DiogoRibeiro7

def expected_utility_logarithmic(simulations, a=1):
    utilities = a * np.log(simulations)
    return np.mean(utilities)

# Evaluate the expected utility of the simulations
expected_utility = expected_utility_logarithmic(simulations)

print(f'Expected Utility: {expected_utility}')

DiogoRibeiro7

def utility_logarithmic(wealth, a=1):
    return a * np.log(wealth)

wealth = np.linspace(1, 100, 100)  # Wealth values from 1 to 100
utility = utility_logarithmic(wealth)

plt.plot(wealth, utility)
plt.xlabel('Wealth')
plt.ylabel('Utility')
plt.title('Logarithmic Utility Function')

DiogoRibeiro7

import numpy as np
import matplotlib.pyplot as plt

def simulate_game():
    tosses = 0
    while np.random.choice(['H', 'T']) == 'T':
        tosses += 1
    return 2**(tosses + 1)

# Simulate the game 10,000 times to approximate the expected payoff

DiogoRibeiro7

def gaussian_prior(mean: float, std: float) -> Callable[[int], float]:
    """
    Create a Gaussian prior distribution centered around the mean.
    
    Parameters:
    - mean (float): The mean of the Gaussian distribution
    - std (float): The standard deviation of the Gaussian distribution
    
    Returns:
    - Callable[[int], float]: A function representing the Gaussian prior

DiogoRibeiro7

from scipy import stats
import numpy as np

def remove_outliers(data: List[float], threshold: float = 1.5) -> List[float]:
    """
    Remove outliers from the data using the Z-score method.
    
    Parameters:
    - data (List[float]): The observed data
    - threshold (float): The Z-score threshold for outlier detection

DiogoRibeiro7

from typing import Callable, List, Tuple
import numpy as np
from scipy.stats import norm

class SegmentChangePointDetector:
    def __init__(self, prior: Callable[[int], float]) -> None:
        """
        Initialize the SegmentChangePointDetector model.
        
        Parameters:

DiogoRibeiro7

from tensorflow.keras.preprocessing.image import ImageDataGenerator
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Conv2D, MaxPooling2D, Flatten, Dense, Dropout

def build_advanced_cnn(input_shape):
    """
    Build an advanced CNN model with dropout layers.
    
    Parameters:
        input_shape (tuple): Shape of input images.

DiogoRibeiro7

import numpy as np
from sklearn.model_selection import train_test_split
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import LSTM, Dense

def preprocess_data(X_raw):
    """
    Normalize the raw data for LSTM processing.
    
    Parameters:

DiogoRibeiro7

import numpy as np
import tensorflow as tf

def preprocess_data(X_raw):
    """
    Preprocess the raw data for model training.
    
    Parameters:
        X_raw (array): The raw feature set.
        

DiogoRibeiro7

from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Conv2D, MaxPooling2D, Flatten, Dense

def build_cnn(input_shape):
    """
    Build a Convolutional Neural Network (CNN) for medical imaging.
    
    Parameters:
        input_shape (tuple): The shape of input images.