root'):
        node_type = NodeType(data.get('type', 'terminal'))

        node = TreeNode(
            node_id=node_id,
            node_type=node_type,
            name=data.get('name', ''),
            value=data.get('value', 0),
            probability=data.get('probability', 1.0),
            parent=parent
        )

        if 'branches' in data:
            for i, branch in enumerate(data['branches']):
                child = build_node(branch, node, f"{node_id}_{i}")
                node.children.append(child)

        return node

    root = build_node(structure)
    return root

2. Expected Monetary Value (EMV)

def calculate_emv(node: TreeNode):
    """
    Calculate Expected Monetary Value using rollback analysis
    """
    results = {}

    def rollback(n):
        if n.node_type == NodeType.TERMINAL:
            return n.value

        if n.node_type == NodeType.CHANCE:
            # EMV is weighted average of outcomes
            emv = sum(child.probability * rollback(child) for child in n.children)
            results[n.node_id] = {'name': n.name, 'emv': emv, 'type': 'chance'}
            return emv

        if n.node_type == NodeType.DECISION:
            # Choose maximum EMV branch
            child_values = [(child, rollback(child)) for child in n.children]
            best_child, best_value = max(child_values, key=lambda x: x[1])
            results[n.node_id] = {
                'name': n.name,
                'emv': best_value,
                'type': 'decision',
                'best_choice': best_child.name,
                'all_choices': {c.name: v for c, v in child_values}
            }
            return best_value

    final_emv = rollback(node)

    return {
        "emv": round(final_emv, 2),
        "node_values": results,
        "optimal_strategy": extract_optimal_strategy(results)
    }

def extract_optimal_strategy(results):
    """Extract optimal decision path"""
    strategy = []
    for node_id, data in results.items():
        if data['type'] == 'decision':
            strategy.append({
                'decision': data['name'],
                'choice': data['best_choice'],
                'emv': round(data['emv'], 2)
            })
    return strategy

3. Expected Value of Perfect Information (EVPI)

def calculate_evpi(decision_node: TreeNode):
    """
    Calculate Expected Value of Perfect Information

    EVPI = EV with perfect information - EMV without information
    """
    # First, get EMV without perfect information
    emv_result = calculate_emv(decision_node)
    emv_without = emv_result['emv']

    # Calculate EV with perfect information
    # For each state of nature, choose best decision
    states = collect_chance_outcomes(decision_node)

    ev_with_perfect = 0
    perfect_decisions = {}

    for state, prob in states.items():
        # For this state, find best decision
        best_value = float('-inf')
        best_decision = None

        for decision_branch in decision_node.children:
            value = get_value_given_state(decision_branch, state)
            if value > best_value:
                best_value = value
                best_decision = decision_branch.name

        ev_with_perfect += prob * best_value
        perfect_decisions[state] = {'decision': best_decision, 'value': best_value}

    evpi = ev_with_perfect - emv_without

    return {
        "evpi": round(evpi, 2),
        "ev_with_perfect_info": round(ev_with_perfect, 2),
        "emv_without_info": round(emv_without, 2),
        "perfect_decisions": perfect_decisions,
        "interpretation": f"Worth up to ${round(evpi, 2)} for perfect information"
    }

def collect_chance_outcomes(node, outcomes=None, current_prob=1.0):
    """Collect all chance outcomes and their probabilities"""
    if outcomes is None:
        outcomes = {}

    if node.node_type == NodeType.TERMINAL:
        return outcomes

    if node.node_type == NodeType.CHANCE:
        for child in node.children:
            outcomes[child.name] = child.probability
            collect_chance_outcomes(child, outcomes, current_prob * child.probability)

    for child in node.children:
        collect_chance_outcomes(child, outcomes, current_prob)

    return outcomes

def get_value_given_state(node, state):
    """Get value of a branch given a specific state occurs"""
    # Simplified - would need full tree traversal
    for child in node.children:
        if child.name == state:
            return child.value if child.node_type == NodeType.TERMINAL else 0
        result = get_value_given_state(child, state)
        if result != 0:
            return result
    return 0

4. Risk Profile Analysis

def create_risk_profile(decision_node: TreeNode, decision_choice: str = None):
    """
    Create risk profile showing probability distribution of outcomes
    """
    outcomes = []

    def collect_outcomes(node, current_prob=1.0, path=None):
        if path is None:
            path = []

        if node.node_type == NodeType.TERMINAL:
            outcomes.append({
                'value': node.value,
                'probability': current_prob,
                'path': ' -> '.join(path)
            })
            return

        if node.node_type == NodeType.CHANCE:
            for child in node.children:
                collect_outcomes(child, current_prob * child.probability,
                               path + [child.name])

        elif node.node_type == NodeType.DECISION:
            if decision_choice:
                for child in node.children:
                    if child.name == decision_choice:
                        collect_outcomes(child, current_prob, path + [child.name])
            else:
                # Use optimal decision
                emv_result = calculate_emv(node)
                best = emv_result['node_values'].get(node.node_id, {}).get('best_choice')
                for child in node.children:
                    if child.name == best:
                        collect_outcomes(child, current_prob, path + [child.name])

    collect_outcomes(decision_node)

    # Aggregate by value
    value_probs = {}
    for outcome in outcomes:
        v = outcome['value']
        value_probs[v] = value_probs.get(v, 0) + outcome['probability']

    # Calculate statistics
    values = [o['value'] for o in outcomes]
    probs = [o['probability'] for o in outcomes]

    expected_value = sum(v * p for v, p in zip(values, probs))
    variance = sum(p * (v - expected_value)**2 for v, p in zip(values, probs))
    std_dev = np.sqrt(variance)

    # Cumulative distribution
    sorted_outcomes = sorted(value_probs.items())
    cumulative = 0
    cdf = []
    for value, prob in sorted_outcomes:
        cumulative += prob
        cdf.append({'value': value, 'cumulative_prob': cumulative})

    return {
        "outcomes": outcomes,
        "probability_distribution": value_probs,
        "statistics": {
            "expected_value": round(expected_value, 2),
            "variance": round(variance, 2),
            "std_deviation": round(std_dev, 2),
            "min_value": min(values),
            "max_value": max(values)
        },
        "cumulative_distribution": cdf
    }

5. Utility Function Analysis

def apply_utility_function(decision_node: TreeNode, risk_attitude: str = 'neutral',
                          risk_parameter: float = None):
    """
    Apply utility function to convert monetary values

    risk_attitude: 'neutral', 'averse', 'seeking'
    """
    def utility(x, attitude, param):
        if attitude == 'neutral':
            return x
        elif attitude == 'averse':
            # Exponential utility: U(x) = 1 - e^(-x/R)
            R = param or 1000  # Risk tolerance
            return 1 - np.exp(-x / R)
        elif attitude == 'seeking':
            # Exponential utility for risk seeking
            R = param or 1000
            return np.exp(x / R) - 1
        return x

    def inverse_utility(u, attitude, param):
        if attitude == 'neutral':
            return u
        elif attitude == 'averse':
            R = param or 1000
            return -R * np.log(1 - u) if u < 1 else float('inf')
        elif attitude == 'seeking':
            R = param or 1000
            return R * np.log(u + 1)
        return u

    # Convert tree to utility values
    def convert_node(n):
        if n.node_type == NodeType.TERMINAL:
            n.utility_value = utility(n.value, risk_attitude, risk_parameter)
        for child in n.children:
            convert_node(child)

    convert_node(decision_node)

    # Calculate expected utility
    def expected_utility(n):
        if n.node_type == NodeType.TERMINAL:
            return n.utility_value

        if n.node_type == NodeType.CHANCE:
            return sum(child.probability * expected_utility(child) for child in n.children)

        if n.node_type == NodeType.DECISION:
            return max(expected_utility(child) for child in n.children)

    eu = expected_utility(decision_node)
    certainty_equivalent = inverse_utility(eu, risk_attitude, risk_parameter)

    # Compare to EMV
    emv_result = calculate_emv(decision_node)

    return {
        "expected_utility": round(eu, 4),
        "certainty_equivalent": round(certainty_equivalent, 2),
        "emv": emv_result['emv'],
        "risk_premium": round(emv_result['emv'] - certainty_equivalent, 2),
        "risk_attitude": risk_attitude,
        "interpretation": interpret_risk_attitude(certainty_equivalent, emv_result['emv'])
    }

def interpret_risk_attitude(ce, emv):
    if abs(ce - emv) < 1:
        return "Risk neutral - indifferent between expected value and certain equivalent"
    elif ce < emv:
        return f"Risk averse - willing to accept ${round(emv - ce, 2)} less for certainty"
    else:
        return f"Risk seeking - requires ${round(ce - emv, 2)} premium over expected value"

6. Sensitivity Analysis

def sensitivity_analysis(decision_node: TreeNode, parameter: str,
                        range_min: float, range_max: float, steps: int = 10):
    """
    Analyze sensitivity of decision to parameter changes
    """
    values = np.linspace(range_min, range_max, steps)
    results = []

    for val in values:
        # Modify parameter (probability or value)
        modify_parameter(decision_node, parameter, val)
        emv_result = calculate_emv(decision_node)

        results.append({
            'parameter_value': round(val, 3),
            'emv': round(emv_result['emv'], 2),
            'best_decision': emv_result['optimal_strategy'][0]['choice']
                           if emv_result['optimal_strategy'] else None
        })

    # Find crossover points
    crossovers = []
    for i in range(1, len(results)):
        if results[i]['best_decision'] != results[i-1]['best_decision']:
            crossovers.append({
                'value': results[i]['parameter_value'],
                'from': results[i-1]['best_decision'],
                'to': results[i]['best_decision']
            })

    return {
        "parameter": parameter,
        "range": {"min": range_min, "max": range_max},
        "results": results,
        "crossover_points": crossovers,
        "recommendation": generate_sensitivity_recommendation(crossovers, results)
    }

def modify_parameter(node, parameter, value):
    """Modify a parameter in the tree"""
    # Implementation depends on parameter specification
    pass

def generate_sensitivity_recommendation(crossovers, results):
    if not crossovers:
        return f"Decision is robust - same choice across entire range"
    return f"Decision switches at {len(crossovers)} point(s) - careful analysis needed"

Process Integration

This skill integrates with the following processes:

multi-criteria-decision-analysis.js
risk-assessment-analysis.js
investment-analysis.js

Output Format

{
  "decision_tree": {
    "emv": 125000,
    "optimal_strategy": [
      {"decision": "Initial", "choice": "Expand", "emv": 125000}
    ]
  },
  "evpi": 15000,
  "risk_profile": {
    "expected_value": 125000,
    "std_deviation": 45000,
    "probability_of_loss": 0.15
  },
  "utility_analysis": {
    "certainty_equivalent": 110000,
    "risk_premium": 15000
  },
  "recommendation": "Choose Expand option with expected value of $125,000"
}

Best Practices

Structure carefully - Clear decision and chance nodes
Validate probabilities - Must sum to 1 at chance nodes
Consider all outcomes - Don't miss important scenarios
Test sensitivity - Understand key drivers
Consider risk attitude - EMV assumes risk neutrality
Document assumptions - Record probability sources

Constraints

Requires probability estimates
Tree complexity grows quickly
Sequential decisions compound uncertainty
Utility functions are subjective