What advanced statistical techniques do you use?

Regression analysis is a statistical technique used in data analysis to examine and quantify the relationship between a dependent variable (the outcome or response variable) and one or more independent variables (predictor variables or factors). It aims to find the best-fitting mathematical model or equation that describes the relationship between these variables. I recently applied regression models to understand the relationship between the process parameters and mechanical properties of additives manufactured metals.

Regression Analysis is the best technique when you are looking to understand the relationship among two variables. It gives a clear indication about how the outcome variable behaves with the change in input variable. But the major drawback of Regression analysis is when the outcome is dependent on multiple inputs. DOE comes into picture when we need to optimise outcome based upon multiple interdependent variables.

Regression Analysis is one the main methods in economic analysis, which is categorized as minor methods in Econometrics. I believe that such analysis can help us to make a better decision in micro and macro levels. In addition, it would be important for whom to seek for a future percpective. However, we cannot overlook its drawbacks. For more sophisticated problems, which you face many factors to consider, it might not work as you expect.

Regression models are one of fundamental concepts in understanding associations between response and predictor variables. Viewing regression function as the conditional mean function one can generalize the concept to other conditional summaries (e.g., quantile regression models the conditional quantiles). A broader view of regression models can be done via conditional densities which may alleviate the need of restrictive assumptions (e.g., homoscedasticity etc.). Moreover higher order moments or quantiles can be estimated via conditional distributions approach. One possibility is to use the so-called copula models which estimates the joint distribution of response and predictor variables and then obtains conditional summaries.

Regression analysis is most useful when the expected relationship is linear. It is also easy to explain, and thus where business intuition is very important it may be useful to use regression rather than other techniques even if losing some precision.

Again in agricultural research there are some factors which you cannot simply by blocking as in a randomized complete block design. The best way to deal with these factors is to treat them as covariance in ANCOVA.

ANOVA and ANCOVA are statistically equivalent to regression. If you know what you are doing, you’ll get the same results. But that doesn’t mean there isn’t a reason to use one over the other, especially if more junior members of your team are running the models. Particularly for experiments (caveat: with continuous outcomes), ANOVA output is more intuitive and easier to teach.

ANOVA, or Analysis of Variance, is a statistical technique with significant importance in various fields. Here are some key aspects highlighting its importance: Comparison of Means: ANOVA is primarily used to compare means across multiple groups. It allows researchers to determine whether there are statistically significant differences in the means of three or more groups. Experimental Design: ANOVA is crucial in experimental design, especially when there are multiple factors or treatments involved. It helps identify which factors have a significant impact on the dependent variable.

Exploratory factor analysis is the art of profiling the mindset of people. The challenge lies in naming underlying factors, especially when one or more items do not appear to "belong" to a factor. It is therefore essential to test data for reliability and construct validity first, besides checking whether all data assumptions for factorability of items are satisfied. Concerning the number of extracted factors, one can use (1) Cattell's scree plot (2) Kaiser's criterion or (3) parallel analysis using Monte Carlo simulation. EFA is not always as straighforward as expected. It's very often an intuitive technique. You just have to have a statistician's hunch.

Factor analysis is a statistical technique with significant importance in various fields. Here are some key reasons why factor analysis is valuable: Dimension Reduction: Factor analysis helps in reducing the dimensionality of a dataset by identifying a smaller number of underlying factors that explain the observed correlations among variables. This is particularly useful when dealing with numerous variables, making the data more manageable and interpretable. Identifying Latent Constructs: It allows researchers to identify latent (unobserved) constructs or factors that may be influencing the observed variables. This helps in understanding the underlying structure of the data and extracting meaningful patterns.

Its not only an exploratory data analysis technique. But can be used to test hypothesis about the underlying factor model. You can answer the question: can these items I have measured be explained by 1 factor? Or do you need more factors.

Are we measuring what we think we’re measuring? Factor analysis is a powerful tool for exploring this question, which too often is skirted over or completely ignored in survey research. Like cluster analysis does with people, factor analysis groups survey items into categories, helping the researcher identify what psychological attributes are being measured and whether they are the ones you intended. You may think your survey is measuring support for 10 different policies or ratings of 10 different TV shows, when in reality you are measuring partisan identity or genre preferences, respectively.

Factor analysis is used to break down a large number of variables into a smaller number of elements. This method creates a single score by combining all variables' highest common variance.

Clustering is an incredibly useful way to start an exploratory data science project. Getting multiple clustering methods to show consistent separation of the data points. Once validated the clusters can be used to train a classifier.

Clustering can be done through several means. Perhaps the most common way is K-Means and its variants. This is a non-parametric algorithm that relies on a distance function (normally euclidean distance) and the number of clusters. The latter can be determined by domain knowledge, or techniques like the elbow method or silhouette scores. Note that we will need to normalize our data appropriately before running this algortihm.

Spatial cluster analysis (Getis-Ord Gi & Anselin Local Moran's) are useful for identifying differences between two spatially referenced variables as well as for describing cluster evolution and persistence. It is frequently applied to a variety of fields, including disease monitoring, spatial epidemiology, landscape ecology, and crime analysis. The Mapping Clusters make use of cluster analysis to identify geographical outliers, hot and cold regions, and other statistical zones. It is essential to identify the precise locations of spatial clusters in order to determine the most likely causes of clustering. I think spatial cluster analysis will become more crucial for pattern recognition as spatial-temporal data volume expands.

Cluster analysis is a fundamental technique in data science and machine learning, aiming to uncover hidden structures or groupings within a dataset. Whether it's segmenting customers for targeted marketing, identifying anomalies in data, or organizing information into meaningful groups, cluster analysis plays a pivotal role in data-driven decision-making.applications.

Cluster analysis is to unsupervised machine learning algorithms as the linear regression models is to supervised machine learning algorithms. To you understand what is the foundation of the unsupervised machine learning, do you need to understand what cluster analysis is.

The goal of time series analysis is to identify the temporal structure in a series of values. Such values cannot be analysed only using a linear regression because a such regression models doesn't incorporate the dependence structure that are natural to time series.

Fourier Transform is a concept you need to get familiar with. It is one of the only straightforward and robust methods to identify periodicities and yield seasonal decomposition. It may be hard to implement at first with nuts and bolts : DC component, incorrect scaling etc. Note that state-of-the-art deep learning architectures generally rely on FFT for seasonal extraction.

Moreover in R and Python I programmed a new walking IQR. And function to find and immdiately use the arima model. My ARMA model is 20 times faster than the models in Python en R

Time series analysis is essential in systems biology for capturing the temporal behavior of biological systems. It records data at consistent time intervals, enabling the understanding of dynamic changes. In life sciences, timing is critical. For example, the effectiveness of a drug can vary depending on when it's administered. Statistical models like ARIMA and machine learning methods like LSTMs are used to identify underlying patterns and seasonality in the data. These models can forecast future events, providing a window for timely interventions. The statistical rigor allows for hypothesis testing, enabling scientists to infer causal relationships between time-dependent variables.

One of the primary advantages of using Bayesian models and methods is its ability to provide a probabilistic inference for decision making. Especially useful to deal with data irregularities (missing and censored values) E.g., in practice, when testing a hypothesis, it can provide the posterior probability of the hypothesis in the light of the available data. This allows the users to choose their own cut-off values or judgement to make a decision instead of arbitrarily dictating a cutoff value like 0.05 for p-values. Routinely we use such judgements in our daily life. E.g., when we are provided with the chance of rain being 30%, we use our own decision to carry an umbrella or not! Posterior probabilities are easy to calibrate in practice.

One of the advantages of using Bayesian methods for statistical inference is the seamless handling of common data irregularities (e.g., missing and/or censored values). Almost any data obtained from observational studies, often have missing values and many clinical trials that measure time to events (e.g., survival times, time to remission etc.) often have censored values due to study termination or limited budget. Whatever might be the reason, simply discarding the missing or censored values (of covariates or responses) often leads to biased estimations (unless the data values are missing completely at random). In such situations, the Bayesian framework allows for seamless imputation using posterior predictive distributions often via MCMs

Bayesian inference also has the benefit of being effective with smaller sample sizes than frequenting statistics, which can allow for faster decision-making that can be updated iteratively when new data are presented

Bayesian inference is really a godsend. You can fit almost anything since the dependence on the hyperprior distribution is negligible. I was truly baffled the first I time used the method!

There are many “advanced” statistical techniques in my tool kit that I use to deliver insight & value. Mixed models, fixed effects models, Bayesian ridge regression, gradient boosting classifiers, a variety of time series models (including state-space models), & custom ensemble models. However, a model’s complexity is not a positive attribute or bragging point - rather, a model’s usefulness in robustly delivering insight with accuracy & clarity should be the goal. A favorite professor famously said he’d rather have a simple OLS model trained on great data than a more complex deep learning neural network model trained on mediocre data to solve a problem… & often, given the same data, would choose OLS over the DLNN simply for transparency.

Measures of central tendency like mean, median, and mode along with charts like histograms, frequency distribution charts, and finally Pareto principle are majorly used by me on a day-to-day basis in describing the overall data. It gives a summary of "what" to expect from the data and the description thereafter helps in lesser turnaround time for me to get back to the business for a remedial solution for the outliers, null values, and substitution values.

Canonical Correlation: This is a multivariate technique that allows one to measure the strength of association between two sets of variables. It is different from Correlation analysis in that; Correlation analysis measures the strength of association between two variables but Canonical Correlation accommodates two sets of variables and each set will have morethan one variable in it.

Extreme Value Analysis (EVA): In the field of climate risk analytics, EVA is used to determine likelihoods of extreme events and the intensity of events at a given frequency. Especially for flood modelling, the EVA is applied. In flood modelling, the relationship between the causing climate hazard, heavy precipitation and the resulting extent and depth of surface flooding, is complex and difficult to model. EVA of precipitation time series, examining for example the likelihood of a historical amount of a 1-in-100-year rainfall for different climate scenarios can help to determine the risks associated to flooding. EVA is a very useful tool in climate risk analytics, even though uncertainties are high and caveats need to be paid attention to.

Because my factoranalyses produce EXACT factorscores I can use them with a lot of other statistics. For example: Canonical correlation, with Anova or regression