1.     Robust Statistical Methods

a.     Interquartile Range (IQR) Method: Instead of relying on mean and standard deviation, the IQR method uses the middle 50% of your data, making it less sensitive to extreme values. Calculate the first (Q1) and third (Q3) quartiles, then identify outliers as data points lying below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR.

b.     Z-Score: Also known as a standard score, measures the number of standard deviations (σ) a data point (X) is from the mean (μ) of the dataset. It's computed using the formula (X−μ)/σ.

c.      Modified Z-Score: An adaptation that utilizes MAD instead of standard deviation. Values with a modified z-score greater than 3.5 are often considered outliers.

Modified Z-Score = 0.6745×((Xi−Median)/MAD)

d.     Median Absolute Deviation (MAD): Similar to IQR, MAD is robust against outliers and uses the median rather than the mean. It's calculated as the median of the absolute deviations from the data’s median:

MAD = median (|X_i - median(X)|)

You can flag data points that deviate from the median by a certain threshold.

2.     Machine Learning Models for Anomaly Detection

a.     Isolation Forest: This algorithm isolates anomalies instead of profiling normal data points. It randomly selects features and splits values between the maximum and minimum values of the selected feature. Anomalies require fewer splits to isolate.

b.     One-Class SVM (Support Vector Machine): It learns the features of the "normal" class and identifies data points that do not conform to this pattern. This is effective for datasets where anomalies are rare compared to normal observations.

c.      Autoencoders (Neural Networks): Autoencoders can learn compressed representations of your data. When an input deviates significantly from the learned pattern, the reconstruction error is high, flagging it as an anomaly.

d.     Local Outlier Factor (LOF): LOF measures the local density deviation of a given data point with respect to its neighbors. Points with a lower density than their neighbors are considered outliers.

3.     Clustering Techniques

a.     DBSCAN (Density-Based Spatial Clustering of Applications with Noise): DBSCAN clusters data based on the density of data points. Points in low-density regions (noise) are considered anomalies.

b.     K-Means Clustering: After clustering the data, calculate the distance of each point to its cluster centroid. Points with distances beyond a certain threshold can be marked as outliers.

4.     Time Series Analysis

If your data has a temporal component (e.g., monthly or yearly reports):

a.     Seasonal Decomposition: Decompose the time series into trend, seasonal, and residual components to identify unusual patterns.

b.     ARIMA Models: Use AutoRegressive Integrated Moving Average models to forecast values and detect anomalies based on forecast errors.

5.     Multivariate Analysis

a.     Principal Component Analysis (PCA): Reduce the dimensionality of your data and identify outliers based on their scores on the principal components.

b.     Mahalanobis Distance: Measures the distance of a point from the mean of a distribution, taking into account the covariance among variables. It’s effective for identifying multivariate outliers.

6.     Rule-Based Methods

a.     Domain-Specific Thresholds: Leverage industry standards or historical data to set realistic thresholds.

b.     Business Logic Rules: Implement rules that consider operational, seasonal and environmental aspects to normalize data.

c.      Benchmarking: Compare entities against each other to identify leaders and laggards in resource efficiency.

7.     Visualization Techniques

Visual tools can provide intuitive insights:

a.     Box Plots: Display the distribution and highlight outliers beyond the whiskers.

b.     Scatter Plots with Trend Lines: Plot data against variable to spot anomalies.

c.      Heatmaps: Visualize data to detect unusual patterns.

8.     Ensemble Methods

Combine multiple models for improved detection:

a.     Hybrid Approaches: Use statistical methods to flag initial outliers and then apply machine learning models for further analysis.

b.     Voting Systems: Aggregate the results from different models; data points flagged by multiple methods are more likely to be true outliers.

9.     Data Quality Checks

a.     Consistency Checks: Verify if the reported values are consistent over time or abruptly change without a plausible reason.

b.     Cross-Verification: Compare reported data with external sources or benchmarks, like industry averages or environmental reports.

10.  Automated Anomaly Detection Systems

Building a system that continuously monitors and alerts on anomalies can be invaluable:

a.     Real-Time Monitoring: Implement dashboards that update as new data comes in, highlighting anomalies instantly.

b.     Alert Mechanisms: Set up notifications for when values exceed certain thresholds or when patterns deviate significantly from the norm.

11.  Advanced Techniques

a.     Gaussian Mixture Models (GMM): Model the data as a mixture of several Gaussian distributions, which can capture more complex patterns than a single distribution.

Bayesian Networks: Use probabilistic graphical models to represent variables and their conditional dependencies, useful for complex datasets.